RECAPITULATION ON THE NATURE AND SUBJECT OF METAPHYSICS. MOTION
LESSON 1: Metaphysics Is the Science of Principles LESSON 2 Are There Non-Sensible Substances and Principles? LESSON 3 All Beings Reduced to Being and Unity LESSON 4 This Science Considers the Principles of Demonstration LESSON 5 The Principle of Non-Contradiction LESSON 6 Contradictories Cannot Be True at the Same Time LESSON 7 Metaphysics Differs from All the Other Sciences LESSON 8 No Science of Accidental Being LESSON 9 The Definition of Motion LESSON 10 The Infinite LESSON 11 Motion and Change LESSON 12 Motion Pertains to Quantity, Quality and Place LESSON 13 Concepts Related to Motion
LESSON 1 Metaphysics Is the Science of Principles
ARISTOTLE’S TEXT Chapter 1: 1059a 18-1060a 2 [1059α]  ὅτι μὲν ἡ σοφία περὶ ἀρχὰς ἐπιστήμη τίς ἐστι, δῆλον ἐκ τῶν πρώτων ἐν οἷς διηπόρηται πρὸς τὰ ὑπὸ τῶν ἄλλων  εἰρημένα περὶ τῶν ἀρχῶν: 899. That wisdom is a science of principles, then, is evident from the first chapters (45-143) of this work, in which problems were raised concerning the statements of other philosophers about the principles of things. ἀπορήσειε δ᾽ ἄν τις πότερον μίαν ὑπολαβεῖν εἶναι δεῖ τὴν σοφίαν ἐπιστήμην ἢ πολλάς: εἰ μὲν γὰρ μίαν, μία γ᾽ ἐστὶν ἀεὶ τῶν ἐναντίων, αἱ δ᾽ ἀρχαὶ οὐκ ἐναντίαι: εἰ δὲ μὴ μία, ποίας δεῖ θεῖναι ταύτας; 900. But one might raise the question whether wisdom must be understood to be one science or many (181, 190). For if it is one, then the objection might be raised that one science always deals with contraries; but principles are not contraries. And if it is not one but many, what kind of sciences must they be assumed to be (190-197)? ἔτι τὰς ἀποδεικτικὰς ἀρχὰς θεωρῆσαι μιᾶς ἢ πλειόνων; εἰ μὲν γὰρ  μιᾶς, τί μᾶλλον ταύτης ἢ ὁποιασοῦν; εἰ δὲ πλειόνων, ποίας δεῖ ταύτας τιθέναι; 901. Further, one might raise the question whether it is the office of one science or of many to study the principles of demonstration? For if it is the office of one science, why should it be the office of this science rather than of another? And if it is the office of many, what kind of sciences must these be admitted to be (198-201)? ἔτι πότερον πασῶν τῶν οὐσιῶν ἢ οὔ; εἰ μὲν γὰρ μὴ πασῶν, ποίων χαλεπὸν ἀποδοῦναι: εἰ δὲ πασῶν μία, ἄδηλον πῶς ἐνδέχεται πλειόνων τὴν αὐτὴν ἐπιστήμην εἶναι. 902. Further, there is the question whether it is the office of wisdom to deal with all substances or not (182)? And if not with all, it is difficult to say with what kind it does deal. But if there is one science of all substances, the problem arises how one science can deal with many subjects (202-204). ἔτι πότερον περὶ τὰς οὐσίας μόνον ἢ καὶ τὰ  συμβεβηκότα [ἀπόδειξίς ἐστιν]; εἰ γὰρ περί γε τὰ συμβεβηκότα ἀπόδειξίς ἐστιν, περὶ τὰς οὐσίας οὐκ ἔστιν: εἰ δ᾽ ἑτέρα, τίς ἑκατέρα καὶ ποτέρα σοφία; ᾗ μὲν γὰρ ἀποδεικτική, σοφία ἡ περὶ τὰ συμβεβηκότα: ᾗ δὲ περὶ τὰ πρῶτα, ἡ τῶν οὐσιῶν. 903. Again, there is the question whether this science is a demonstration of substances alone, or also of accidents (184, 205-207); for if it is a demonstration of accidents, it is not a demonstration of substances. But if there is a different science of accidents, what is the character of each, and which of the two is wisdom? For a demonstrative science of accidents is wisdom; but that which deals with primary things is the science of substances. ἀλλ᾽ οὐδὲ περὶ τὰς ἐν τοῖς φυσικοῖς εἰρημένας αἰτίας  τὴν ἐπιζητουμένην ἐπιστήμην θετέον: οὔτε γὰρ περὶ τὸ οὗ ἕνεκεν (τοιοῦτον γὰρ τὸ ἀγαθόν, τοῦτο δ᾽ ἐν τοῖς πρακτοῖς ὑπάρχει καὶ ταῖς οὖσιν ἐν κινήσει: καὶ τοῦτο πρῶτον κινεῖ—τοιοῦτον γὰρ τὸ τέλος—τὸ δὲ πρῶτον κινῆσαν οὐκ ἔστιν ἐν τοῖς ἀκινήτοις): 904. But the science which we are seeking must not be assumed to be the one which deals with the causes mentioned in the Physics. For it does not deal with the final cause, because such is the good, and this is found in the sphere of practical affairs and in things which are in motion. And it is the first thing which causes motion (for the end is such a nature); but there is no first mover in the realm of immobile things (192). ὅλως δ᾽ ἀπορίαν ἔχει πότερόν ποτε περὶ τὰς αἰσθητὰς οὐσίας ἐστὶν ἡ ζητουμένη νῦν ἐπιστήμη ἢ οὔ, περὶ δέ τινας ἑτέρας. [1059β]  εἰ γὰρ περὶ ἄλλας, ἢ περὶ τὰ εἴδη εἴη ἂν ἢ περὶ τὰ μαθηματικά. τὰ μὲν οὖν εἴδη ὅτι οὐκ ἔστι, δῆλον 905. And in general there is the question whether the science which is now being sought is concerned with sensible substances, or whether it is not concerned with these but with certain others (183). For, if it deals with other substances, it must be concerned with either the separate Forms or with the objects of mathematics. Now it is evident that separate Forms do not exist. (ὅμως δὲ ἀπορίαν ἔχει, κἂν εἶναί τις αὐτὰ θῇ, διὰ τί ποτ᾽ οὐχ ὥσπερ ἐπὶ τῶν μαθηματικῶν,  οὕτως ἔχει καὶ ἐπὶ τῶν ἄλλων ὧν ἔστιν εἴδη: λέγω δ᾽ ὅτι τὰ μαθηματικὰ μὲν μεταξύ τε τῶν εἰδῶν τιθέασι καὶ τῶν αἰσθητῶν οἷον τρίτα τινὰ παρὰ τὰ εἴδη τε καὶ τὰ δεῦρο, τρίτος δ᾽ ἄνθρωπος οὐκ ἔστιν οὐδ᾽ ἵππος παρ᾽ αὐτόν τε καὶ τοὺς καθ᾽ ἕκαστον: 906. But nevertheless even if one were to assume that these separate Forms exist, the problem would arise why the same thing should not be true of the other things of which there are Forms as is true of the objects of mathematics. I mean that they place the objects of mathematics between the Forms and sensible things as a kind of third class of entities besides the Forms and the things which exist here. But there is no third man or horse over and above man-in-himself and horse-in-itself and singular men and horses. εἰ δ᾽ αὖ μὴ ἔστιν ὡς λέγουσι,  περὶ ποῖα θετέον πραγματεύεσθαι τὸν μαθηματικόν; οὐ γὰρ δὴ περὶ τὰ δεῦρο: τούτων γὰρ οὐθέν ἐστιν οἷον αἱ μαθηματικαὶ ζητοῦσι τῶν ἐπιστημῶν): οὐδὲ μὴν περὶ τὰ μαθηματικὰ ἡ ζητουμένη νῦν ἐστὶν ἐπιστήμη (χωριστὸν γὰρ αὐτῶν οὐθέν): ἀλλ᾽ οὐδὲ τῶν αἰσθητῶν οὐσιῶν: φθαρταὶ γάρ. 907. If, however, the situation is not as they say, with what kind of things must the mathematician be assumed to deal? For he is not concerned with the things which exist here, because none of these are the kind of things which the mathematical sciences study. Nor is the science which we are now seeking concerned with the objects of mathematics; for no one of these is capable of existing separately. Nor does it deal with sensible substances, for these are corruptible (208-219). ὅλως δ᾽ ἀπορήσειέ  τις ἂν ποίας ἐστὶν ἐπιστήμης τὸ διαπορῆσαι περὶ τῆς τῶν μαθηματικῶν ὕλης. οὔτε γὰρ τῆς φυσικῆς, διὰ τὸ περὶ τὰ ἔχοντα ἐν αὑτοῖς ἀρχὴν κινήσεως καὶ στάσεως τὴν τοῦ φυσικοῦ πᾶσαν εἶναι πραγματείαν, οὐδὲ μὴν τῆς σκοπούσης περὶ ἀποδείξεώς τε καὶ ἐπιστήμης: περὶ γὰρ αὐτὸ τοῦτο τὸ  γένος τὴν ζήτησιν ποιεῖται. λείπεται τοίνυν τὴν προκειμένην φιλοσοφίαν περὶ αὐτῶν τὴν σκέψιν ποιεῖσθαι. 908. And in general one might raise the question to what science it belongs to consider the problem about the matter of the mathematical sciences (627). It is not the office of the philosophy of nature, for this science is wholly concerned with things which have in themselves a principle of rest and of motion. Nor is it the office of the science which investigates demonstration and scientific knowledge, for it is about this class of things that it makes its investigations. It follows, then, that it pertains to the philosophy which we have proposed to investigate these things. διαπορήσειε δ᾽ ἄν τις εἰ δεῖ θεῖναι τὴν ζητουμένην ἐπιστήμην περὶ τὰς ἀρχάς, τὰ καλούμενα ὑπό τινων στοιχεῖα: ταῦτα δὲ πάντες ἐνυπάρχοντα τοῖς συνθέτοις τιθέασιν. μᾶλλον δ᾽ ἂν δόξειε  τῶν καθόλου δεῖν εἶναι τὴν ζητουμένην ἐπιστήμην: πᾶς γὰρ λόγος καὶ πᾶσα ἐπιστήμη τῶν καθόλου καὶ οὐ τῶν ἐσχάτων, ὥστ᾽ εἴη ἂν οὕτω τῶν πρώτων γενῶν. 909. And one might raise the question whether the science which is now being sought must deal with the principles which are called elements by some thinkers (184). But all men suppose these to be present in composite things. And it would seem rather that the science which is now being sought ought to deal with universals, for every intelligible nature and every science is of universals and not of extremes (228), so that in this way they would deal with the primary genera. ταῦτα δὲ γίγνοιτ᾽ ἂν τό τε ὂν καὶ τὸ ἕν: ταῦτα γὰρ μάλιστ᾽ ἂν ὑποληφθείη περιέχειν τὰ ὄντα πάντα καὶ μάλιστα ἀρχαῖς ἐοικέναι διὰ  τὸ εἶναι πρῶτα τῇ φύσει: φθαρέντων γὰρ αὐτῶν συναναιρεῖται καὶ τὰ λοιπά: πᾶν γὰρ ὂν καὶ ἕν. ᾗ δὲ τὰς διαφορὰς αὐτῶν ἀνάγκη μετέχειν εἰ θήσει τις αὐτὰ γένη, διαφορὰ δ᾽ οὐδεμία τοῦ γένους μετέχει, ταύτῃ δ᾽ οὐκ ἂν δόξειε δεῖν αὐτὰ τιθέναι γένη οὐδ᾽ ἀρχάς. 910. And these would become being and unity; for these most of all might be thought to contain all existing things and to be principles in the highest degree, because they are first by nature; for when they have been destroyed, everything else is destroyed, since everything is a being and one. But if one supposes them to be genera, then inasmuch as it is necessary for differences to participate in them, and no difference participates in a genus, it would seem that they must not be regarded either as genera or as principles. ἔτι δ᾽ εἰ μᾶλλον  ἀρχὴ τὸ ἁπλούστερον τοῦ ἧττον τοιούτου, τὰ δ᾽ ἔσχατα τῶν ἐκ τοῦ γένους ἁπλούστερα τῶν γενῶν (ἄτομα γάρ, τὰ γένη δ᾽ εἰς εἴδη πλείω καὶ διαφέροντα διαιρεῖται), μᾶλλον ἂν ἀρχὴ δόξειεν εἶναι τὰ εἴδη τῶν γενῶν. ᾗ δὲ συναναιρεῖται τοῖς γένεσι τὰ εἴδη, τὰ γένη ταῖς ἀρχαῖς ἔοικε μᾶλλον: ἀρχὴ γὰρ τὸ συναναιροῦν. [1060α]  τὰ μὲν οὖν τὴν ἀπορίαν ἔχοντα ταῦτα καὶ τοιαῦτ᾽ ἐστὶν ἕτερα. 911. Further, if what is more simple is more of a principle than what is less simple, and the ultimate members resulting from the subdivision of different genera are more simple than the genera themselves (for these members are indivisible, whereas genera are divided into many different species), it would seem that species are principles to a greater degree than genera. But since species are involved in the destruction of their genera, genera are like principles to a greater degree; for whatever involves something else in its destruction is a principle of that thing (229-234). These and other such points, then, are the ones which cause difficulties. COMMENTARY Quia particulares scientiae quaedam eorum quae perscrutatione indigent praetermittunt, necesse fuit quamdam scientiam esse universalem et primam, quae perscrutetur ea, de quibus particulares scientiae non considerant. Huiusmodi autem videntur esse tam communia quae sequuntur ens commune (de quibus nulla scientia particularis considerat, cum non magis ad unam pertineant quam ad aliam, sed ad omnes communiter), quam etiam substantiae separatae, quae excedunt considerationem omnium particularium scientiarum. Et ideo Aristoteles huiusmodi scientiam nobis tradens, postquam perscrutatus est de communibus, accedit ad tractandum specialiter de substantiis separatis, ad quarum cognitionem ordinantur non solum ea quae in hac scientia tractata sunt, sed etiam quae in aliis scientiis tractantur. 2146. Because the particular sciences disregard certain things which should be investigated, there must be a universal science which examines these things. Now such things seem to be the common attributes which naturally belong to being in general (none of which are treated by the particular sciences since they do not pertain to one science rather than to another but to all in general) and to the separate substances, which lie outside the scope of every particular science. Therefore, in introducing us to such knowledge, Aristotle, after he has investigated these attributes, begins to deal particularly with the separate substances, the knowledge of which constitutes the goal to which the things studied both in this science and in the other sciences are ultimately directed. Et ideo ad manifestiorem considerationem de substantiis separatis habendam, primo sub quodam compendio recolligit ea quae dicta sunt tam in hoc libro, quam in libro physicorum, utilia ad cognitionem substantiarum separatarum. Secundo de ipsis substantiis separatis inquirit, circa medietatem sequentis libri, ibi, sed quoniam tres sunt substantiae. Now in order that a clearer understanding of the separate substances may be had, Aristotle first (899:C 2146) makes a summary of the points discussed both in this work and in the Physics’ which are useful for knowing the separate substances. Second (1055:C 2488), he investigates the separate substances in themselves (in the middle of the following book: “Since there are”). Prima pars dividitur in duas. In prima recolligit ea quae praecedunt considerationem substantiae. In secunda recolligit ea quae ad considerationem substantiae pertinent, ibi (in principio sequentis libri), de substantia quidem theorica. The first part is divided into two. In the first he summarizes the points which act as a preface to the study of substances. In the second (1023:C 2416) he restates the things that pertain to the study of substances (at the beginning of the following book: “The study here”). Tria autem praemiserat ante considerationem substantiae. Primo moverat dubitationes in tertio libro, quas in hoc primo recolligit. Secundo determinaverat ea quae ad considerationem huius scientiae pertinent, in quarto libro, quae et hic secundo loco recolligit, ibi, quoniam autem philosophi scientia. Tertio determinat de ente imperfecto, scilicet de ente per accidens, et de motu, et infinito, et de quibus partim determinaverat in secundo et sexto huius, partim in tertio physicorum. Et de his in tertio loco hic recolligit, ibi, quoniam autem simpliciter ens et cetera. He prefaced his study of substances by doing three things. First, he raised the questions given in Book 111, which he now restates under the first point of discussion. Second (924:C 2194), he expressed his views about the things that pertain to the study of this science. These are given in Book IV and are restated here under the second point of discussion (“Since the science”). Third (963:C 2268), he drew his conclusions about imperfect being, i.e., accidental being, motion, and the infinite, about which he had partly established the truth in Books II (152:C 299) and VI (543-59:C 1171-1244) of this work, and partly in Book III of the Physics; and he gives a summary restatement of these under the third point of discussion (“Since the term being”). Prima pars dividitur in duas. Primo movet dubitationem circa considerationem huius scientiae. In secunda circa res, de quibus in hac scientia determinatur, ibi, adhuc unum oportet poni. The first part is divided into two. First, he raises a question about the study of this science; and second (912:C 2173), about the things established in this science (“Further, there is”). Circa primum duo facit. Primo inquirit quomodo sit consideratio huius scientiae circa principia et substantias. Secundo circa quae principia, et circa quas substantias, ibi, sed nec circa dicta a physicis. In regard to the first he does two things. First, he asks in what way the study of this science is concerned with principles and substances. Second (904: C 2156), he asks with what principles and what substances it deals (“But the science”). Circa primum duo facit. Primo dubitationes movet de consideratione huius scientiae circa principia. Secundo de consideratione huius scientiae circa substantias, ibi, adhuc utrum omnium substantiarum. In regard to the first he does two things. First, he raises questions about the study of the principles of this science; and second (902:C 2152), about this science’s study of substances (“Further, there is the question”). Circa primum tria facit. Primo supponit considerationem huius scientiae esse circa principia, dicens, quod manifestum est ex primo libro, in quo disputavit contra ea quae alii philosophi dixerunt de primis rerum principiis, quod sapientia est scientia quaedam circa principia. Ostensum est enim in prooemio istius libri, quod sapientia considerat causas altissimas et maxime universales, et est nobilissima scientiarum. In treating the first point (899) he does three things. First, he assumes that the investigations of this science are concerned with principles. He says that it is evident from Book I (45-143:C 93-272), in which he argued against the statements that other philosophers have made about the first principles of things, that wisdom is a science of principles. For it was shown in the Prologue to this work that wisdom considers the highest and most universal causes, and that it is the noblest of the sciences. 2147. But one might (900). Secundo ibi, dubitabit autem movet quaestionem de consideratione huius scientiae quae sapientia dicitur, circa principia rerum; dicens quod aliquis potest dubitare, utrum oporteat sapientiam quae considerat principia, esse unam scientiam aut multas. Second, he raises a question about the study of the principles by this science which is called wisdom. He says that one can ask whether wisdom, which considers principles, must be one science or many. Et si dicatur quod est una, videtur hoc esse in contrarium, quia plura, de quibus consideratur in una scientia, sunt contraria, eo quod unum contrariorum est ratio ad cognoscendum alterum, propter hoc videntur sub una arte cadere. Sed principia rerum, cum sint plura, non sunt contraria, alioquin non possent convenire in uno principiato. Sapientia ergo quae est de principiis, non videtur esse una scientia. Si vero dicatur quod non est una, sed plures, non est eas assignare. 2148. However, if we say that it is one, this seems to be inconsistent, because many of the things studied in one science are contraries, since one contrary is the basis for knowing the other, and thus both contraries seem to fall under one art. But since the principles of things are many, they are not contraries, otherwise they could not be combined in one subject. Hence, wisdom, which is concerned with principles, does not seem to be one science. And if it is not one science but many, it is impossible to state what these sciences are. Est autem veritas quod sapientia est una scientia, quae tamen considerat plura principia, inquantum reducuntur ad unum genus, quia et hac ratione contraria sub una scientia cadunt, inquantum sunt unius generis. 2149. Now the truth of the matter is that, while wisdom is one science, it considers many principles inasmuch as they are reduced to one genus, because contraries fall under one science since they belong to one genus. 2150. Further, one might (901). Tertio ibi, adhuc speculari movet dubitationem de consideratione huius scientiae circa principia demonstrationis; dicens, quod adhuc dubitabile est, utrum speculari principia demonstrativa, ut, omne totum est maius sua parte, et similia, sit unius scientiae, aut plurium. Et si dicatur quod unius, videtur difficile assignare, quare magis sit istius scientiae quam alicuius alterius, cum omnes scientiae communiter eis utantur. Si autem detur quod sit plurium scientiarum, videbitur difficile assignare plures scientias tales. Third, he raises a question about the study which this science makes of the principles of demonstration. He says that it is still a problem whether the study of the principles of demonstration (for example, every whole is greater than one of its parts, and the like) belongs to the study of one science or many. If one claims that such a study belongs to one science, it seems difficult to explain why it belongs to this science rather than to another, since all sciences make common use of these principles. But if one claims that it belongs to many sciences, it seems difficult to give many such sciences. Est autem veritas, quod una scientia principaliter considerat ista principia, ad quam consideratio pertinet communium, qui sunt termini illorum principiorum, sicut ens et non ens, totum et pars, et alia huiusmodi; et ab ea aliae scientiae huiusmodi principia accipiunt. 2151. Now the truth of the matter is that there is one science which is chiefly concerned with these principles, and this is the one which investigates the common terms involved in these principles, such as being and non-being, whole and part, and the like; and the other sciences receive such principles from this science. 2152. Further, there is (902). Deinde cum dicit adhuc utrum movet dubitationes de consideratione huius scientiae circa substantias. Et quaerit duo. Primo utrum haec scientia consideret de omnibus substantiis, aut non. Et si detur quod non, difficile est assignare de quibus substantiis consideret, et de quibus non. Et si detur quod de omnibus consideret, cum sit una, remanet dubium, quomodo eadem scientia possit esse de pluribus, cum una scientia sit unius. Then he raises questions about this science's study of substances; and there are two of these. First, he asks whether or not this science considers all substances. If one claims that it does not, it is difficult to indicate what substances it does consider and what not. And if one claims that it considers all substances, the question remains how one and the same science can deal with many substances, since each science treats of one thing. Et veritas est, quod haec scientia est de omnibus substantiis, licet de quibusdam principalius, scilicet de substantiis separatis, inquantum omnes conveniunt in uno genere, quod est ens per se. 2153. The truth is that, although this science deals especially with the separate substances, it does treat all substances inasmuch as all belong to one common class of essential being. 2154. Again, there is (903). Secundo ibi, adhuc utrum quaerit utrum demonstratio sit solum circa substantias, aut etiam circa accidentia. Si enim demonstratio proprie esset circa accidentia, quia ad demonstrationem pertinet concludere per se accidentia de substantiis, non erit demonstratio circa substantias. Sed si dicatur, quod alia demonstrativa scientia est substantiarum, et alia accidentium per se, quaerendum restat quae sit utraque earum, et si utraque earum sit digna nomine sapientiae. Quia ex una parte videtur quod illa quae circa accidentia sit sapientia, quia demonstratio proprie est accidentium, et demonstrativa scientia certissima est. Et sic videtur quod sapientia sit demonstrativa quae est circa accidentia. Ex alia parte videtur quod sit circa substantias; quia cum substantia sit prima in entibus, scientia quae est circa substantias videtur esse prima. Second, he asks whether there is demonstration only with regard to substances or also with regard to accidents; for, if demonstration, properly speaking, were concerned with accidents, there would be no demonstration with regard to substances, since it is the function of demonstration to infer the essential accidents of substances. But if one claims that there is one demonstrative science of substances and an. other of essential accidents, the question remains as to which science each of these is, and whether each is worthy of the name of wisdom. For, on the one hand, it does seem that the science which deals with accidents is wisdom, because demonstration is properly concerned with accidents, and demonstrative science is the most certain. Thus it seems that wisdom, which is a demonstrative science, deals with accidents But, on the other hand, it seems to deal with substances; for since substances are the primary kind of being, it seems that the science which treats of them is the primary science. Est autem veritas quod sapientia substantias et accidentia considerat, inquantum conveniunt in ente, quod est eius subiectum; sed substantias principaliter, sicut per se prima entia, et de his accidentia demonstrat. 2155. Now the truth is that wisdom considers both substances and accidents inasmuch as they have being in common, which constitutes the subject of wisdom; but its demonstrations are concerned chiefly with substances, which are the primary kind of essential beings, and of these it demonstrates the accidents. 2156. But the science (904). Deinde cum dicit sed non movet quaestiones magis speciales de consideratione huius scientiae. Et primo circa quas substantias sit consideratio huius scientiae. Secundo circa quae principia, ibi, dubitabit autem utique. Then he raises more specific questions about the study of this science. First (904:C 2156), he asks about the substances which this science considers; and second (909:C 2166), about the principles which it considers (“And one might”). Circa primum movet quatuor quaestiones. Et prima quaestio pertinet ad causas substantiarum sensibilium; dicens, quod non videtur ponendum hanc scientiam quam quaerimus, circa quatuor genera causarum, de quibus dictum est in libro physicorum; quia maxime videretur esse circa causam finalem, quae est potissima inter alias. Sed non videtur esse haec scientia circa id cuius gratia, idest circa causam finalem: quia finis habet rationem boni. Bonum autem consistit in operationibus, et in his quae sunt in motu. Unde in immobilibus, sicut in mathematicis, nihil demonstratur per causam finalem. Et manifestum est quod finis est quod primum movet. Movet enim efficientem. Primum autem movens non videtur esse in rebus immobilibus. In treating the first point he raises four questions. The first (904) has to do with the causes of sensible substances. He says that it does not seem that we should hold that the science which we are seeking is concerned with the four classes of causes discussed in the Physics, because it seems to deal especially with the final cause, which is the most important of all. But this science does not seem to deal with “the final cause,” or goal, because an end or goal has the nature of the good. Now the good relates to operations and to things which are in motion. Hence in the case of immovable things, such as the objects of mathematics, nothing is demonstrated by way of the final cause. It is also evident that the end is what first moves a thing, for it moves the efficient cause. But there does not seem to be a first cause of motion in the case of immovable things. Est autem veritas, quod haec scientia considerat dicta genera causarum, et praecipue causam formalem et finalem. Et ulterius finis qui est primum movens, est omnino immobile, ut infra ostendetur. 2157. Now the truth of the matter is that this science considers the classes of causes mentioned, especially the formal and final cause. And furthermore, the end, which is the first cause of motion, is altogether immovable, as will be shown below (1069:C 2526). 2158. And in general (905). Secundo ibi, totaliter autem movet quaestionem de consideratione substantiarum sensibilium; et quaerit, utrum haec scientia sit circa substantias sensibiles, aut non. Si enim sit circa substantias sensibiles, non videtur differre a scientia naturali: si autem circa alias substantias, difficile est assignare circa quas alias. Aut enim est circa species, idest circa ideas, quas Platonici posuerunt; aut est circa mathematica, quae etiam quidam posuerunt esse media inter ideas et substantias sensibiles, sicut sunt superficies, et lineae, et figurae, et alia huiusmodi. Sed manifestum est per superiores libros, quod species non sunt, idest ideae separatae, et de mathematicis statim quaeretur. Second, he raises a question about the study of sensible substances. He asks whether this science is concerned with sensible substances or not. For if it is concerned with them, it does not seem to differ from the philosophy of nature. But if it is concerned with other substances, it is difficult to state what these substances are. For it must deal with either “the separate Forms,” i.e., the Ideas, which the Platonists posited, or with the objects of mathematics, which some supposed to exist as an intermediate class of things between the Ideas and sensible substances, for example, surfaces, lines, figures and the like. But it is evident from the previous books that “separate Forms do not exist,” i.e., separate Ideas; and so he immediately raises the question about the objects of mathematics. Est autem veritas huius quaestionis, quod ista scientia determinat de substantiis sensibilibus, inquantum sunt substantiae, non inquantum sunt sensibiles et mobiles. Hoc enim proprie pertinet ad naturalem. Sed propria consideratio huius scientiae est de substantiis, quae non sunt ideae, nec mathematica separata, sed primi motores, ut infra patebit. 2159. Now the true answer to this question is that this science deals with sensible substances inasmuch as they are substances, but not inasmuch as they are sensible and movable; for this latter belongs properly to the philosophy of nature. But the proper study of this science has to do with substances which are neither Ideas nor separate mathematical entities but primary movers, as will be seen below (1055:C 2488). 2160. But nevertheless (906). Tertio ibi, attamen dubitationem movet tertiam dubitationem ex incidenti. Quia enim dixerat manifestum esse quod non sunt species separatae, movet dubitationem de mathematicis, utrum sint separatae. Et ostendit primo quod non: quia si aliquis ponat species separatas, et mathematica separata praeter substantias sensibiles, quare non est ita in omnibus quae habent species, sicut in mathematicis? Ut sicut mathematica ponitur media inter species et sensibilia, quasi quaedam tertia entia praeter species et particularia quae sunt hic, ut linea mathematica praeter speciem lineae et lineam sensibilem, ita poneretur tertius homo, et tertius equus praeter auton, idest per se hominem, et per se equum, quae appellabant Platonici ideas, et equum et hominem singulares. Sed in his Platonici media non ponebant, sed solum in mathematicis. Third, he raises a third difficulty as a secondary issue. For, since he had said that there are evidently no separate Forms, he poses the question whether the objects of mathematics are separate. First, he shows that they are not. For if one claims that there are separate Forms and separate mathematical entities over and above sensible substances, why is not the same thing true of all things which have Forms as is true of the objects of mathematics? So that just as the objects of mathematics are assumed “ to be intermediate between the separate Forms and sensible substances as a third class of things over and above the separate Forms and the singular things which exist here (for example, a mathematical line over and above the Form of a line and the perceptible line), in a similar fashion there should be a third man and a third “horse over and above man-in-himself and horse-in-itself” (i.e., the ideal man and the ideal horse, which the Platonists called Ideas) and individual men and horses. But the Platonists did not posit intermediates in such cases as these but only in that of the objects of mathematics. 2161. If, however (907). Postea vero cum dicit si autem obiicit in contrarium: quia si non sunt mathematica separata, difficile est assignare circa quae mathematicae scientiae negocientur. Non enim negociari videntur circa sensibilia inquantum huiusmodi; quia in istis sensibilibus non sunt tales lineae et tales circuli, quales scientiae mathematicae quaerunt. Unde videtur necesse ponere quasdam lineas et quosdam circulos separatos. Then he argues on the other side of the question; for, if the objects of mathematics are not separate, it is difficult to indicate the things with which the mathematical sciences deal. For they do not seem to deal with sensible things as such, because no lines and circles such as the mathematical sciences investigate are found in sensible things. It seems necessary to hold, then, that there are certain separate lines and circles. Est autem veritas, quod mathematica non sunt separata a sensibilibus secundum se, sed solum secundum rationem, ut supra ostensum est in sexto, et infra declarabitur. 2162. Now the truth of the matter is that the objects of mathematics are not separate from sensible things in being but only in their intelligible structure, as has been shown above in Book VI (537:C 1162) and will be considered below (919:C 2185). Et quia hanc dubitationem ex incidenti interposuerat de separatione mathematicorum ea occasione, quia dixerat manifestum esse, quod species non sunt separatae: consequenter cum dicit, neque etiam circa mathematica, redit ad quaestionem principalem, qua quaerebatur circa quas substantias sit ista scientia. Et cum ostenderit quod non sit circa species, quia species non sunt separatae, nunc ostendit eadem ratione, quod non est circa mathematica, quia nec ipsa sunt separata, scilicet secundum esse. Sed non videtur esse circa sensibiles substantias, cum sint corruptibiles et in motu existentes. 2163. And since he had interjected as a secondary issue this difficulty about the separateness of the objects of mathematics because he had said that forms evidently are not separate, therefore when he says, “Nor is the science which we are now seeking concerned with the objects of mathematics,” he returns to the main question that was raised, namely, with what kind of substances this science deals. And since he had shown that it does not deal with separate Forms (for there are no separate Forms), he now shows by the same reasoning that it does not deal with the objects of mathematics; for neither are they separate in being. And it does not seem to deal with sensible substances, because these are destructible and in motion. Est autem veritas huius quaestionis, quae supra posita est. 2164. The true answer to this question is the one given above. 2165. And in general one might (908). Quartam dubitationem ponit ibi, totaliter autem et quaerit cuius scientiae sit dubitare de materia mathematicarum scientiarum, idest inquirere de quibus mathematicae considerent. Non enim hoc est scientiae naturalis, propter hoc quod totum negocium naturalis philosophiae est circa ea, quae habent in seipsis principium motus et quietis, quae naturalia dicuntur. Unde de hac dubitatione se non intromittit. Similiter etiam consideratio huius dubitationis non videtur pertinere ad illam scientiam, quae intendit de demonstratione et scientia mathematicorum, quae dicitur mathematica scientia; quia huiusmodi scientia praesupponit huiusmodi materiam, sive huiusmodi subiectum; et circa ipsum aliqua inquirit. Unde relinquitur quod ad hanc philosophiam pertineat considerare, de quo tractant scientiae mathematicae. Then he gives a fourth difficulty by asking to what science it belongs “to consider the problems about the matter of the mathematical sciences,” i.e., to investigate the things with which the mathematical sciences are concerned. This does not pertain to the philosophy of nature, because it is wholly concerned with those things which have in themselves a principle of rest and of motion and are called natural beings. Therefore he does not examine this problem. Similarly, the investigation of this problem does not seem to belong to that science which is called mathematical, which has as its aim the demonstration and knowledge of mathematical entities; for this kind of science presupposes matter of this sort or a subject of this sort, and some science does investigate this subject. It follows, then, that it is the business of this philosophical science to consider the things of which the mathematical sciences treat. 2166. And one might (909). Deinde cum dicit dubitabit autem inquirit circa qualia principia sit consideratio huius scientiae. Et circa hoc movet tres quaestiones. Primo enim quaerit, utrum haec scientia sit circa principia, quae a quibusdam elementa dicuntur. Quod videtur ex hoc, quod omnes ponunt huiusmodi principia esse inexistentia, idest intrinseca composito. Et ita oportet ad cognitionem compositorum, quod ipsa cognoscantur. Sed ex alia ratione videtur, quod ista scientia sit magis universalium, quia omnis ratio et omnis scientia videtur esse universalium et non extremorum, idest particularium, ad quae divisio communium terminatur: et sic videtur, quod ista scientia maxime sit priorum generum. Then he asks what kind of principles this science investigates. In regard to this he raises three questions. First, he asks whether this science studies the principles which are called elements by some thinkers. This question seems to refer to the common supposition that principles of this kind are present in, i.e., intrinsic to, the composite, so that in order to know composite things these principles must be known. But from another point of view it seems that this science is concerned with more universal things, because every intelligible nature and every science seems to be “of universals and not of extremes,” i.e., not about the particular things in which the division of common genera terminates. Thus it seems that this science has to do especially with the first genera. Et veritas est, quod haec scientia praecipue considerat communia; non tamen quod communia sint principia, sicut Platonici posuerunt. Considerat autem et principia intrinseca rerum, sicut materiam et formam. 2167. But the truth is that this science deals chiefly with common attributes, yet without making the common factors principles in a Platonic sense. However, it does consider the intrinsic principles of things—matter and form. 2168. And these would (910). Secundo ibi, haec autem movet secundam dubitationem. Videtur enim ex una parte, quod unum et ens sint principia et genera, quia haec maxime videntur continere omnia suo ambitu communitatis. Et maxime videntur esse principia, quia sunt prima naturaliter, quia eis interemptis interimuntur alia. Omnia enim sunt ens et unum: unde si auferatur unum et ens, omnia alia auferuntur; sed non convertitur. Et sic videntur esse prima naturaliter, cum prius naturaliter dicatur a quo non convertitur consequentia essendi. Second, he raises the second problem. For, on the one hand, it seems that unity and being are principles and genera, because these most of all seem to contain all things within their general ambit. And they seem to be principles because they are first by nature; for when they are destroyed, other things are too; for everything is a being and one. Hence, if being and unity are destroyed, everything else is destroyed, but not the other way around. Ex alia parte videtur, quod unum et ens non sint genera, et per consequens nec principia, si genera sunt principia. Nulla enim differentia participat actu genus; quia differentia sumitur a forma, genus autem a materia. Sicut rationale a natura intellectiva, animal a natura sensitiva. Forma autem non includitur in essentia materiae actu, sed materia est in potentia ad ipsam. Et similiter differentia non pertinet ad naturam generis, sed genus habet differentiam potestate. Et propter hoc differentia non participat genus; quia cum dico rationale, significo aliquid habens rationem. Nec est de intellectu rationalis quod sit animal. Illud autem participatur, quod est de intellectu participantis. Et propter hoc dicitur, quod differentia non participat genus. Nulla autem posset differentia sumi, de cuius intellectu non esset unum et ens. Unde unum et ens non possunt habere aliquas differentias. Et ita non possunt esse genera, cum omne genus habeat differentias. 2169. But, on the other hand, it seems that unity and being are not genera, and therefore they are not principles if genera are principles. For no difference participates actually in a genus, because difference is derived from form and genus from matter; for example, rational is taken from intellective nature, and animal from sensory nature. Now form is not included actually in the essence of matter, but matter is in potentiality to form. And similarly difference does not belong to the nature of a genus, but a genus contains differences potentially. And for this reason a difference does not participate in a genus, because, when I say “rational,” I signify something having reason. Nor does it belong to the intelligibility of rational that it should be animal. Now that is participated in which is included in the intelligibility of the thing which participates; and for this reason it is said that a difference does not participate in a genus. But there cannot be any difference whose intelligibility does not contain unity and being. Hence unity and being cannot have any differences. Thus, they cannot be genera, since every genus has differences. Est autem veritas, quod unum et ens non sunt genera, sed sunt omnibus communia analogice. 2170. Now the truth of the matter is that unity and being are not genera but are common to all things analogically. 2171. Further, if what (911). Tertiam quaestionem ponit ibi, adhuc autem et est dubitatio, utrum principia sint magis genera quam species. Et primo ostendit quod species magis sint principia quam genera; quia quod est simplicius, est magis principium. Sed species videntur esse simpliciores. Sunt enim indivisibilia, ad quae terminatur divisio generis formalis. Sed genera in plura et differentia specie dividuntur: ergo magis videntur principia esse species quam genera. Sed ex ea parte qua genera constituunt species, et non e converso, videntur genera esse magis principia. Hoc enim est de ratione principii, quod eo remoto alia removentur. Then he raises the third question. The problem now is whether genera are principles to a greater degree than species. First, he shows that species are principles to a greater degree than genera; for what is more simple is a principle to a greater degree. But species seem to be more simple, for they are the indivisible things in which the formal division of a genus terminates. But genera are divided into many different species, and therefore species seem to be principles to a greater degree than genera. But in view of the fact that genera constitute species, and not vice versa, genera seem to be principles to a greater degree; for the intelligible structure of a principle is such that, when it is destroyed, other things are destroyed. Est autem veritas quod universalia sunt principia, scilicet in cognoscendo; et sic genera magis sunt principia, quia simpliciora. Et quod dividantur in plura quam species, hoc est, quia continent plura in potentia. Sed species continent plura in actu. Unde sunt magis divisibiles per modum resolutionis compositi in simplicia. 2172. Now the truth is that universals are principles, namely, of knowing; and thus genera are principles to a greater degree because they are simpler. The reason why they are divided into more members than species are is that they contain more members potentially. But species contain many members actually. Hence they are divisible to a greater degree by the method of dissolving a composite into its simple constituents.
LESSON 2 Are There Non-Sensible Substances and Principles?
ARISTOTLE’S TEXT Chapter 2: 1060a 3-1060b 3 ἔτι πότερον δεῖ τιθέναι τι παρὰ τὰ καθ᾽ ἕκαστα ἢ οὔ, ἀλλὰ τούτων ἡ ζητουμένη ἐπιστήμη; ἀλλὰ ταῦτα ἄπειρα:  τά γε μὴν παρὰ τὰ καθ᾽ ἕκαστα γένη ἢ εἴδη ἐστίν, ἀλλ᾽ οὐδετέρου τούτων ἡ ζητουμένη νῦν ἐπιστήμη. διότι γὰρ ἀδύνατον τοῦτο, εἴρηται. 912. Further, there is the question whether or not we must posit the existence of something besides singular things; and if not, then the science which we are now seeking must deal with these things. But they are infinite in number. And what exists apart from singular things are genera and species; but the science which we are now seeking deals with neither of these. The reason why this is impossible has already been stated (909-911). καὶ γὰρ ὅλως ἀπορίαν ἔχει πότερον δεῖ τινὰ ὑπολαβεῖν οὐσίαν εἶναι χωριστὴν παρὰ τὰς αἰσθητὰς οὐσίας καὶ τὰς δεῦρο, ἢ οὔ, ἀλλὰ ταῦτ᾽ εἶναι τὰ ὄντα καὶ  περὶ ταῦτα τὴν σοφίαν ὑπάρχειν. ζητεῖν μὲν γὰρ ἐοίκαμεν ἄλλην τινά, καὶ τὸ προκείμενον τοῦτ᾽ ἔστιν ἡμῖν, λέγω δὲ τὸ ἰδεῖν εἴ τι χωριστὸν καθ᾽ αὑτὸ καὶ μηδενὶ τῶν αἰσθητῶν ὑπάρχον. 913. And in general the problem is whether one must suppose that there is some substance which is separable from sensible substances (i.e., the things which exist here and now), or that the latter are beings and the things with which wisdom deals. For we seem to be looking for another kind of substance, and this constitutes the object of our study: I mean, to know whether there is something which is separable in itself and belongs to no sensible thing. ἔτι δ᾽ εἰ παρὰ τὰς αἰσθητὰς οὐσίας ἔστι τις ἑτέρα οὐσία, παρὰ ποίας τῶν αἰσθητῶν δεῖ τιθέναι ταύτην εἶναι;  τί γὰρ μᾶλλον παρὰ τοὺς ἀνθρώπους ἢ τοὺς ἵππους ἢ τῶν ἄλλων ζῴων θήσει τις αὐτὴν ἢ καὶ τῶν ἀψύχων ὅλως; τό γε μὴν ἴσας ταῖς αἰσθηταῖς καὶ φθαρταῖς οὐσίαις ἀϊδίους ἑτέρας κατασκευάζειν ἐκτὸς τῶν εὐλόγων δόξειεν ἂν πίπτειν. 914. Further, if there is another kind of substance apart from sensible substances, from what kind of sensible substances must it be assumed to be separate? For why should we suppose that it exists apart from men and from horses rather than from other animals or non-living things generally? Yet to devise various eternal substances equal in number to sensible and corruptible ones would seem to be unreasonable. εἰ δὲ μὴ χωριστὴ τῶν σωμάτων ἡ ζητουμένη νῦν ἀρχή,  τίνα ἄν τις ἄλλην θείη μᾶλλον τῆς ὕλης; αὕτη γε μὴν ἐνεργείᾳ μὲν οὐκ ἔστι, δυνάμει δ᾽ ἔστιν. μᾶλλόν τ᾽ ἂν ἀρχὴ κυριωτέρα ταύτης δόξειεν εἶναι τὸ εἶδος καὶ ἡ μορφή: τοῦτο δὲ φθαρτόν, ὥσθ᾽ ὅλως οὐκ ἔστιν ἀΐδιος οὐσία χωριστὴ καὶ καθ᾽ αὑτήν. ἀλλ᾽ ἄτοπον: ἔοικε γὰρ καὶ ζητεῖται σχεδὸν  ὑπὸ τῶν χαριεστάτων ὡς οὖσά τις ἀρχὴ καὶ οὐσία τοιαύτη: πῶς γὰρ ἔσται τάξις μή τινος ὄντος ἀϊδίου καὶ χωριστοῦ καὶ μένοντος; 915. But if the principle we are now seeking is not separable from bodies, what could be more of a principle of things than matter? Yet matter does not exist actually but only potentially; and thus it would seem rather that the specifying principle or form is a more important principle than matter. But the form is corruptible [according to some]; and so in general there is no eternal substance which is separate and exists of itself. But this is absurd; for such a principle and substance seems to exist and is sought by almost all accomplished thinkers as something that exists. For how will there be order in the world if there is not a principle which is eternal, separable and permanent (235-246)? ἔτι δ᾽ εἴπερ ἔστι τις οὐσία καὶ ἀρχὴ τοιαύτη τὴν φύσιν οἵαν νῦν ζητοῦμεν, καὶ αὕτη μία πάντων καὶ ἡ αὐτὴ τῶν ἀϊδίων τε καὶ φθαρτῶν, ἀπορίαν ἔχει διὰ τί ποτε τῆς  αὐτῆς ἀρχῆς οὔσης τὰ μέν ἐστιν ἀΐδια τῶν ὑπὸ τὴν ἀρχὴν τὰ δ᾽ οὐκ ἀΐδια (τοῦτο γὰρ ἄτοπον): εἰ δ᾽ ἄλλη μέν ἐστιν ἀρχὴ τῶν φθαρτῶν ἄλλη δὲ τῶν ἀϊδίων, εἰ μὲν ἀΐδιος καὶ ἡ τῶν φθαρτῶν, ὁμοίως ἀπορήσομεν (διὰ τί γὰρ οὐκ ἀϊδίου τῆς ἀρχῆς οὔσης καὶ τὰ ὑπὸ τὴν ἀρχὴν ἀΐδια;): φθαρτῆς δ᾽  οὔσης ἄλλη τις ἀρχὴ γίγνεται ταύτης κἀκείνης ἑτέρα, καὶ τοῦτ᾽ εἰς ἄπειρον πρόεισιν. 916. Again, if there is some substance and principle of such a nature as that now being sought, and this one principle belongs to everything and is one and the same for both corruptible and eternal things, the question arises why it is, if this principle is the same for all, that some of the things which come under it should be eternal and some not; for this is absurd. But if all corruptible things have one principle, and eternal things another, we shall face the same problem if the principle of corruptible things is eternal; for if it is eternal, why are not the things which fall under this principle also eternal? But if it is corruptible, it in turn must have some other principle, and this again must have another, and so on to infinity (250-265). εἰ δ᾽ αὖ τις τὰς δοκούσας μάλιστ᾽ ἀρχὰς ἀκινήτους εἶναι, τό τε ὂν καὶ τὸ ἕν, θήσει, πρῶτον μὲν εἰ μὴ τόδε τι καὶ οὐσίαν ἑκάτερον αὐτῶν σημαίνει, [1060β]  πῶς ἔσονται χωρισταὶ καὶ καθ᾽ αὑτάς; τοιαύτας δὲ ζητοῦμεν τὰς ἀϊδίους τε καὶ πρώτας ἀρχάς. εἴ γε μὴν τόδε τι καὶ οὐσίαν ἑκάτερον αὐτῶν δηλοῖ, πάντ᾽ ἐστὶν οὐσίαι τὰ ὄντα: κατὰ  πάντων γὰρ τὸ ὂν κατηγορεῖται (κατ᾽ ἐνίων δὲ καὶ τὸ ἕν): οὐσίαν δ᾽ εἶναι πάντα τὰ ὄντα ψεῦδος. 917. But on the other hand, if one were to posit those principles which are thought to be the most unchangeable, namely, being and unity, then, first, if each of these does not signify a particular thing or a substance, how will they be separable and exist of themselves? Yet the eternal and primary principles for which we are looking must be such. But if each of these does signify a particular thing or a substance, all beings will be substances; for being is predicated of all things, and unity is predicated of some. But it is false that all beings are substances. ἔτι δὲ τοῖς τὴν πρώτην ἀρχὴν τὸ ἓν λέγουσι καὶ τοῦτ᾽ οὐσίαν, ἐκ δὲ τοῦ ἑνὸς καὶ τῆς ὕλης τὸν ἀριθμὸν γεννῶσι πρῶτον καὶ τοῦτον οὐσίαν φάσκουσιν εἶναι, πῶς ἐνδέχεται τὸ λεγόμενον ἀληθὲς εἶναι;  τὴν γὰρ δυάδα καὶ τῶν λοιπῶν ἕκαστον ἀριθμῶν τῶν συνθέτων πῶς ἓν δεῖ νοῆσαι; περὶ τούτου γὰρ οὔτε λέγουσιν οὐδὲν οὔτε ῥᾴδιον εἰπεῖν. 918. Again, how can the statement of those be true who say that unity is the first principle and a substance, and who generate number as the first thing produced from the unit and matter and say that it is substance? For how are we to understand that the number two and each of the other numbers composed of units is one? For they say nothing about this, nor is it easy to do so. εἴ γε μὴν γραμμὰς ἢ τὰ τούτων ἐχόμενα (λέγω δὲ ἐπιφανείας τὰς πρώτας) θήσει τις ἀρχάς, ταῦτά γ᾽ οὐκ εἰσὶν οὐσίαι χωρισταί, τομαὶ δὲ καὶ διαιρέσεις αἱ μὲν  ἐπιφανειῶν αἱ δὲ σωμάτων (αἱ δὲ στιγμαὶ γραμμῶν), ἔτι δὲ πέρατα τῶν αὐτῶν τούτων: πάντα δὲ ταῦτα ἐν ἄλλοις ὑπάρχει καὶ χωριστὸν οὐδέν ἐστιν. 919. But if someone maintains that lines and what is derived from these (I mean surfaces) are the first principles of things, these are not separable substances but sections and divisions; the former of surfaces, and the latter of bodies (and points are the sections and divisions of lines); and further they are the limits of these same things. And all of these exist in other things, and none are separable. ἔτι πῶς οὐσίαν ὑπολαβεῖν εἶναι δεῖ τοῦ ἑνὸς καὶ στιγμῆς; οὐσίας μὲν γὰρ πάσης γένεσις ἔστι, στιγμῆς δ᾽ οὐκ ἔστιν: διαίρεσις γὰρ ἡ στιγμή. 920. Again, how are we to understand that the unit and the point have substance. For every substance is generated but not the point; for the point amounts to a division (266-283). παρέχει  δ᾽ ἀπορίαν καὶ τὸ πᾶσαν μὲν ἐπιστήμην εἶναι τῶν καθόλου καὶ τοῦ τοιουδί, τὴν δ᾽ οὐσίαν μὴ τῶν καθόλου εἶναι, μᾶλλον δὲ τόδε τι καὶ χωριστόν, ὥστ᾽ εἰ περὶ τὰς ἀρχάς ἐστιν ἐπιστήμη, πῶς δεῖ τὴν ἀρχὴν ὑπολαβεῖν οὐσίαν εἶναι; 921. There is also the problem that, while every science must be about universals and about such and such a universal, a substance is not a universal but is rather a particular and separable thing. Hence, if there is a science of principles, how are we to understand substance to be a principle (288-293) ? ἔτι πότερον ἔστι τι παρὰ τὸ σύνολον ἢ οὔ (λέγω δὲ τὴν ὕλην καὶ  τὸ μετὰ ταύτης); εἰ μὲν γὰρ μή, τά γε ἐν ὕλῃ φθαρτὰ πάντα: εἰ δ᾽ ἔστι τι, τὸ εἶδος ἂν εἴη καὶ ἡ μορφή: τοῦτ᾽ οὖν ἐπὶ τίνων ἔστι καὶ ἐπὶ τίνων οὔ, χαλεπὸν ἀφορίσαι: ἐπ᾽ ἐνίων γὰρ δῆλον οὐκ ὂν χωριστὸν τὸ εἶδος, οἷον οἰκίας. 922. Again, the question arises whether or not there is any principle apart from the concrete whole? And by this I mean the matter and what is joined to it. For if not, then everything that is in matter is corruptible. But if there is some principle, it must be the specifying principle or form. Therefore it is difficult to determine in what cases this exists apart and in what not; for in some cases it is evident that the form is not separable, for example, in that of a house (235-247). ἔτι πότερον αἱ ἀρχαὶ εἴδει ἢ ἀριθμῷ αἱ αὐταί; εἰ γὰρ ἀριθμῷ  ἕν, πάντ᾽ ἔσται ταὐτά. 923. Again, there is the question whether principles are the same specifically or numerically? For if they are the same numerically, all things will be the same (248-249). COMMENTARY Postquam movit dubitationem de consideratione huius scientiae, hic movet dubitationem de his quae in hac scientia considerantur. Et primo de substantiis. Secundo de principiis, ibi, adhuc autem siquidem est. 2173. Having raised a question about the study of this science, Aristotle now raises a question about the things which are considered in this science. He does this, first (912:C 2173), with regard to substances; and second (916:C 2180), with regard to principles (“Again, if”). Circa hoc movet duas dubitationes: quarum prima est, utrum oporteat aliquid poni in rerum natura existere praeter singularia, aut non. Et si dicatur quod non, videtur sequi, quod haec scientia, quae nunc quaeritur, sit singularium, et quaelibet alia. Sed hoc videtur impossibile; quia singularia sunt infinita, et infinitorum non est scientia. Si autem dicatur, quod aliquid existit praeter singularia, oportet quod sint vel genera, vel species; et sic haec scientia esset de generibus vel speciebus. Sed quare hoc sit impossibile, dictum est prius; quia nec genera nec species videntur esse principia, cum tamen haec sit scientia de principiis. In treating the first issue he raises two questions. First, he asks whether or not it is necessary to posit the existence of something else in reality over and above singular things. Now if one claims that it is not, then it seems to follow that the science which we are now investigating must be concerned with singular things. But this seems to be impossible, because singular things are infinite in number, and the infinite is unknowable. And if one claims that it is necessary to posit the existence of something apart from singular things, they must be genera or species; and then this science would deal with genera and species. First, he explains why this is impossible; for it seems that neither genera nor species are principles, yet this science deals with principles. Et veritas haec est, quia nihil est in rerum natura praeter singularia existens, sed tantum in consideratione intellectus abstrahentis communia a propriis. 2174. The truth of the matter is that in reality there are only singular things, and that anything else exists only in the consideration of the intellect, which abstracts common attributes from particular ones. 2175. And in general (913). Secundam dubitationem ponit ibi, etenim et est utrum sit aliqua substantia separabilis praeter sensibiles substantias, quae sunt hic et nunc. Et haec quaestio necessaria est hic ad quaerendum; quia si nihil est praeter sensibilia, tunc sola sensibilia sunt entia. Et, cum sapientia sit scientia entium, sequitur quod sapientia sit circa sola sensibilia, cum tamen in hac scientia videamur quaerere quamdam aliam naturam separatam. Et sic ad propositum huius scientiae pertinet quaerere, si est aliquid separatum a sensibilibus, vel non. Et quicquid horum detur, sequitur alia quaestio. Then he states the second question: whether there is some substance which exists apart from sensible substances existing here and now. This question must be raised here because, if there is nothing apart from sensible substances, only sensible substances are beings. And since wisdom is the science of beings, wisdom must be concerned only with sensible substances, even though we seem in this science to be looking for some other separate reality. It belongs to this science, then, to investigate whether or not there is something apart from sensible substances. And whichever alternative is taken, another question arises. 2176. Further, if there (914). Et ideo consequenter dicit adhuc autem movet quaestionem quae videtur sequi, si ponatur aliquid separabile a sensibilibus; quae quidem quaestio est, utrum praeter omnes substantias sensibiles sit aliquid separabile, aut praeter quasdam tantum. Si praeter quasdam tantum, difficile est assignare rationem praeter quales substantiarum sensibilium oportet ponere substantiam separatam, et praeter quales non. Non enim videtur esse ratio aliqua, quare praeter homines et equos sensibiles sit homo et equus separatus, et non similiter de aliis animalibus, et etiam de aliis inanimatis. Si autem praeter omnia sensibilia sit aliqua substantia separata, sequitur quod oporteat ponere aliquas substantias separatas, perpetuas, aequales numero substantiis sensibilibus et corruptibilibus; ut scilicet, sicut est homo corruptibilis, ita sit homo incorruptibilis, et equus, et bos, et etiam in rebus naturalibus aliis. Et hoc videtur cadere in irrationabilia. He therefore poses the question which seems to arise if one claims that there is something separate from sensible substances. The question is whether this separate thing exists apart from all sensible substances or only apart from some. And if only apart from some, it is hard to explain why we should posit a separate substance apart from some sensible substances and not from others. For there does not seem to be any reason why there should be a separate man and a separate horse apart from the men and horses we perceive by the senses, and why this should not be true also of other animals and other non-living things. But if there is some separate substance apart from all sensible substances, it follows that we must posit the existence of certain separate substances which are eternal and equal in number to sensible and corruptible substances. Thus, just as there is a corruptible man, in a similar way there would be an incorruptible man, and the same with horse and ox, and also with other natural bodies. This seems to be absurd. 2177. But if the principle (915). Deinde cum dicit si autem movet aliam quaestionem, quae videtur sequi, si non sit aliqua substantia separata a sensibilibus. Et est quaestio quid sit primum principium, utrum scilicet materia vel forma: ex his enim duobus componuntur substantiae sensibiles. Videtur enim primo aspectu quod nihil magis possit poni principium quam materia, quae est primum subiectum, et semper manet, sicut primi naturales posuerunt. Sed hoc, ut videtur, non potest esse principium, quia materia non est in actu, sed in potentia. Et ita, cum actus naturaliter sit prior potentia, ut in nono habitum est, videtur quod sit principium species et forma quae est actus. Then he raises another question which seems to follow if there is no substance separate from sensible substances. This question asks what the first principle is, whether matter or form; for sensible substances are composed of these two principles. For at first glance it seems that nothing can be more of a principle of things than matter, which is the first subject and always continues to exist, as the first philosophers of nature claimed. Yet it would seem that matter cannot be a principle, because it is not an actuality but a potentiality. Hence, since actuality is naturally prior to potentiality, as has been pointed out in Book IX (785:C 1856), the specifying principle or form, which is an actuality, seems to be this principle. Sed nec forma potest esse principium, ut videtur, quia forma sensibilis videtur esse corruptibilis. Et ita, si forma sensibilis sit primum principium, videtur sequi quod nulla substantia sit perpetua, quae sit separabilis, et secundum se existens. Quod videtur inconveniens: quia a famosis philosophis quaeritur aliquod principium perpetuum et separatum, et aliqua talis substantia: et hoc rationabiliter. Non enim esset ordo perpetuitatis in rebus, nisi esset aliquod principium separabile et perpetuum, quod daret rebus perpetuitatem. 2178. But it seems that form cannot be a principle because a sensible form appears to be corruptible. If a sensible form were the first principle, then, it would seem to follow that there would be no eternal substance, separable and existing of itself. But this is clearly absurd because some such principle, eternal and separate, and some such substance, is sought by [almost all] the famous philosophers. This is reasonable, for there would not be a perpetual order of things in the world if there were no separate and eternal principle which causes things to be perpetual. Et veritas harum quaestionum est, quod est aliqua substantia separata a sensibilibus; non quidem species rerum sensibilium, ut Platonici posuerunt, sed primi motores, ut infra ostendetur. 2179. The true answer to this question is that there are certain substances which are separate from sensible substances; and these are not the Forms of sensible things, as the Platonists claimed, but the primary movers, as will be shown below (1056:C 2492). 2180. Again, if there (916). Deinde cum dicit adhuc autem movet quaestionem de principiis. Et primo qualia sunt. Secundo quae sunt, ibi, si autem rursus aliquid. Tertio quomodo se habeant adinvicem, ibi, adhuc autem primum principium. Then he raises the question about principles. First, he asks what kinds of principles there are; second (917:C 2182), what they are (“But on the other hand”); and third (918:C :2184), how they are related to one another (“Again, how can”). Quaerit ergo si sit aliqua substantia separata et principium ut nunc quaerimus, utrum sit aliquod principium omnium, scilicet corruptibilium et incorruptibilium, vel non. Si sit principium aliquod omnium, dubitatio remanet, quare ex eodem principio, quaedam sunt perpetua, quaedam non perpetua. Si autem aliud est principium corruptibilium, et aliud incorruptibilium, adhuc remanet dubitatio, quare, cum principium sit perpetuum, ea quae sunt ex primo non sunt perpetua. Si autem principium sit corruptibile, omne autem corruptibile est generabile, omne autem generabile habet principium, sequitur quod principium corruptibile habeat aliquod principium, et illud, aliud, et sic in infinitum. Quod est impossibile, ut ostensum est supra in secundo. He accordingly asks (916) whether or not, if there is some separate substance and principle such as we are now seeking, it is the principle of all things, corruptible and incorruptible. Now if there is such a principle of all things, the question arises why some of the things which come from the same principle are eternal and some ire not. But if there is one principle for corruptible things and another for incorruptible ones, there remains the question why, if the principle is eternal the things coming from it are not themselves eternal. But if the principle of things is corruptible, and every corruptible thing is capable of being generated, and everything capable of being generated has a principle, it follows that the corruptible principle will have a principle, and that this will have another, and so on to infinity, as has been made clear above in Book II (153:C 301). Et veritas est, quod primum principium omnium est incorruptibile. Sed quaedam propter longe distare ab eo sunt corruptibilia, in quibus generatio et corruptio causatur per causam mediam quae est incorruptibilis secundum substantiam, variabilis secundum ubi. 2181. The truth of the matter is that the first principle of all things is incorruptible, and that some things are corruptible because of their great distance from that principle. These are the things in which generation and corruption are caused by an intermediate cause which is incorruptible as regards its substance but changeable as regards place. 2182. But on the other hand (917). Deinde cum dicit si autem quaerit quae sunt principia. Et primo quaerit de opinione illorum, qui posuerunt principia unum et ens, quia sunt maxime immobilia. Qualitercumque enim varietur aliquid, semper remanet unum et ens. Then he asks what the principles of things are. First, he examines the opinions of those men who claimed that the principles are unity and being because these are the most unchangeable. For no matter how a thing varies, it always remains one. Sed ex eorum opinione consurgit duplex dubitatio. Quarum una est, utrum unum et ens significat hoc aliquid et substantiam. Si enim non, non potuerunt esse separabilia et per se existentia. Sed talia principia quaerimus, quae sint perpetua et separata existentia. Si autem significat hoc aliquid et substantiam, sequitur quod omnia sint substantiae et nihil sit accidens: quia ens praedicatur de omnibus entibus, unum autem praedicatur de quibusdam. Quaedam vero sunt, quae in multitudine consistunt; de quibus vere manifestum est qualiter praedicetur unum. Hoc autem est falsum, quod omnia sint substantiae. Unde videtur quod unum et ens non significent substantiam. 2183. But the opinion of these men gives rise to two questions. The first is whether unity and being signify a particular thing, i.e., a substance; for, if they do not, they cannot be separable and exist of themselves. But we are looking for such principles which are eternal and exist separately. Yet if they do signify a particular thing or substance, it follows that all things are substances, and that nothing is an accident; for being is predicated of any existing thing at all, and unity is predicated of some. Now there are some things which involve multiplicity in their being, and the different ways in which unity is predicated truly of these is clear enough. But it is false that all things are substances; and therefore it seems that unity and being do not signify substance. 2184. Again, how can (918). Adhuc autem secunda dubitatio quam ponit talis est. Ponentes enim unum principium et substantiam, dicunt, quod ex uno et ex materia generatur numerus tamquam primus effectus. Et hunc, scilicet numerum, dicunt esse substantiam. Sed hoc non videtur esse verum. Quia, si numerus componitur ex uno et materia, oportet quod sit aliquid unum, sicut quod componitur ex anima et materia, oportet quod sit animatum. Sed quomodo dualitas et quilibet aliorum numerorum qui sunt compositi ex multis unitatibus, sunt unum, ut dicunt Platonici? Nec facile est assignare, ut possit dici esse derelictum ab eis, quasi de facili intelligibile. The second question or problem which he raises runs as follows: those who maintain that unity, or the unit, is the principle and substance of things say that number is generated as a first product from the unit and matter. And this, i.e., number, they call substance. But evidently this is not true, because, if a number is composed of the unit and matter, it must be something one, just as what is composed of a living principle and matter must be something living. But in what way is the number two or any other number, which is composed of units, one, as the Platonists claimed? This is not easy to explain, inasmuch as it can be said that they neglected to account for this as though it were easy to understand. 2185. But if someone (919). Secundo ibi, si vero prosequitur aliam opinionem de principiis. Quidam enim posuerunt lineas et habita, idest consequenter se habentia ad eas, scilicet superficies, esse principia, quia ponebant corpora componi ex superficiebus et superficies ex lineis. Sed manifestum est, quod huiusmodi non sunt substantiae separabiles et per se existentes, quia sunt quaedam decisiones et divisiones, lineae quidem superficierum, superficies corporum, puncta vero linearum. Et sunt etiam termini eorumdem: puncta, scilicet linearum, et sic de aliis. Punctum enim quod est in extremitate lineae, est terminus lineae. Quod autem significatur actu infra lineam, est decisio lineae. Et similiter est de linea ad superficiem, et de superficie ad corpus. Manifestum est autem, quod termini et decisiones sunt existentia in aliis sicut in subiectis. Unde non possunt esse separabilia. Et sic lineae et superficies non sunt principia. Second, he examines another opinion about the principles of things. For sonic claimed that “lines and what is derived from them,” namely, surfaces, are principles, because they held that bodies are composed of surfaces, and surfaces of lines. But it is clear that such things are not separate substances which exist of themselves; for such things are sections and divisions: lines being sections and divisions of surfaces, surfaces of bodies, and points of lines. They are also the limits of these things, i.e., points are the limits of lines, and so forth; for a point, which is at the extremity of a line, is the limit of a line. Now what is signified as actually within a line is a section of the line. The same thing is true of, a line in relation to a surface, and of a surface in relation to a body; for it is evident that limits and sections are entities which exist in other things as their subjects. Hence they cannot exist apart. Lines and surfaces, then, are not principles of things. 2186. Again, how are we (920). Deinde cum dicit adhuc quomodo inducit aliam rationem; dicens quod non potest opinari quod sit aliqua substantia unitatis et puncti, quia substantia non incipit esse nisi per generationem. Cum autem linea dividitur in actu, ipsa divisio est punctum. Then he introduces another argument. He says that it cannot be understood that the unit and the point have a substance, because substance begins to exist only by way of generation. But when a line is actually divided, the division itself is a point. Est autem harum quaestionum veritas, quod nec unum nec lineae et superficies sunt principia. 2187. The correct answer to these questions is that neither units nor lines nor surfaces are principles. 2188. There is also the problem (921). Tertio ibi, exhibet autem ponit quaestionem de uno et ente, et de dimensionibus, movet quaestionem de substantiis. Et primo quaerit utrum substantiae sint principia. Et videtur quod non: quia omnis scientia est universalium, et quaelibet scientia est talis universalis, idest alicuius subiecti universalis determinati. Sed substantia non est de numero universalium, sed magis est hoc aliquid separabile, idest per se existens. Et ita videtur quod de substantiis non sit scientia. Sed scientia est circa principia: ergo substantia non est principium. After the question about unity and being and dimensions he now raises the question about substances. First, he asks whether substances are principles. The answer seems to be that they are not; for every science is concerned with universals and with “such and such a universal,” i.e., some definite universal subject. Now a substance is not included among universals, but is rather a particular thing which exists of itself. Hence it seems that there is no science of substances. But a science is concerned with principles. Therefore substances are not principles. Et veritas est quod, licet universalia non per se existant, tamen naturas eorum quae per se subsistunt est considerare universaliter. Et secundum hoc accipiuntur genera et species in praedicamento substantiae, quae dicuntur secundae substantiae, de quibus est scientia. Quaedam etiam per se existentes sunt principia, quae, quia immateriales, pertinent ad intelligibilem cognitionem, licet excedant intellectus nostri comprehensionem. 2189. The truth is that, although universals do not exist of themselves, it is still necessary to consider universally the natures of things which subsist of themselves. Accordingly, genera and species, which are called second substances, are put in the category of substance; and of these there is scientific knowledge. And certain things which exist of themselves are principles; and these, because they are immaterial, pertain to intelligible knowledge, even though they surpass the comprehension of our intellect. 2190. Again, the question (922). Adhuc utrum secundo quaerit, utrum sit aliquod principium praeter synolon, idest praeter simul totum quod est compositum, aut non. Et exponit synolon quod est materia, et quod cum materia componitur. Si enim non sit aliquid praeter compositum ex materia et forma, quae autem sunt in materia dicuntur corruptibilia, sequitur quod nihil sit perpetuum. Et si est aliquid praeter compositum, hoc erit species et forma; et remanebit dubitatio in quibus forma separatur, et in quibus non. Manifestum est enim quod in quibusdam forma non separatur. Forma enim domus non separatur a materia. Unde et Platonici non posuerunt ideas rerum artificialium, quia formae rerum artificialium sunt actus, quae non possunt per se existere. Second, he asks whether or not there is any “principle apart from the concrete whole,” i.e., the natural whole or composite. He explains that by concrete whole he means matter, or the thing composed of matter. For if there is no principle apart from the composite of matter and form, and those principles which are said to be in matter are corruptible, it follows that nothing is eternal. And if there is some principle apart from the composite, it must be the specifying principle or form. Then the question arises in which cases the form is separate and in which it is not. For it is obvious that in some cases the form is not separate; the form of a house, for example, is not separate from matter. It was for this reason that the Platonists did not posit Ideas or Forms of artificial things, because the forms of such things are actualities which cannot exist of themselves. Et veritas est quod est aliquid praeter materiam, non tamen forma rerum sensibilium. 2191. The correct answer to this question is that there is some principle apart from matter, and this is not the form of sensible things. 2192. Again, there is (923). Deinde cum dicit adhuc utrum quaerit qualiter principia se habeant adinvicem; utrum scilicet omnium principia sint eadem numero, aut specie tantum. Si enim sint eadem numero, sequitur quod omnia sint eadem numero. Si autem non sunt eadem numero, oportebit quaerere causam diversitatis. He now asks how the principles of all things are related to one another: whether they are the same numerically or only specifically. For, if they are the same numerically, it follows that all things -are the same numerically. But if they are not the same numerically, this difference will have to be accounted for. Et veritas est quod, loquendo de principiis extrinsecis, unum numero sunt; cum id quod est primum principium omnium, sit agens et finis. Principia vero intrinseca, scilicet materia et forma, non sunt unum numero omnium, sed secundum analogiam, ut infra ostendetur. 2193. The truth is that, if one is speaking of the extrinsic principles of things, they are the same numerically, since the first principle of all things is an agent and final cause. But the intrinsic principles of things-matter and form-are not the same numerically but only analogically, as will be shown below (1049-54:C 2474-87).
LESSON 3 All Beings Reduced to Being and Unity
ARISTOTLE’S TEXT Chapter 3: 1060b 31-1061b 17 ἐπεὶ δ᾽ ἐστὶν ἡ τοῦ φιλοσόφου ἐπιστήμη τοῦ ὄντος ᾗ ὂν καθόλου καὶ οὐ κατὰ μέρος, τὸ δ᾽ ὂν πολλαχῶς καὶ οὐ καθ᾽ ἕνα λέγεται τρόπον: εἰ μὲν οὖν ὁμωνύμως κατὰ δὲ κοινὸν μηδέν, οὐκ ἔστιν ὑπὸ μίαν ἐπιστήμην (οὐ γὰρ ἓν γένος  τῶν τοιούτων), εἰ δὲ κατά τι κοινόν, εἴη ἂν ὑπὸ μίαν ἐπιστήμην. 924. Since the science of the philosopher treats of being as being in general and not of some part of it, and the term being is used in many senses and not merely in one, it follows that, if being is used equivocally and not with a common meaning, being does not fall under one science (for such terms do not have a common class). But if the term is used according to one common meaning, being will fall under one science. ἔοικε δὴ τὸν εἰρημένον λέγεσθαι τρόπον καθάπερ τό τε ἰατρικὸν καὶ ὑγιεινόν: καὶ γὰρ τούτων ἑκάτερον πολλαχῶς λέγομεν. [1061α]  λέγεται δὲ τοῦτον τὸν τρόπον ἕκαστον τῷ τὸ μὲν πρὸς τὴν ἰατρικὴν ἐπιστήμην ἀνάγεσθαί πως τὸ δὲ πρὸς ὑγίειαν τὸ δ᾽ ἄλλως, πρὸς ταὐτὸ δ᾽ ἕκαστον. ἰατρικὸς γὰρ λόγος καὶ μαχαίριον λέγεται τῷ τὸ μὲν ἀπὸ τῆς ἰατρικῆς  ἐπιστήμης εἶναι τὸ δὲ ταύτῃ χρήσιμον. ὁμοίως δὲ καὶ ὑγιεινόν: τὸ μὲν γὰρ ὅτι σημαντικὸν ὑγιείας τὸ δ᾽ ὅτι ποιητικόν. ὁ δ᾽ αὐτὸς τρόπος καὶ ἐπὶ τῶν λοιπῶν. τὸν αὐτὸν δὴ τρόπον καὶ τὸ ὂν ἅπαν λέγεται: τῷ γὰρ τοῦ ὄντος ᾗ ὂν πάθος ἢ ἕξις ἢ διάθεσις ἢ κίνησις ἢ τῶν ἄλλων τι τῶν τοιούτων  εἶναι λέγεται ἕκαστον αὐτῶν ὄν. 925. Therefore the term seems to be used in the way mentioned, like the terms medical and healthy; for each of these is used in many senses. Now the term is used in each of these ways because of some kind of reference. Thus the former is used in reference to the science of medicine; the latter, to health; and still another, to something else; yet in each case the term is referred to the same thing. For both a discussion and a knife are called medical: the one because it comes from the science of medicine, and the other because it is useful to it. The same is true of the term healthy; for one thing is called healthy because it is a sign of health, and another because it produces it. The same is true of other terms. Hence the same thing is true of every instance of being; for each thing is called a being because it is either a modification or a state or a disposition or a motion or something else of this kind which belongs to being as being. ἐπεὶ δὲ παντὸς τοῦ ὄντος πρὸς ἕν τι καὶ κοινὸν ἡ ἀναγωγὴ γίγνεται, καὶ τῶν ἐναντιώσεων ἑκάστη πρὸς τὰς πρώτας διαφορὰς καὶ ἐναντιώσεις ἀναχθήσεται τοῦ ὄντος, εἴτε πλῆθος καὶ ἓν εἴθ᾽ ὁμοιότης καὶ ἀνομοιότης αἱ πρῶται τοῦ ὄντος εἰσὶ διαφοραί, εἴτ᾽  ἄλλαι τινές: ἔστωσαν γὰρ αὗται τεθεωρημέναι. 926. And since every being is referred to something one and common, each of the contrarieties may also be referred to the primary differences and contrarieties of being, whether the primary differences are plurality and unity, likeness and unlikeness, or any others; for these have been considered (304). διαφέρει δ᾽ οὐδὲν τὴν τοῦ ὄντος ἀναγωγὴν πρὸς τὸ ὂν ἢ πρὸς τὸ ἓν γίγνεσθαι. καὶ γὰρ εἰ μὴ ταὐτὸν ἄλλο δ᾽ ἐστίν, ἀντιστρέφει γε: τό τε γὰρ ἓν καὶ ὄν πως, τό τε ὂν ἕν. 927. And it makes no difference whether an existing thing is referred to being or to unity. For even if they are not the same but different, they are nevertheless interchangeable; for what is one is somehow a being, and what is a being is somehow one. ἐπεὶ δ᾽ ἐστὶ τὰ ἐναντία πάντα τῆς αὐτῆς καὶ μιᾶς ἐπιστήμης θεωρῆσαι, λέγεται  δ᾽ ἕκαστον αὐτῶν κατὰ στέρησιν—καίτοι γ᾽ ἔνια ἀπορήσειέ τις ἂν πῶς λέγεται κατὰ στέρησιν, ὧν ἔστιν ἀνὰ μέσον τι, καθάπερ ἀδίκου καὶ δικαίου—περὶ πάντα δὴ τὰ τοιαῦτα τὴν στέρησιν δεῖ τιθέναι μὴ τοῦ ὅλου λόγου, τοῦ τελευταίου δὲ εἴδους: οἷον εἰ ἔστιν ὁ δίκαιος καθ᾽ ἕξιν τινὰ  πειθαρχικὸς τοῖς νόμοις, οὐ πάντως ὁ ἄδικος ἔσται τοῦ ὅλου στερούμενος λόγου, περὶ δὲ τὸ πείθεσθαι τοῖς νόμοις ἐκλείπων πῃ, καὶ ταύτῃ ἡ στέρησις ὑπάρξει αὐτῷ: τὸν αὐτὸν δὲ τρόπον καὶ ἐπὶ τῶν ἄλλων. 928. Now since it is the office of one and the same science to study all contraries, and one of each pair involves privation (though one might be puzzled how some contraries are predicated privatively, i.e., those which have an intermediate, as just and unjust), in all such cases it is necessary to hold that the privation of the one is not the privation of the whole notion of the other, but only of the last species. For example, if a man is just because of some habitual tendency to obey the laws, the unjust man will not always be deprived of the perfection completely but will fail to obey the laws in some respect; and in this respect privation will belong to him. The same holds true in other cases. καθάπερ δ᾽ ὁ μαθηματικὸς περὶ τὰ ἐξ ἀφαιρέσεως τὴν θεωρίαν ποιεῖται (περιελὼν γὰρ πάντα  τὰ αἰσθητὰ θεωρεῖ, οἷον βάρος καὶ κουφότητα καὶ σκληρότητα καὶ τοὐναντίον, ἔτι δὲ καὶ θερμότητα καὶ ψυχρότητα καὶ τὰς ἄλλας αἰσθητὰς ἐναντιώσεις, μόνον δὲ καταλείπει τὸ ποσὸν καὶ συνεχές, τῶν μὲν ἐφ᾽ ἓν τῶν δ᾽ ἐπὶ δύο τῶν δ᾽ ἐπὶ τρία, καὶ τὰ πάθη τὰ τούτων ᾗ ποσά ἐστι  καὶ συνεχῆ, καὶ οὐ καθ᾽ ἕτερόν τι θεωρεῖ, καὶ τῶν μὲν τὰς πρὸς ἄλληλα θέσεις σκοπεῖ καὶ τὰ ταύταις ὑπάρχοντα, [1061β]  τῶν δὲ τὰς συμμετρίας καὶ ἀσυμμετρίας, τῶν δὲ τοὺς λόγους, ἀλλ᾽ ὅμως μίαν πάντων καὶ τὴν αὐτὴν τίθεμεν ἐπιστήμην τὴν γεωμετρικήν), τὸν αὐτὸν δὴ τρόπον ἔχει καὶ περὶ τὸ ὄν. 929. Now the mathematician in a sense studies things which are gotten by taking something away; for he speculates by removing from things all sensible qualities, such as heaviness and lightness, hardness and its contrary, and also heat and cold and other sensible contrarieties, and leaves only the quantified and the continuous (some things being such in one, some in two, and some in three dimensions). And he studies the properties of the quantified and the continuous as such and not in any other respect. And of some he considers the relative positions and attributes, and of others the commensurability and incommensurability, and of others the ratios; yet we claim that there is only one science of all these things, namely, geometry. The same holds true of being. τὰ γὰρ τούτῳ συμβεβηκότα καθ᾽ ὅσον ἐστὶν ὄν, καὶ  τὰς ἐναντιώσεις αὐτοῦ ᾗ ὄν, οὐκ ἄλλης ἐπιστήμης ἢ φιλοσοφίας θεωρῆσαι. τῇ φυσικῇ μὲν γὰρ οὐχ ᾗ ὄντα, μᾶλλον δ᾽ ᾗ κινήσεως μετέχει, τὴν θεωρίαν τις ἀπονείμειεν ἄν: ἥ γε μὴν διαλεκτικὴ καὶ ἡ σοφιστικὴ τῶν συμβεβηκότων μέν εἰσι τοῖς οὖσιν, οὐχ ᾗ δ᾽ ὄντα οὐδὲ περὶ τὸ ὂν αὐτὸ καθ᾽ ὅσον  ὄν ἐστιν: ὥστε λείπεται τὸν φιλοσόφον, καθ᾽ ὅσον ὄντ᾽ ἐστίν, εἶναι περὶ τὰ λεχθέντα θεωρητικόν. 930. For an investigation of the attributes of being as being, and of the contrarieties of being as being, belong to no other science than [first] philosophy; for one would not assign to the philosophy of nature the study of things insofar as they are beings but rather insofar as they participate in motion. For dialectics and sophistry are concerned with the accidents of existing things, but not as beings, nor do they deal with being as being. It follows, then, that it is the philosopher who speculates about the things which we have mentioned, insofar as they are beings. ἐπεὶ δὲ τό τε ὂν ἅπαν καθ᾽ ἕν τι καὶ κοινὸν λέγεται πολλαχῶς λεγόμενον, καὶ τἀναντία τὸν αὐτὸν τρόπον (εἰς τὰς πρώτας γὰρ ἐναντιώσεις καὶ διαφορὰς τοῦ ὄντος ἀνάγεται), τὰ δὲ τοιαῦτα δυνατὸν  ὑπὸ μίαν ἐπιστήμην εἶναι, διαλύοιτ᾽ ἂν ἡ κατ᾽ ἀρχὰς ἀπορία λεχθεῖσα, λέγω δ᾽ ἐν ᾗ διηπορεῖτο πῶς ἔσται πολλῶν καὶ διαφόρων ὄντων τῷ γένει μία τις ἐπιστήμη. 931. And since every being is referred to some one common meaning, which is used in many senses, and the same applies to contraries (for they are referred to the primary differences and contrarieties of being), and such things can fall under one science, the difficulty which was stated at the beginning of this work (900-904) is solved in this way. I mean the question how there can be one science of things which are many and different in genus. COMMENTARY Postquam movit quaestiones, hic incipit colligere ea quae pertinent ad considerationem huius scientiae; et dividitur in duas partes. In prima ostendit de quibus haec scientia considerat. In secunda comparat hanc scientiam ad alias, ibi, omnis autem scientia. 2194. Having raised the foregoing questions, Aristotle now begins to assemble the things that belong to the consideration of this science. This is divided into two parts. In the first (924:C 2194) he indicates the things which this science considers. In the second (956:C 2247) he compares this science with the others (“Every science”). Prima dividitur in duas partes. In prima ostendit quod ad hanc scientiam pertinet considerare de omnibus entibus. In secunda, quod ad hanc pertinet considerare de principiis demonstrativis, ibi, quoniam autem. The first part is divided into two members. First, he shows that it is the office of this science to consider all beings; and second (932:C 2206), that it has to consider the principles of demonstration (“And since the mathematician”). Circa primum duo facit. Primo ostendit quod omnium est reductio aliqualiter ad unum. Secundo ostendit quod de omnibus reductis ad unum est consideratio huius scientiae, ibi, quemadmodum autem. In considering the first part he does two things. First, he shows that all things are somehow reduced to one. Second (929:C 2202), he shows that the study of this science extends to all things insofar as they are somehow reduced to some one thing (“Now the mathematician”). Circa primum duo facit. Primo ostendit, quod necessarium est ad praesentem considerationem inquirere, utrum omnia reducantur aliqualiter ad unum; dicens, quod quia scientia philosophiae est de ente inquantum est ens, ita quod considerat de ente secundum universalem rationem entis, et non secundum rationem entis alicuius particularis; cum ens multipliciter et non uno modo dicatur, si ista multiplicitas esset pura aequivocatio, quae non diceretur secundum aliquid commune, non caderent omnia entia sub una scientia, quia non reducerentur aliquo modo ad unum genus. Oportet autem unam scientiam esse unius generis. Sed si ista multiplicitas habeat aliquod commune, omnia entia possunt esse sub una scientia. Unde ad quaestionem qua quaerebatur, utrum ista scientia sit una, cum sit de pluribus et diversis, necessarium est considerare, utrum omnia entia reducantur ad aliquid unum, vel non. In treating the first part he does two things. First, he shows that in view of the goal of our present study it is necessary to ask whether all things are somehow reduced to one. He says that, since the science of philosophy treats being as being in such a way as to consider being in terms of its universal character and not merely in terms of the intelligible character of any particular being, and since the term being is used in many senses and not just in one, if the many senses of being were purely equivocal without any common meaning, not all beings would fall under one science, because they would not in any way be reduced to one common class. And one science must deal with one class of things. But if the many senses of being have one common meaning, all beings can then fall under one science. Hence, in order to answer the question that was raised as to whether this science is one even though it treats many different things, we must consider whether or not all beings are reduced to some one thing. 2195. Therefore the term (925). Videtur itaque ostendit quod omnia reducuntur ad aliquid unum. Et circa hoc duo facit. Primo ostendit propositum. Secundo manifestat quoddam quod poterat esse dubium, ibi, quoniam autem fiunt. Here he shows that all things are reduced to some one thing. In treating this he does two things. First (925:C 2195), he explains his thesis. Second (928:C 2200), he clears up a point that might present a difficulty (“Now since”). Prima dividitur in duas. In prima ostendit quod omnium reductio est ad unum. In secunda ostendit ad quod omnia reducantur, ibi, differt autem nihil. The first is divided into two parts. In the first he shows that all things are reduced to one. In the second (92-7:C 2197), he explains what this one thing is to which all things are reduced (“And it makes no difference”) - Circa primum duo facit. Primo ostendit quod omnia entia reducuntur ad aliquod unum commune ens. Secundo, quod omnes contrarietates reducuntur ad unam contrarietatem, ibi, quoniam autem contraria omnia et cetera. In regard to the first part he does two things. First, he shows that all beings are reduced to one common being; and second (926:C 2198), that all contrarieties are reduced to one contrariety (“And since every”). Dicit ergo primo, quod ens videtur dici modo praedicto, scilicet quod dicatur multipliciter secundum aliquid commune. Quod manifestat per duo exempla, scilicet medicativum et salubre. He accordingly says, first (925), that the term being is used in the way mentioned above; i.e., it is used of many things according to some common meaning. He makes this clear by means of two examples: the terms medical and healthy. Utrumque enim eorum dicitur secundum diversos modos, tamen per reductionem ad aliquod unum. Medicativum enim aliquid dicitur multipliciter, secundum quod hoc refertur sic ad medicamentum, et id aliter. Et similiter salubre dicitur multipliciter secundum quod hoc refertur sic ad sanitatem, et id aliter. Utrobique tamen idem est ad quod fit reductio licet diversis modis. Sicut sermo dicitur medicans, eo quod est a scientia medicativa. Cultellus autem dicitur medicativus, eo quod est utilis eidem scientiae sicut instrumentum. Et similiter hoc dicitur salubre, quia est significativum sanitatis, sicut urina. Hoc autem, quia est factivum sanitatis, sicut potio medicinalis. Et similiter est in aliis quae hoc eodem modo dicuntur. 2196. For both of these terms are used variously, yet in such a way that they are reduced or referred to some one thing. The term medical is used in many ways inasmuch as it is referred in one sense to a medicine and in another to something else. And similarly the term healthy is used in many ways inasmuch as it is referred in one sense to health and in another to something else. Yet in both cases the various senses have reference to the same thing, though in different ways. For example, a discussion is called medical because it comes from the science of medicine, and a knife is called medical because it is an instrument that is used by the same science. Similarly one thing is called healthy because it is a sign of health, as urine, and another because it causes health, as a medication. The same applies to other terms which are used in a similar way. Manifestum est enim quod quae sic dicuntur, media sunt inter univoca et aequivoca. In univocis enim nomen unum praedicatur de diversis secundum rationem totaliter eamdem; sicut animal de equo et de bove dictum, significat substantiam animatam sensibilem. In aequivocis vero idem nomen praedicatur de diversis secundum rationem totaliter diversam. Sicut patet de hoc nomine, canis, prout dicitur de stella, et quadam specie animalis. In his vero quae praedicto modo dicuntur, idem nomen de diversis praedicatur secundum rationem partim eamdem, partim diversam. Diversam quidem quantum ad diversos modos relationis. Eamdem vero quantum ad id ad quod fit relatio. Esse enim significativum, et esse effectivum, diversum est. Sed sanitas una est. Et propter hoc huiusmodi dicuntur analoga, quia proportionantur ad unum. Et similiter est de multiplicitate entis. Nam ens simpliciter, dicitur id quod in se habet esse, scilicet substantia. Alia vero dicuntur entia, quia sunt huius quod per se est, vel passio, vel habitus, vel aliquid huiusmodi. Non enim qualitas dicitur ens, quia ipsa habeat esse, sed per eam substantia dicitur esse disposita. Et similiter est de aliis accidentibus. Et propter hoc dicit quod sunt entis. Et sic patet quod multiplicitas entis habet aliquid commune, ad quod fit reductio. 2197. It is evident that terms which are used in this way are midway between univocal and equivocal terms. In the case of univocity one term is predicated of different things with absolutely one and the same meaning; for example, the term animal, which is predicated of a horse and of an ox, signifies a living, sensory substance. In the case of equivocity the same term is predicated of various things with an entirely different meaning. This is clear in the case of the term dog, inasmuch as it is predicated both of a constellation and of a certain species of animal. But in the case of those things which are spoken of in the way mentioned previously, the same term is predicated of various things with a meaning that is partly the same and partly different—different regarding the different modes of relation, and the same regarding that to which it is related; for to be a sign of something and to be a cause of something are different, but health is one. Terms of this kind, then, are predicated analogously, because they have a proportion to one thing. The same holds true also of the many ways in which the term being is used; for being in an unqualified sense means what exists of itself, namely, substance; but other things are called beings because they belong to what exists of itself, namely, modifications or states or anything else of this kind. For a quality is called a being, not because it has an act of existence, but because a substance is said to be disposed by it. It is the same with other accidents. This is why he says that they belong to a being (or are of a being). It is evident, then, that the many senses of the term being have a common meaning to which they are reduced. 2198. And since (926). Deinde cum dicit quoniam autem ostendit quod reductio omnium contrarietatum fit ad unam primam. Quia enim omnium entium fit reductio ad aliquid unum commune, contrarietates autem entium, quae sunt oppositae differentiae, per se consequuntur entia, necesse est quod contrarietates reducantur ad aliquam primam contrarietatem quaecumque sit illa; sive pluralitas et unum, sive similitudo et dissimilitudo, sive quaecumque aliae sint primae differentiae entis. Et huiusmodi contrarietates debent considerari in scientia quae determinat de entibus. Next he shows that all contrarieties are reduced to one first contrariety. Since all beings are reduced to one common meaning, and the contrarieties of beings, which are opposite differences, are in themselves a natural consequence of beings, it follows that contrarieties must be reduced to some primary contrariety, whatever it may be, whether it is plurality and unity, likeness and unlikeness, or whatever else are primary differences of beings. And contrarieties of this kind have to be considered in the science which establishes what is true about beings. 2199. And it makes (927). Deinde cum dicit differt autem ostendit quid sit illud commune ad quod fit reductio omnium entium; et dicit quod nihil differt utrum fiat reductio ad ens vel unum. Si enim dicatur quod ens et unum non sunt idem, sed differunt ratione secundum quod unum addit indivisibilitatem supra ens; tamen manifestum est quod adinvicem convertuntur; quia omne unum est aliqualiter ens, et omne ens est aliqualiter unum. Et sicut substantia est proprie et per se ens, ita proprie et per se unum. Quomodo autem unum ad ens se habeat, supra dictum est in quarto et decimo. Then he indicates what this common thing is to which all things are reduced. He says that it makes no difference whether things are reduced to being or to unity; for if it is said that being and unity are not the same conceptually but differ inasmuch as unity adds the note of indivisibility to being, none the less it is evident that they are interchangeable; for everything that is one is somehow a being, and everything that is a being is somehow one; because, just as a substance is a being properly and of itself, so too it is one properly and of itself. The way in which unity is related to being has been explained above in Book IV (301-04:C 548-60) and in Book X (832:C 1974). 2200. Now since (928). Deinde cum dicit quoniam autem removet quamdam dubitationem; dicens, quod omnia contraria pertinent ad considerationem unius scientiae. Et huius ratio potissima videtur esse, quia in omnibus contrariis unum dicitur secundum privationem, quod cognoscitur ex suo opposito. Remanet dubitatio quomodo contraria dicuntur secundum privationem inter quae est medium, cum in oppositis privative non sit medium. Then he removes a difficulty. He says that, since all contraries are investigated by one science (and the most cogent reason seems to be that in each pair of contraries one contrary is used privatively, and this is known from its opposite term), the difficulty arises how contraries which have an intermediate can be predicated as privations, since in the case of opposites which are privatively opposed there is no intermediate. Et ad hoc respondendum est quod in talibus contrariis, alterum contrariorum non ponitur privatio quasi tollens totam rationem alterius oppositi; sed quia est privatio ultimae speciei; inquantum scilicet tollit completam rationem totius speciei. Sicut si aliquis dicitur iustus, eo quod est obediens legibus secundum habitum aliquem, non semper dicetur iniustus eo quod sit privatus tota ratione iustitiae, quod in nullo obediat legibus; sed quia persuasus est, ut in aliis deficiat ab obedientia legis. Et sic inest ei privatio iustitiae, inquantum deficit a perfecta ratione iustitiae. Et propter hoc potest habere medium; quia non omnis qui caret iustitia, totaliter iustitia privatur, sed aliqua parte. Et hoc est medium quod diversificatur secundum magis et minus. Et similiter est in aliis contrariis. Sed privatio visus dicitur in hoc, quod totaliter aliquis caret visu. Et ideo inter caecitatem et visionem non est medium. 2201. The answer to this must be that in the case of such contraries one opposite is not posited as a privation removing all the intelligible notes of the other but as the privation of the last species inasmuch as it detracts from the complete intelligible constitution of the whole species. For instance, if someone is said to be just because he habitually obeys the laws, he will not always be said to be unjust, as if he were deprived of the entire notion of justice, which would be the case if he obeyed the laws in no way—but rather because he fails to obey them in some respects. Hence the privation of justice will be found in him to the extent that he falls short of the perfection of justice. It is for this reason that he can be in an intermediate state, because not everyone who lacks justice is completely deprived of it but only of some part of it. And this intermediate state is one that differs in degree. The same holds true of other contraries. The privation of sight, however, is said to consist in the total lack of sight, and therefore there is no intermediate state between blindness and sight. 2202. Now the mathematician (929). Deinde cum dicit quemadmodum autem ostendit quod de omnibus entibus reductis ad unum, sit consideratio huius scientiae. Et circa hoc tria facit. Primo exemplo geometriae ostendit, quod ad unam scientiam pertinet considerare omnia quae reducuntur ad ens; dicens quod sicut mathematica habet considerationem circa ea quae sunt ex ablatione, idest circa abstracta, quae quidem abstractio fit non ex hoc quod ponat ea de quibus considerat in rerum natura esse separata a sensibilibus, sed quia considerat ea absque consideratione sensibilium. Speculatur enim mathematica auferens a sua consideratione omnia sensibilia, sicut levitatem, gravitatem, duritiem, mollitiem, caliditatem et frigiditatem, et omnes alias sensibiles contrarietates, et derelinquit in sua consideratione solummodo quantum et continuum, sive sit continuum ad unam tantum dimensionem, ut linea, sive ad duas, ut superficies, sive ad tres, ut corpus; et considerat primo passiones horum inquantum sunt continua, et non secundum aliquid aliud. Non enim considerat passiones superficiei secundum quod est superficies lignea vel lapidea. Et similiter rationes eorum adinvicem. Considerando figuras etiam considerat accidentia quae existunt in figuris, et considerat mensurationes et incommensurationes quantitatum, ut patet in decimo Euclidis, et rationes, idest proportiones earum, ut patet in quinto. Sed tamen de omnibus his est una scientia quae est geometria. Here he shows that the investigations of this science extend to all beings insofar as they are reduced to one thing. In treating this he makes a tripartite division. First, he shows by an example from geometry that it is the office of one science to consider all things which are reduced to being. He says that the science of mathematics studies “those things which are gotten by taking something away,” i.e., abstract things. It makes this abstraction, not because it supposes that the things which it considers are separate in reality from sensible things, but because it considers them without considering sensible qualities. For the science of mathematics carries on its investigations by removing from the scope of its study all sensible qualities, such as lightness, heaviness, hardness, softness, heat and cold, and all other sensible qualities, and retains as its object of study only the quantified and the continuous, whether it is continuous in one dimension, as a line, or in two, as a surface, or in three, as a body. And it is primarily interested in the properties of these inasmuch as they are continuous and not in any other respect; for it does not consider the properties of surface inasmuch as it is the surface of wood or of stone. Similarly it considers the relationships between its objects. And in considering figures it also studies their accidents, and how quantities are commensurable or incommensurable, as is clear in Book X of Euclid, “and their ratios,” or proportions, as is clear in Book V of the same work. Yet there is one science of all these things, and this is geometry. Et sicut est de mathematico, ita est de philosopho qui considerat ens, et praetermittit considerare omnia particularia entia, et considerat ea tantum quae pertinent ad ens commune; quae licet sint multa, tamen, de omnibus est una scientia, inquantum scilicet reducuntur omnia in unum, ut dictum est. 2203. Now what was true for the mathematician is also true for the philosopher who studies being. He passes over a study of all particular beings and considers them only inasmuch as they pertain to being in general. And though these are many, there is nevertheless a single science of all of them inasmuch as all are reduced to one thing, as has been pointed out. 2204. For an investigation (930). Secundo ibi, huic enim ostendit cuius scientiae sit praedicta considerare: dicens, quod considerare accidentia entis inquantum est ens, non est alterius scientiae, quam huius philosophiae. Si enim esset alterius, maxime videretur esse naturalis scientiae et dialecticae, quae videntur maxime inter scientias esse communes. Naturalis quidem secundum opinionem antiquorum, qui non ponebant alias substantias, nisi sensibiles: sic enim sequeretur, quod ad naturalem pertineret considerare de omnibus substantiis, et per consequens de omnibus entibus, quae reducuntur ad substantiam. Dialectica autem videtur esse communis, et similiter sophistica, quia considerant quaedam accidentia entibus, scilicet intentiones, et rationes generis et speciei, et alia huiusmodi. Unde relinquitur quod philosophus consideret praedicta inquantum sunt accidentia entis. Second, he indicates what science it is that considers the above-mentioned things. He says that the study of the attributes of being as being does not belong to any other science but only to this branch of philosophy. If it did belong to another science, it would mostly seem to belong to the philosophy of nature or to dialectics, which seemingly are the most common of the sciences. Now according to the opinion of the ancient philosophers who did not posit any substances other than sensible ones, it would seem to be the philosophy of nature that is the common science. In this way it would follow that it is the function of the philosophy of nature to consider all substances, and consequently all beings, which are reduced to substance.-But dialectics would seem to be the common science, and also sophistry, because these consider certain accidents of beings, namely, intentions and the notions of genus and species and the like. It follows, then, that it is the philosopher who has to consider the above-mentioned things, inasmuch as they are accidents of being. 2205. And since every (931). Tertio ibi, quoniam autem ex dictis infert conclusionem principaliter intentam; dicens quod quia ens dicitur multipliciter secundum aliquid unum, et omnia contraria reducuntur ad primam contrarietatem entis, et talia sic reducta in unum possunt cadere sub una scientia, ut dictum est; per hoc solvitur dubitatio prius mota, utrum scilicet multorum differentium genere sit una scientia. Third, from what has been said, he draws his thesis as his chief conclusion. He says that, since being is used in many senses in reference to some one thing, and since all contrarieties are referred to the first contrariety of being, such things organized in this way can fall under one science, as has been pointed out. Thus he solves the question previously raised: whether there is one science of things which are many and generically different.
LESSON 4 This Science Considers the Principles of Demonstration
ARISTOTLE’S TEXT Chapter 4: 1061b 17-1061b 33 ἐπεὶ δὲ καὶ ὁ μαθηματικὸς χρῆται τοῖς κοινοῖς ἰδίως, καὶ τὰς τούτων ἀρχὰς ἂν εἴη θεωρῆσαι τῆς πρώτης φιλοσοφίας. ὅτι γὰρ  ἀπὸ τῶν ἴσων ἴσων ἀφαιρεθέντων ἴσα τὰ λειπόμενα, κοινὸν μέν ἐστιν ἐπὶ πάντων τῶν ποσῶν, ἡ μαθηματικὴ δ᾽ ἀπολαβοῦσα περί τι μέρος τῆς οἰκείας ὕλης ποιεῖται τὴν θεωρίαν, οἷον περὶ γραμμὰς ἢ γωνίας ἢ ἀριθμοὺς ἢ τῶν λοιπῶν τι ποσῶν, οὐχ ᾗ δ᾽ ὄντα ἀλλ᾽ ᾗ συνεχὲς αὐτῶν ἕκαστον ἐφ᾽  ἓν ἢ δύο ἢ τρία: ἡ δὲ φιλοσοφία περὶ τῶν ἐν μέρει μέν, ᾗ τούτων ἑκάστῳ τι συμβέβηκεν, οὐ σκοπεῖ, περὶ τὸ ὂν δέ, ᾗ ὂν τῶν τοιούτων ἕκαστον, θεωρεῖ. 932. And since the mathematician uses the common axioms in a particular way, it must be the office of first philosophy to study principles of this kind. For the axiom or principle that “when equals are subtracted from equals the remainders are equal” is common to all quantities. But mathematics, assuming [principles of this kind], makes a study of some part of the quantified as its proper subject matter, for example, lines or angles or number or some of the other kinds of quantity. Yet it does not consider them inasmuch as they are beings but inasmuch as each is continuous in one, two or three dimensions. Philosophy, however, does not investigate those things which are in some part of matter insofar as each has some attribute, but it considers each of these particular things from the standpoint of being insofar as it is being. τὸν αὐτὸν δ᾽ ἔχει τρόπον καὶ περὶ τὴν φυσικὴν ἐπιστήμην τῇ μαθηματικῇ: τὰ συμβεβηκότα γὰρ ἡ φυσικὴ καὶ τὰς ἀρχὰς θεωρεῖ τὰς τῶν ὄντων  ᾗ κινούμενα καὶ οὐχ ᾗ ὄντα (τὴν δὲ πρώτην εἰρήκαμεν ἐπιστήμην τούτων εἶναι καθ᾽ ὅσον ὄντα τὰ ὑποκείμενά ἐστιν, ἀλλ᾽ οὐχ ᾗ ἕτερόν τι): διὸ καὶ ταύτην καὶ τὴν μαθηματικὴν ἐπιστήμην μέρη τῆς σοφίας εἶναι θετέον. 933. Now what applies in the case of the science of mathematics is also true of the philosophy of nature; for the philosophy of nature studies the attributes and principles of beings inasmuch as they are moved, not inasmuch as they are beings. But, as we have said, the primary science considers these attributes and principles insofar as their subjects are beings, and not in any other respect. For this reason it is necessary to hold that this science and the science of mathematics are parts of wisdom (319-23; 900-01). COMMENTARY Postquam philosophus ostendit quomodo consideratio huius scientiae est circa entia, et ea quae consequuntur ens inquantum huiusmodi; hic ostendit quomodo consideratio huius scientiae est de primis principiis demonstrationis. 2206. Having shown how the investigations of this science are concerned with beings and with the attributes which belong to being as being, the Philosopher now shows how the investigations of this science are concerned with the first principles of demonstration. Et dividitur in duas partes. In prima ostendit quod ad hanc scientiam pertinet considerare de his. In secunda determinat de quodam principio demonstrationis quod est inter alia primum, ibi, est autem quoddam et cetera. This is divided into two parts. In the first (932:C 2206) he shows that it is the office of this science to consider these first principles of demonstration. In the second (934:C 2211) he draws his conclusions about one principle of demonstration which is prior to the others (“There is a principle”). Circa primum duo facit. Primo ostendit propositum ex consideratione scientiae mathematicae. Secundo ex consideratione scientiae naturalis, ibi, eodem autem. In regard to the first he does two things. First (932:C 2206), he clarifies his thesis by considering the science of mathematics; and second (933:C 2209), by considering the philosophy of nature (“Now what applies”). Utitur autem in prima parte tali ratione. Quaecumque communia a scientiis particularibus accipiuntur particulariter, et non secundum quod sunt in sua communitate, pertinent ad considerationem huius scientiae. Sed prima principia demonstrationis accipiuntur a mathematica et ab aliis particularibus scientiis particulariter tantum: ergo eorum consideratio secundum quod sunt communia, pertinet ad hanc scientiam, quae considerat de ente inquantum est ens. In the first part he uses the following argument: all the common axioms which are used by the particular sciences in a way peculiar to themselves and not in their common aspect belong to the consideration of this science. But the first principles of demonstration are used by the science of mathematics and by other particular sciences in a way peculiar to themselves. Therefore an investigation of these principles insofar as they are common belongs to the science which considers being as being. Dicit ergo quod mathematicus utitur principiis communibus proprie, idest secundum quod appropriantur suae materiae. Oportet autem quod ad primam philosophiam pertineat considerare principia huiusmodi secundum suam communitatem. Sic enim accepta sunt principia suiipsorum secundum quod sunt alicui materiae particulari appropriata. Et hoc quod dixerat manifestat per exemplum. 2207. He accordingly says that, since the mathematician uses “the common axioms in a particular way,” i.e., insofar as they are adapted to his subject matter, it must be the function of first philosophy to consider such principles in their common aspect. For these principles are taken as principles of the sciences insofar as they are adapted to some particular subject matter. He clarifies his statement by an example. Nam hoc principium: si ab aequalibus aequalia demas, quae relinquuntur aequalia sunt, est commune in omnibus quantis, in quibus inveniuntur aequale et inaequale. Sed mathematica assumunt huiusmodi principia ad propriam considerationem circa aliquam partem quanti, quae est materia sibi conveniens. Non est enim aliqua mathematica scientia, quae consideret ea quae sunt quantitatis communia, inquantum est quantitas. Hoc enim est primae philosophiae. Sed considerant mathematicae scientiae ea quae sunt huius vel illius quantitatis, sicut arithmetica ea quae sunt numeri, et geometria ea quae sunt magnitudinis. Unde arithmeticus accipit praedictum principium, secundum quod pertinet ad numeros tantum; geometra autem secundum quod pertinet ad lineas vel ad angulos. Non autem considerat geometra hoc principium circa entia inquantum sunt entia; sed circa ens inquantum est continuum, vel secundum unam dimensionem ut linea, vel secundum duas ut superficies, vel secundum tres ut corpus. Sed philosophia prima non intendit de partibus entis inquantum aliquid accidit unicuique eorum; sed cum speculatur unumquodque communium talium, speculatur circa ens inquantum est ens. 2208. The principle that “when equals are subtracted from equals the remainders are equal” is common to all instances of quantity which admit of equality and inequality. But the science of mathematics presupposes principles of this kind in order to make a special study of that part of quantity which constitutes its proper subject matter; for there is no mathematical science which considers the attributes common to quantity as quantity, because this is the work of first philosophy. The mathematical sciences rather consider those attributes which belong to this or to that quantity; for example, arithmetic considers the attributes that belong to number, and geometry considers those that belong to continuous quantity. Thus the arithmetician uses the above-mentioned principle only inasmuch as it has to do with numbers, and the geometer uses it inasmuch as it has to do with lines and with angles. The geometer, however, does not consider this principle inasmuch as it relates to beings as beings but inasmuch as it relates to being as continuous, whether it is continuous in one dimension, as a line; or in two, as a surface; or in three, as a body. But first philosophy does not study the parts of being inasmuch as each has certain accidents; but when it studies each of these common attributes, it studies being as being. 2209. Now what applies (933). Deinde cum dicit eodem autem ostendit idem ex consideratione naturalis scientiae; dicens, quod eodem modo se habet naturalis scientia quantum ad hoc sicut et mathematica; quia naturalis scientia speculatur accidentia entium, et principia, non inquantum sunt entia, sed inquantum sunt mota. Sed prima scientia est de his secundum quod sunt entia, et non secundum aliquid aliud. Et ideo naturalem scientiam et mathematicam oportet partes esse primae philosophiae, sicut particularis scientia pars dicitur esse universalis. Then he makes the same thing clear by considering the philosophy of nature. He says that what applies in the case of the science of mathematics is also true of the philosophy of nature; for while the philosophy of nature studies the attributes and principles of beings, it does not consider beings as beings but as mobile. The first science, on the other hand, deals with these inasmuch as they are being, and not in any other respect. Hence, the philosophy of nature and the science of mathematics must be parts of first philosophy, just as any particular science is said to be a part of a universal science. Quod autem huiusmodi principia communia pertineant ad considerationem primae philosophiae, huius ratio est quia cum omnes primae propositiones per se sint, quorum praedicata sunt de ratione subiectorum; ad hoc quod sint per se notae quantum ad omnes, oportet quod subiecta et praedicata sint nota omnibus. Huiusmodi autem sunt communia, quae in omnium conceptione cadunt; ut ens et non ens, et totum et pars, aequale et inaequale, idem et diversum, et similia quae sunt de consideratione philosophi primi. Unde oportet, quod propositiones communes, quae ex huiusmodi terminis constituuntur, sint principaliter de consideratione philosophi primi. 2210. The reason why common principles of this kind belong to the consideration of first philosophy is this: since all first self-evident propositions are those of which the predicate is included in the definition of the subject, then in order that propositions may be self-evident to all, it is necessary that their subjects and predicates should be known to all. Common notions of this type are those which are conceived by all men, as being and non-being, whole and part, equal and unequal, same and different, and so on. But these belong to the consideration of first philosophy; and therefore common propositions composed of such terms must belong chiefly to the consideration of first philosophy.
LESSON 5 The Principle of Non-Contradiction
ARISTOTLE’S TEXT Chapters 5 & 6: 1061b 34-1062b 19 ἔστι δέ τις ἐν τοῖς οὖσιν ἀρχὴ περὶ ἣν οὐκ ἔστι διεψεῦσθαι,  τοὐναντίον δὲ ἀναγκαῖον ἀεὶ ποιεῖν, λέγω δὲ ἀληθεύειν, οἷον ὅτι οὐκ ἐνδέχεται τὸ αὐτὸ καθ᾽ ἕνα καὶ τὸν αὐτὸν χρόνον εἶναι καὶ μὴ εἶναι, [1062α]  καὶ τἆλλα τὰ τοῦτον αὑτοῖς ἀντικείμενα τὸν τρόπον. 934. There is a principle in existing things about which it is impossible to make a mistake, but of which one must always do the contrary, I mean acknowledge it as true, namely, that the same thing cannot both be and not be at one and the same time; and the same is also true of other things which are opposed in this way (326-328). καὶ περὶ τῶν τοιούτων ἁπλῶς μὲν οὐκ ἔστιν ἀπόδειξις, πρὸς τόνδε δὲ ἔστιν: οὐ γὰρ ἔστιν ἐκ πιστοτέρας ἀρχῆς αὐτοῦ τούτου ποιήσασθαι συλλογισμόν, δεῖ δέ γ᾽  εἴπερ ἔσται τὸ ἁπλῶς ἀποδεδεῖχθαι. 935. And while there is no demonstration in the strict sense of such principles, one may employ an argument ad hominem; for it is impossible to construct a syllogism from a more certain principle than this one. But this would be necessary if there were demonstration of it in the strict sense (329-330). πρὸς δὲ τὸν λέγοντα τὰς ἀντικειμένας φάσεις τῷ δεικνύντι διότι ψεῦδος ληπτέον τι τοιοῦτον ὃ ταὐτὸ μὲν ἔσται τῷ μὴ ἐνδέχεσθαι ταὐτὸ εἶναι καὶ μὴ εἶναι καθ᾽ ἕνα καὶ τὸν αὐτὸν χρόνον, μὴ δόξει δ᾽ εἶναι ταὐτόν: οὕτω γὰρ μόνως ἂν ἀποδειχθείη πρὸς τὸν  φάσκοντα ἐνδέχεσθαι τὰς ἀντικειμένας φάσεις ἀληθεύεσθαι κατὰ τοῦ αὐτοῦ. 936. Now anyone who wants to prove to an opponent making statements opposite to one’s own that he is wrong must take some such principle which is the same as this one—that the same thing cannot both be and not be at the same time—but apparently is not the same. For this will be the only method of demonstration that can be used against one who says that opposite statements can be truly made about the same subject. τοὺς δὴ μέλλοντας ἀλλήλοις λόγου κοινωνήσειν δεῖ τι συνιέναι αὑτῶν: μὴ γιγνομένου γὰρ τούτου πῶς ἔσται κοινωνία τούτοις πρὸς ἀλλήλους λόγου; δεῖ τοίνυν τῶν ὀνομάτων ἕκαστον εἶναι γνώριμον καὶ δηλοῦν τι, καὶ μὴ  πολλά, μόνον δὲ ἕν: ἂν δὲ πλείονα σημαίνῃ, φανερὸν ποιεῖν ἐφ᾽ ὃ φέρει τοὔνομα τούτων. ὁ δὴ λέγων εἶναι τοῦτο καὶ μὴ εἶναι, τοῦτο ὅ φησιν οὔ φησιν, ὥσθ᾽ ὃ σημαίνει τοὔνομα τοῦτ᾽ οὔ φησι σημαίνειν: τοῦτο δ᾽ ἀδύνατον. ὥστ᾽ εἴπερ σημαίνει τι τὸ εἶναι τόδε, τὴν ἀντίφασιν ἀδύνατον ἀληθεύειν. 937. Accordingly, those who are to join in some discussion must understand each other to some extent. And if this does not happen, how will they join in a common discussion? Therefore each of the terms used must be understood and must signify something, and not many things but only one. But if a term does signify many things, it must be made clear to which of these it refers. Hence, one who says that this is and is not, totally denies what he affirms, and thus denies that the term signifies what it signifies. But this is impossible. Hence, if to be this has some meaning, the contradictory cannot be said to be true of the same subject (332-340). ἔτι δ᾽ εἴ  τι σημαίνει τοὔνομα καὶ τοῦτ᾽ ἀληθεύεται, δεῖ τοῦτ᾽ ἐξ ἀνάγκης εἶναι: τὸ δ᾽ ἐξ ἀνάγκης ὂν οὐκ ἐνδέχεταί ποτε μὴ εἶναι: τὰς ἀντικειμένας ἄρα οὐκ ἐνδέχεται φάσεις καὶ ἀποφάσεις ἀληθεύειν κατὰ τοῦ αὐτοῦ. 938. Again, if a term signifies something and this is affirmed truly, it must necessarily be so; and what is necessarily so cannot not be. Hence opposite affirmations and negations cannot be true of the same subject (337-338). ἔτι δ᾽ εἰ μηθὲν μᾶλλον ἡ φάσις ἢ ἡ ἀπόφασις ἀληθεύεται, ὁ λέγων ἄνθρωπον ἢ  οὐκ ἄνθρωπον οὐθὲν μᾶλλον ἀληθεύσει: δόξειε δὲ κἂν οὐχ ἵππον εἶναι φάσκων τὸν ἄνθρωπον ἢ μᾶλλον ἢ οὐχ ἧττον ἀληθεύειν ἢ οὐκ ἄνθρωπον, ὥστε καὶ ἵππον φάσκων εἶναι τὸν αὐτὸν ἀληθεύσει (τὰς γὰρ ἀντικειμένας ὁμοίως ἦν ἀληθεύειν): συμβαίνει τοίνυν τὸν αὐτὸν ἄνθρωπον εἶναι καὶ ἵππον  ἢ τῶν ἄλλων τι ζῴων. ἀπόδειξις μὲν οὖν οὐδεμία τούτων ἐστὶν ἁπλῶς, πρὸς μέντοι τὸν ταῦτα τιθέμενον ἀπόδειξις. 939. Again, if the affirmation is in no way truer than the negation, it will not be truer to say that something is a man than to say that it is not a man. And it would also seem that it is either more or not less true to say that a man is not a horse than to say that he is not a man. Hence one will also be right in saying that the same thing is a horse; for it was assumed that opposite statements are equally true. Therefore it follows that the same thing is a man and a horse, or any other animal (343-345). Hence, while there is no demonstration in the strict sense of these principles, there is still a demonstration ad hominem against one who makes these assumptions. ταχέως δ᾽ ἄν τις καὶ αὐτὸν τὸν Ἡράκλειτον τοῦτον ἐρωτῶν τὸν τρόπον ἠνάγκασεν ὁμολογεῖν μηδέποτε τὰς ἀντικειμένας φάσεις δυνατὸν εἶναι κατὰ τῶν αὐτῶν ἀληθεύεσθαι: νῦν δ᾽  οὐ συνιεὶς ἑαυτοῦ τί ποτε λέγει, ταύτην ἔλαβε τὴν δόξαν. ὅλως δ᾽ εἰ τὸ λεγόμενον ὑπ᾽ αὐτοῦ ἐστὶν ἀληθές, οὐδ᾽ ἂν αὐτὸ τοῦτο εἴη ἀληθές, [1062β]  λέγω δὲ τὸ ἐνδέχεσθαι τὸ αὐτὸ καθ᾽ ἕνα καὶ τὸν αὐτὸν χρόνον εἶναί τε καὶ μὴ εἶναι: καθάπερ γὰρ καὶ διῃρημένων αὐτῶν οὐδὲν μᾶλλον ἡ κατάφασις ἢ ἡ ἀπόφασις ἀληθεύεται, τὸν αὐτὸν τρόπον καὶ τοῦ συναμφοτέρου  καὶ τοῦ συμπεπλεγμένου καθάπερ μιᾶς τινὸς καταφάσεως οὔσης οὐθὲν μᾶλλον <ἢ> ἡ ἀπόφασις [ἢ] τὸ ὅλον ὡς ἐν καταφάσει τιθέμενον ἀληθεύσεται. 940. And perhaps if one had questioned Heraclitus himself in this way, he would quickly have forced him to admit that opposite statements can never be true of the same subjects. But he adopted this view without understanding his own statement (328). And in general if what he said is true, not even this statement will be true—I mean that the same thing can both be and not be at one and the same time. For just as when they are separated the affirmation will not be truer than the negation (346), in a similar way when both are combined and taken together as though they were one affirmation, the negation will not be truer than the whole statement regarded as an affirmation. ἔτι δ᾽ εἰ μηθὲν ἔστιν ἀληθῶς καταφῆσαι, κἂν αὐτὸ τοῦτο ψεῦδος εἴη τὸ φάναι μηδεμίαν ἀληθῆ κατάφασιν ὑπάρχειν. εἰ δ᾽ ἔστι τι, λύοιτ᾽ ἂν τὸ  λεγόμενον ὑπὸ τῶν τὰ τοιαῦτα ἐνισταμένων καὶ παντελῶς ἀναιρούντων τὸ διαλέγεσθαι. 941. Again, if it is possible to affirm nothing truly, even this statement-that no affirmation is true-will be false (396-397). But if there is a true affirmation, this will refute what is said by those who raise such objections and completely destroy discussion. Chapter 6 παραπλήσιον δὲ τοῖς εἰρημένοις ἐστὶ καὶ τὸ λεχθὲν ὑπὸ τοῦ Πρωταγόρου: καὶ γὰρ ἐκεῖνος ἔφη πάντων εἶναι χρημάτων μέτρον ἄνθρωπον, οὐδὲν ἕτερον λέγων ἢ τὸ δοκοῦν ἑκάστῳ  τοῦτο καὶ εἶναι παγίως: τούτου δὲ γιγνομένου τὸ αὐτὸ συμβαίνει καὶ εἶναι καὶ μὴ εἶναι, καὶ κακὸν καὶ ἀγαθὸν εἶναι, καὶ τἆλλα τὰ κατὰ τὰς ἀντικειμένας λεγόμενα φάσεις, διὰ τὸ πολλάκις τοισδὶ μὲν φαίνεσθαι τόδε εἶναι καλὸν τοισδὶ δὲ τοὐναντίον, μέτρον δ᾽ εἶναι τὸ φαινόμενον ἑκάστῳ. 942. The statement made by Protagoras is similar to those mentioned; for he said that man is the measure of all things, meaning simply that whatever appears so to anyone is just as it appears to him. But if this is true, it follows that the same thing is and is not, and is good and evil, and that other statements involving opposites are true; because often a particular thing appears to be good to some and just the opposite to others, and that which appears to each man is the measure. COMMENTARY Postquam ostendit philosophus quod principia communia demonstrationis sunt principaliter de consideratione huius philosophiae, hic determinat de primo principio inter ea. Necesse est enim quod sicut omnia entia reducuntur ad aliquod primum, ita oportet quod principia demonstrationis reducantur ad aliquod principium, quod principalius cadit in consideratione huius philosophiae. Hoc autem est, quod non contingit idem simul esse et non esse. Quod quidem ea ratione primum est, quia termini eius sunt ens et non ens, qui primo in consideratione intellectus cadunt. 2211. Having shown that a study of the common principles of demonstration belongs chiefly to the consideration of this philosophical science, the Philosopher now deals with the first of these principles (934:C 2212). For just as all beings must be referred to one first being, in a similar fashion all principles of demonstration must be referred to some principle which pertains in a more basic way to the consideration of this philosophical science. This principle is that the same thing cannot both be and not be at the same time. It is the first principle because its terms, being and non-being, are the first to be apprehended by the intellect. Dividitur autem haec pars in duas. In prima determinat veritatem circa illud principium. In secunda excludit errorem, ibi, ad dicentem autem. 2212. This part is divided into two members. In the first (934:C 2211) he establishes the truth of this principle. In the second (936:C 2214) he rejects an error (“Now anyone who”). Circa primum duo facit de isto principio. Primo dicit quod est quoddam principium demonstrativum in entibus circa quod non contingit mentiri, scilicet secundum interiorem rationem. Sed necessarium est semper facere contrarium, scilicet dicere verum circa ipsum. Et hoc principium est, quod non contingit idem esse et non esse secundum unum et idem tempus, et aliis conditionibus servatis quae consueverunt in contradictione apponi, scilicet secundum idem, simpliciter, et alia huiusmodi. Impossibile enim est quod aliquis opinetur hoc principium esse falsum: opinaretur enim contradictoria esse simul vera, et sic idem haberet simul contrarias opiniones: nam contrariae opiniones sunt quae sunt de contrariis. Sicut opinio, qua quis opinatur Socratem sedere, est contraria opinioni, qua quis opinatur eum non sedere. In reference to the first part he does two things regarding this principle. First, he says that in regard to beings there is a principle of demonstration “about which it is impossible to make a mistake” (i.e., so far as its meaning is concerned), but of which we “must always do the contrary,” namely, acknowledge it as true. This principle is that the same thing cannot both be and not be at one and the same time, granted of course that the other conditions which it is customary to give in the case of a contradiction are fulfilled, namely, in the same respect, in an unqualified sense, and the like. For no one can think that this principle is false, because, if someone were to think that contradictories may be true at the same time, he would then have contrary opinions at the same time; for opinions about contradictories are contrary. For example, the opinion that “Socrates is sitting” is contrary to the opinion that “Socrates is not sitting.” 2213. And while (935). Et de talibus secundo dicit, quod de praedicto principio et similibus non potest esse simpliciter demonstratio, sed potest esse demonstratio ad hominem. Quod autem non possit simpliciter demonstrari, probat ex hoc, quod non contingit facere syllogismum ad hoc principium demonstrandum ex aliquo principio magis noto; quod oporteret si contingeret illud principium simpliciter demonstrare. Sed ad hominem contingit hoc principium demonstrare, qui concedit aliquid aliud, licet minus notum, et hoc negat. Second, he says that, while there cannot be demonstration in the strict sense of the above-mentioned principle and other similar ones, one may offer an argument ad hominem in support of it. That it cannot be demonstrated in the strict sense he proves thus: no one can prove this principle by constructing a syllogism from some principle which is better known. But such would be necessary if that principle were to be demonstrated in the strict sense. However, this principle can be demonstrated by using an argument ad hominem against one who admits some other statement, though less known, and denies this one. 2214. Now anyone who (936). Deinde cum dicit ad dicentem excludit opinionem negantium illud principium; et dividitur in partes duas. Primo disputat contra negantes hoc principium. Secundo ostendit quomodo ad hanc opinionem possit responderi, ibi, solvetur autem. Then he rejects the opinion of those who deny this principle; and this is divided into two parts. First (936:C 2214), he argues against those who deny this principle. Second (943:C 2225), he shows how one can meet this opinion (“Now this difficulty”). Circa primum, duo facit. Primo disputat contra negantes hoc principium simpliciter. Secundo descendit ad speciales opiniones, ibi, cito autem. In regard to the first he does two things. First (936:C 2214), he argues against those who unqualifiedly deny this principle. Second (940:C 2221), he turns his attention to certain particular opinions (“And perhaps”). Circa primum duo facit. Primo ponit modum disputandi contra hunc errorem; dicens, quod ille, qui contra ponentem contradictorias propositiones esse veras, vult ostendere quod sit falsum, debet sumere aliquid tale quod idem sit huic principio,- scilicet non contingere idem esse et non esse, secundum idem tempus,- sed non videatur idem. Si enim videretur idem, non concederetur ab adversario. Si autem non esset idem, non posset concludere propositum, quia huiusmodi principium non potest ex notioribus ostendi. Et ideo hoc solum modo potest sumi demonstratio contra dicentem, quod contradictoria verificantur de eodem; ut scilicet illud quod sumitur sit idem conclusioni, sed non videatur idem. In regard to the first he does two things. First, he gives the method of arguing against this error. He says that in arguing against an opponent who claims that contradictory propositions may be true, anyone who wants to show that this opinion is false ought to take some such principle which is the same as this one—that the same thing cannot both be and not be at the same time—but apparently is not the same. For, if it were evidently the same, it would not be admitted by an opponent. Yet if it were not the same, he could not prove his thesis, because a principle of this kind cannot be demonstrated from some principle which is better known. Hence, it is only in this way that a demonstration can be made against those who say that contradictories may be true of the same subject, namely, by assuming as a premise what is in fact the same as the conclusion but apparently is not. 2215. Accordingly (937). Futuros itaque secundo procedit ad disputandum contra praedictum errorem. Et circa hoc facit tres rationes. Quarum prima est, quod si duo homines debeant adinvicem communicare rationem, ut scilicet unus alteri rationem suam communicet disputando, oportet unum ipsorum intelligere aliquid, quod ab alio dicitur: quia si hoc non esset, non communicarent adinvicem in sermone secundum rationem. Et ita frustra acciperetur disputatio contra eum, qui hoc negaret. Second, he begins to argue dialectically against the above-mentioned error; and in regard to this he gives three arguments, First, he argues as follows: if two men are to join in a discussion in such a way that one may communicate his view to the other in a dispute, each must understand something that the other is saying. For if this were not the case, no statement would be understood by both of them; and thus an argument with an opponent would be pointless. Si autem unus ex eis intelligeret quod alius dicit, oportet quod unumquodque nominum quae proferuntur, sit notum in sua significatione; et per consequens, quod significet aliquid, et non multa, sed solum unum. Et si significet multa, quod manifestetur ad quod illorum multorum significandum utatur nomine; alias nesciret unus, quid alius vellet dicere. 2216. However, if one of them is to understand what the other is saying, each of the terms used must be understood according to its proper meaning and must therefore signify some one thing and not many things. And if it should signify many, it will be necessary to make clear which of the many things it signifies; otherwise one would not know what the other person means. Hoc igitur supposito, quod nomen significet unum, manifestum est, quod ille, qui dicit esse hoc, et non est hoc, puta quod Socrates est homo, et non homo, illud unum quod attribuit Socrati, quod scilicet est homo, negat cum adiungit quod non est homo: et sic negat iam quod primo significavit. Unde relinquitur quod nomen non significet id quod significat, quod est impossibile. Sequitur ergo quod si nomen aliquid determinate significat, quod impossibile est contradictionem verificari de eodem. 2217. Now granted that a term signifies one thing, it is evident that one who says both that this is and that this is not, for example, that Socrates is a man and that he is not a man, denies the one thing which he attributed to Socrates, namely, that he is a man, when he adds that he is not a man; and thus he denies what he first signified. Hence it follows that a word does not signify what it signifies. But this is impossible. Consequently, if a term signifies some definite thing, the contradictory cannot be truly affirmed of the same subject. 2218. Again, if a term (938). Secundam rationem ponit ibi, adhuc autem quae talis est. Si nomen significet aliquid, et hoc quod significatur per nomen verificatur de eodem de quo primo praedicatur nomen, necesse est hoc inesse ei, de quo praedicatur nomen, dum propositio vera fuit. Manifestum est enim quod haec conditionalis est vera - si Socrates est homo, Socrates est homo. Omnis autem conditionalis vera est necessaria. Unde necesse est, quod si consequens sit verum quod antecedens sit verum; quoniam concluditur quod necesse est quamlibet propositionem esse veram dum vera est. Sed quod est aliquando non contingit tunc non esse, quia necesse esse et non contingens non esse aequipollent. Ergo dum haec est vera - Socrates est homo - non contingit hanc esse veram - Socrates non est homo. Et sic patet quod non contingit oppositas affirmationes et negationes simul verificari de eodem. Then he gives the second argument, which runs as follows: if a term signifies some attribute, and the attribute signified by the term is truly affirmed of the same subject of which the term is first predicated, this attribute must belong to the subject of which the term is predicated so long as the proposition is true. For this conditional proposition, “If Socrates is a man, Socrates is a man,” is clearly true. Now every true conditional proposition is a necessary one. Hence, if the consequent is true, the antecedent must be true. But what is, cannot sometimes not be, because to be necessary and to be incapable of not being are equivalent. Therefore so long as the proposition “Socrates is a man” is true, the proposition “Socrates is not a man” cannot be true. Thus it is evident that opposite affirmations and negations cannot be true of the same subject at the same time. 2219. Again, if the affirmation (939). Tertiam rationem ponit ibi, adhuc autem quae talis est. Si affirmatio non est vera magis quam negatio ei opposita, ille qui dicit Socratem esse hominem, non magis verum dicit quam ille qui dicit Socratem non esse hominem. Sed manifestum est, quod ille qui dicit hominem non esse equum, aut magis verum dicit, aut non minus, quam ille, qui dicit hominem non esse hominem. Ita ergo per locum a simili vel a minori, verum dicet, qui hominem dicet non esse equum. Sed, si opposita contradictorie sunt simul vera: si haec est vera - homo non est equus,- et haec erit vera - homo est equus. Et ita sequitur, quod homo sit equus et quodcumque aliud animalium. Then he gives the third argument, which is as follows: if an affirmation is not truer than the negation opposed to it, one who says that Socrates is a man does not speak with greater truth than one who says that Socrates is not a man. But it is evident that one who says that a man is not a horse speaks either with greater or with no less truth than one who says that a man is not a man. Hence, according to this argument, he who says that a man is not a horse will speak with equal or no less truth. But if contradictory opposites are true at the same time, for example, if the proposition “Man is not a horse” is true, and the proposition “Man is a horse” is also true, then it follows that a man is a horse and also any other animal. Sed, quia posset aliquis calumniari praedictas rationes, ex hoc quod ea quae assumuntur in eis sunt minus nota quam conclusio quae intenditur; ideo respondet dicens quod nulla praedictarum rationum est demonstrativa simpliciter, sed tamen potest esse demonstratio ad hominem qui ponit hanc rationem, quem oportebit concedere ea quae assumuntur, licet sint minus nota simpliciter quam id quod negat. 2220. But because someone could criticize the foregoing arguments on the grounds that the things assumed in them are less known than the intended conclusion, he therefore answers this by saying that no one of the foregoing arguments is demonstrative in the strict sense, although there can be an argument ad hominem against an opponent who gives this argument, because the things assumed must be admitted to be true even though they are less known, absolutely than what he denies. 2221. And perhaps (940). Deinde cum dicit cito autem excludit praedictum errorem descendendo ad speciales opinantes. Et primo ad Heraclitum. Secundo ad Protagoram, ibi, simile autem. Then he rejects the above error by considering certain particular thinkers. He does this, first (940:C 2221), with regard to Heraclitus; and second (942:C 2224), with regard to Protagoras (“The statement”). Ponebat autem Heraclitus duo, scilicet quod affirmatio et negatio sit simul vera. Ex quo sequebatur quod omnis propositio tam affirmativa quam negativa sit vera. Item ponebat quod inter affirmationem et negationem sit aliquod medium. Et sic sequebatur quod contingeret neque affirmationem neque negationem esse veram. Et per consequens omnem propositionem esse falsam. Now Heraclitus posited two things: first, that an affirmation and a negation may be true at the same time (and from this it would follow that every proposition, affirmative as well as negative, is true); and second, that there may be an intermediate between affirmation and negation (and from this it would follow that neither an affirmation nor a negation can be true). Consequently every proposition is false. Primo ergo inducit rationem contra primum. Secundo contra secundum, ibi, adhuc autem. 2222. First (940:C 2222), he raises an argument against Heraclitus’ first position; and second (941:C 2223), against his second position (“Again, if it is possible”). Dicit ergo, quod de facili aliquis hoc modo disputando ad hominem coget ipsum Heraclitum, qui fuit auctor huius propositionis, confiteri quod oppositae propositiones non verificantur de eodem. Videtur enim hanc opinionem accepisse quod verificentur de eodem, ex hoc quod non intellexit seipsum quid diceret. Hoc autem modo cogeretur negare quod dicit: quia si illud quod dictum est ab eo, verum est, scilicet quod contingat idem secundum unum et idem tempus esse et non esse, sequitur quod hoc ipsum non erit verum. Sicuti enim si divisim accipiantur affirmatio et negatio, non magis vera est affirmatio quam negatio, ita et si accipiantur affirmatio et negatio simul tamquam ex eis una affirmatio fiat, non erit minus negatio vera huius totius compositi ex affirmatione et negatione, quam ipsa tota affirmatio opposita. Manifestum est enim quod contingit aliquam propositionem copulativam esse veram, sicut aliquam simplicem propositionem, et contingit accipere eius negationem. Sive autem illa copulativa componatur ex duabus affirmativis, sicut cum dicitur - Socrates sedet et disputat,- sive ex duabus negativis, sicut cum dicitur - verum esse Socratem non esse lapidem neque asinum,- sive ex affirmatione et negatione, ut cum dicitur,- verum est Socratem sedere et non disputare,- semper tamen copulativa verificata sumitur in virtute unius affirmativae. Et ille qui dicit eam esse falsam, assumit negationem quasi totius copulativae. Qui ergo dicit simul esse verum, hominem esse et non esse, assumit hoc ut quamdam affirmationem; et hoc non esse verum est eius negatio. Si ergo affirmatio et negatio est simul vera, sequitur quod haec etiam negatio sit vera, qua dicitur non esse verum, scilicet quod affirmatio et negatio sint simul vera. Oportet enim, si aliqua negatio est simul vera cum affirmatione sibi opposita, quod omnis negatio sit simul vera cum affirmatione sibi opposita. Eadem enim est ratio in omnibus. He accordingly says, first (940), that by giving an argument ad hominem in this way one may easily bring even Heraclitus, who was the author of this statement, to admit that opposite propositions may not be true of the same subject. For he seems to have accepted the opinion that they may be true of the same subject because he did not understand his own statement. And he would be forced to deny his statement in the following way: if what he said is true, namely, that one and the same thing can both be and not be at one and the same time, it follows that this very statement will not be true; for if an affirmation and a negation are taken separately, an affirmation is not truer than a negation; and if an affirmation and a negation are taken together in such a way that one affirmation results from them, the negation will not be less true of the whole statement made up of the affirmation and the negation than of the opposite affirmation. For it is clearly possible for some copulative proposition to be true, just as for some simple proposition; and it is possible to take its negation. And whether the copulative proposition be composed of two affirmative propositions, as when we say “Socrates is sitting and arguing,” or of two negative propositions, as when we say “It is true that Socrates is not a stone or an ass,” or of an affirmative proposition and a negative proposition, as when we say “It is true that Socrates is sitting and not arguing,” nevertheless a copulative proposition is always taken to be true because one affirmative proposition is true. And he who says that it is false takes the negation as applying to the whole copulative proposition. Hence he who says that it is true that man is and is not at the same time, takes this as a kind of affirmation; and that this is not true is the negation of this. Hence, if an affirmation and a negation are true at the same time, it follows that the negation which states that this is not true, i.e., that an affirmation and a negation are true at the same time, is equally true. For if any negation is true at the same time as the affirmation opposed to it, every negation must be true at the same time as the affirmation opposed to it; for the reasoning is the same in all cases. 2223. Again, if it is possible (941). Deinde cum dicit adhuc autem inducit rationem contra hoc, quod ponebatur quod nulla affirmatio sit vera. Si enim nihil contingat verum affirmare, qui autem dicit nullam affirmationem veram esse, aliquid affirmat, hoc scilicet quod verum sit nullam affirmationem esse veram; ergo hoc ipsum falsum erit. Et si aliquid affirmative dictum verum sit, removebitur opinio talium qui contra omnia instant. Et qui ista positione utuntur, auferunt totaliter disputationem; quia si nihil est verum, non potest aliquid concedi ex quo disputatio possit procedere. Et si affirmatio et negatio sint simul vera, non erit significare aliquid per sermonem, ut supra dictum est. Et sic cessabit disputatio. Then he introduces an argument against the second position of Heraclitus: that no affirmation is true. For if it is possible to affirm that nothing is true, and if one who says that no affirmation is true does affirm something, namely, that it is true that no affirmation is true, then this statement will be false. And if some affirmative statement is true, the opinion of people such as those who oppose all statements will be rejected. And those who adopt this position destroy the whole debate, because if nothing is true, nothing can be conceded on which an argument may be based. And if an affirmation and a negation are true at the same time, it will be impossible to signify anything by a word, as was said above (937:C 2215), and then the argument will cease. 2224. The statement (942). Deinde cum dicit simile autem descendit ad opinionem Protagorae: et dicit quod id quod dictum est a Protagora, simile est dictis ab Heraclito, et ab aliis qui ponunt affirmationem et negationem simul esse veram. Dicit enim Protagoras quod homo est mensura omnium rerum, scilicet secundum sensum et intellectum, ut in nono dictum est: quasi esse rei sequatur apprehensionem intellectus et sensus. Et sic qui dicit hominem esse mensuram omnium, nihil aliud dicit quam hoc esse verum quod videtur unicuique. Quo posito sequitur quod idem sit et non sit, et quod idem simul sit bonum et malum. Et simile est in aliis oppositis, eo quod multoties videtur hominibus aliquibus aliquid esse bonum, et aliis videtur contrarium, et ipsum videri est mensura rerum secundum opinionem Protagorae; ut scilicet intantum sit verum rem esse, inquantum videtur. Here he considers the opinion of Protagoras. He says that the statement made by Protagoras is similar to the one made by Heraclitus and by others who claim that an affirmation and a negation are true at the same time. For Protagoras says that man is the measure of all things, i.e., according to the intellect and the senses, as has been explained in Book IX (753:C 1800), as if the being of a thing depended upon intellectual and sensory apprehension. And one who says that man is the measure of all things merely says that whatever appears so to anyone is true. But if this is maintained, it follows that the same thing both is and is not and is both good and evil at the same time. The same thing is also true of other opposites, because often something seems to be good to some and just the opposite to others, and the way in which things seem or appear is the measure of all things according to the opinion of Protagoras; so that, inasmuch as a thing appears, to that extent it is true.
LESSON 6 Contradictories Cannot Be True at the Same Time
ARISTOTLE’S TEXT Chapter 6: 1062b 20-1063b 35  λύοιτο δ᾽ ἂν αὕτη ἡ ἀπορία θεωρήσασι πόθεν ἐλήλυθεν ἡ ἀρχὴ  τῆς ὑπολήψεως ταύτης: 943. Now this difficulty may be solved by considering the origin of this view. ἔοικε γὰρ ἐνίοις μὲν ἐκ τῆς τῶν φυσιολόγων δόξης γεγενῆσθαι, τοῖς δ᾽ ἐκ τοῦ μὴ ταὐτὰ περὶ τῶν αὐτῶν ἅπαντας γιγνώσκειν ἀλλὰ τοῖσδε μὲν ἡδὺ τόδε φαίνεσθαι τοῖσδε δὲ τοὐναντίον. 944. For it seems to have arisen in some cases from the opinion of the philosophers of nature, and in others from the fact that not all men apprehend the same thing in the same way, but something appears pleasant to some and the opposite to others (352). τὸ γὰρ μηδὲν ἐκ μὴ ὄντος  γίγνεσθαι, πᾶν δ᾽ ἐξ ὄντος, σχεδὸν ἁπάντων ἐστὶ κοινὸν δόγμα τῶν περὶ φύσεως: ἐπεὶ οὖν οὐ λευκὸν γίγνεται λευκοῦ τελέως ὄντος καὶ οὐδαμῇ μὴ λευκοῦ [νῦν δὲ γεγενημένον μὴ λευκόν], γίγνοιτ᾽ ἂν ἐκ μὴ ὄντος λευκοῦ τὸ γιγνόμενον [μὴ] λευκόν: ὥστε ἐκ μὴ ὄντος γίγνοιτ᾽ ἂν κατ᾽ ἐκείνους, εἰ μὴ  ὑπῆρχε λευκὸν τὸ αὐτὸ καὶ μὴ λευκόν. οὐ χαλεπὸν δὲ διαλύειν τὴν ἀπορίαν ταύτην: εἴρηται γὰρ ἐν τοῖς φυσικοῖς πῶς ἐκ τοῦ μὴ ὄντος γίγνεται τὰ γιγνόμενα καὶ πῶς ἐξ ὄντος. 945. For the view that nothing comes from non-being but everything from being is a doctrine common to nearly all those who have dealt with nature. Thus, since the not-white comes from what is actually white, and not from the not-white, should the not-white have come to be, what becomes not-white will have come to be from what is not not-white. Hence whiteness must come from non being according to them, unless the white and the not-white are the same. But it is not hard to solve this difficulty; for we have stated in our physical treatises in what sense things which come to be come from non-being, and in what sense they come from being (355-356). #964;ό γε μὴν ὁμοίως προσέχειν ταῖς δόξαις καὶ ταῖς φαντασίαις τῶν πρὸς αὑτοὺς διαμφισβητούντων εὔηθες: δῆλον  γὰρ ὅτι τοὺς ἑτέρους αὐτῶν ἀνάγκη διεψεῦσθαι. φανερὸν δὲ τοῦτ᾽ ἐκ τῶν γιγνομένων κατὰ τὴν αἴσθησιν: οὐδέποτε γὰρ τὸ αὐτὸ φαίνεται τοῖς μὲν γλυκὺ τοῖς δὲ τοὐναντίον, [1063α]  μὴ διεφθαρμένων καὶ λελωβημένων τῶν ἑτέρων τὸ αἰσθητήριον καὶ κριτήριον τῶν λεχθέντων χυμῶν. τούτου δ᾽ ὄντος τοιούτου τοὺς ἑτέρους μὲν ὑποληπτέον μέτρον εἶναι τοὺς δ᾽ ἄλλους οὐχ  ὑποληπτέον. ὁμοίως δὲ τοῦτο λέγω καὶ ἐπὶ ἀγαθοῦ καὶ κακοῦ, καὶ καλοῦ καὶ αἰσχροῦ, καὶ τῶν ἄλλων τῶν τοιούτων. οὐδὲν γὰρ διαφέρει τοῦτ᾽ ἀξιοῦν ἢ τὰ φαινόμενα τοῖς ὑπὸ τὴν ὄψιν ὑποβάλλουσι τὸν δάκτυλον καὶ ποιοῦσιν ἐκ τοῦ ἑνὸς φαίνεσθαι δύο, δύο δεῖν εἶναι διὰ τὸ φαίνεσθαι τοσαῦτα, καὶ πάλιν ἕν:  τοῖς γὰρ μὴ κινοῦσι τὴν ὄψιν ἓν φαίνεται τὸ ἕν. 946. But it is also foolish to occupy oneself equally with both opinions and with the fanciful statements of those who argue against themselves, because it is evident that one or the other of them must be wrong. This is clear from the facts of sensory perception; for the same thing never appears sweet to some and the opposite to others unless in some the organ of the sense which distinguish the above-mentioned savors has been impaired or injured. And such being the case, some must be taken as the measure and the others not. And I say that the same thing applies in the case of good and evil, of beautiful and ugly, and o other attributes of this kind. For to maintain this view is not different from maintaining that what appears to those who push their finger under their eye an make one object appear to be two must therefore be two because it appears to be so many, and yet that it must be one because to those who do not move their eye the one object appears to be one (369-375). ὅλως δὲ ἄτοπον ἐκ τοῦ φαίνεσθαι τὰ δεῦρο μεταβάλλοντα καὶ μηδέποτε διαμένοντα ἐν τοῖς αὐτοῖς, ἐκ τούτου περὶ τῆς ἀληθείας τὴν κρίσιν ποιεῖσθαι: δεῖ γὰρ ἐκ τῶν ἀεὶ κατὰ ταὐτὰ ἐχόντων καὶ μηδεμίαν μεταβολὴν ποιουμένων τἀληθὲς θηρεύειν,  τοιαῦτα δ᾽ ἐστὶ τὰ κατὰ τὸν κόσμον: ταῦτα γὰρ οὐχ ὁτὲ μὲν τοιαδὶ πάλιν δ᾽ ἀλλοῖα φαίνεται, ταὐτὰ δ᾽ ἀεὶ καὶ μεταβολῆς οὐδεμιᾶς κοινωνοῦντα. 947. And in general seeing that things here are subject to change and never remain the same, it would be unfitting to base our judgment of the truth on this. For in pursuing the truth one must start with those things which are always the same and never undergo a single change. Such things are those which contain the world; for they do not appear at one time to be such and at another different but they are always the same and admit of no change (365). ἔτι δ᾽ εἰ κίνησις ἔστι, καὶ κινούμενόν τι, κινεῖται δὲ πᾶν ἔκ τινος καὶ εἴς τι: δεῖ ἄρα τὸ κινούμενον εἶναι ἐν ἐκείνῳ ἐξ οὗ κινήσεται καὶ οὐκ  εἶναι ἐν αὐτῷ, καὶ εἰς τοδὶ κινεῖσθαι καὶ γίγνεσθαι ἐν τούτῳ, τὸ δὲ κατὰ τὴν ἀντίφασιν μὴ συναληθεύεσθαι κατ᾽ αὐτούς. 948. Further, if there is motion, there is also something that is moved; and everything is moved from something and to something. Therefore that which is moved must be in that from which it is moved, and yet not be in it; and it must be moved to this and come to be in it; but contradictories cannot be true at the same time, as they claim. καὶ εἰ κατὰ τὸ ποσὸν συνεχῶς τὰ δεῦρο ῥεῖ καὶ κινεῖται, καί τις τοῦτο θείη καίπερ οὐκ ἀληθὲς ὄν, διὰ τί κατὰ τὸ ποιὸν οὐ μενεῖ; φαίνονται γὰρ οὐχ ἥκιστα τὰ κατὰ τὰς ἀντιφάσεις  ταὐτοῦ κατηγορεῖν ἐκ τοῦ τὸ ποσὸν ὑπειληφέναι μὴ μένειν ἐπὶ τῶν σωμάτων, διὸ καὶ εἶναι τετράπηχυ τὸ αὐτὸ καὶ οὐκ εἶναι. ἡ δ᾽ οὐσία κατὰ τὸ ποιόν, τοῦτο δὲ τῆς ὡρισμένης φύσεως, τὸ δὲ ποσὸν τῆς ἀορίστου. 949. And if things here are in a state of continuous change and motion as regards quantity, and one were to suppose this even though it is not true, why should they not be permanent as regards quality? For the view that contradictories may be predicated of the same subject seems to be based largely on the assumption that the quantity of bodies does not remain constant; and for this reason they say that the same thing is and is not four cubits long. But a thing’s substance involves quality, and this is of a determinate nature, whereas quantity is of an indeterminate nature (365). ἔτι διὰ τί προστάττοντος τοῦ ἰατροῦ τοδὶ τὸ σιτίον προσενέγκασθαι προσφέρονται;  τί γὰρ μᾶλλον τοῦτο ἄρτος ἐστὶν ἢ οὐκ ἔστιν; ὥστ᾽ οὐθὲν ἂν διέχοι φαγεῖν ἢ μὴ φαγεῖν: νῦν δ᾽ ὡς ἀληθεύοντες περὶ αὐτὸ καὶ ὄντος τοῦ προσταχθέντος σιτίου τούτου προσφέρονται τοῦτο: καίτοι γ᾽ οὐκ ἔδει μὴ διαμενούσης παγίως μηδεμιᾶς φύσεως ἐν τοῖς αἰσθητοῖς ἀλλ᾽ ἀεὶ πασῶν κινουμένων  καὶ ῥεουσῶν. 950. Further, when a physician orders them to take some particular food, why do they take it? For why is this particular food bread rather than not bread? Hence it would make no difference whether they ate it or not. But they take the food prescribed as though they know the truth about it and that it is the food prescribed. Yet they should not do this if there is no nature which remains fixed in the sensible world, but everything is always in a state of motion and flux (349). ἔτι δ᾽ εἰ μὲν ἀλλοιούμεθα ἀεὶ καὶ μηδέποτε διαμένομεν οἱ αὐτοί, τί καὶ θαυμαστὸν εἰ μηδέποθ᾽ ἡμῖν ταὐτὰ φαίνεται καθάπερ τοῖς κάμνουσιν [1063β]  (καὶ γὰρ τούτοις διὰ τὸ μὴ ὁμοίως διακεῖσθαι τὴν ἕξιν καὶ ὅθ᾽ ὑγίαινον, οὐχ ὅμοια φαίνεται τὰ κατὰ τὰς αἰσθήσεις, αὐτὰ μὲν οὐδεμιᾶς διά γε τοῦτο μεταβολῆς κοινωνοῦντα τὰ αἰσθητά, αἰσθήματα δ᾽ ἕτερα ποιοῦντα τοῖς κάμνουσι καὶ μὴ τὰ αὐτά:  τὸν αὐτὸν δὴ τρόπον ἔχειν καὶ τῆς εἰρημένης μεταβολῆς γιγνομένης ἴσως ἀναγκαῖόν ἐστιν); εἰ δὲ μὴ μεταβάλλομεν ἀλλ᾽ οἱ αὐτοὶ διατελοῦμεν ὄντες, εἴη ἄν τι μένον. 951. Again, if we are always undergoing change and never remain the same, what wonder is it if to us, as to those who are ill, things never appear the same? For to them also, since they are not in the same condition as when they were well, sensible qualities do not appear to be the same; yet sensible things themselves need not for this reason undergo any change, but they cause different, and not the same, impressions in those who are ill. And perhaps the same thing must happen to those who are well if the above-mentioned change takes place (950). However, if we do not change but always remain the same, there will be something permanent (357-359). πρὸς μὲν οὖν τοὺς ἐκ λόγου τὰς εἰρημένας ἀπορίας ἔχοντας οὐ ῥᾴδιον διαλῦσαι μὴ τιθέντων τι καὶ τούτου μηκέτι λόγον ἀπαιτούντων:  οὕτω γὰρ πᾶς λόγος καὶ πᾶσα ἀπόδειξις γίγνεται: μηθὲν γὰρ τιθέντες ἀναιροῦσι τὸ διαλέγεσθαι καὶ ὅλως λόγον, ὥστε πρὸς μὲν τοὺς τοιούτους οὐκ ἔστι λόγος, πρὸς δὲ τοὺς διαποροῦντας ἐκ τῶν παραδεδομένων ἀποριῶν ῥᾴδιον ἀπαντᾶν καὶ διαλύειν τὰ ποιοῦντα τὴν ἀπορίαν ἐν αὐτοῖς: δῆλον δ᾽ ἐκ τῶν  εἰρημένων. ὥστε φανερὸν ἐκ τούτων. 952. Hence, in the case of those who raise the foregoing difficulties as a result of reasoning, it is not easy to meet their arguments unless they assume something and do not demand a reason for it; for every argument and demonstration comes about in this way. For those who admit nothing destroy discussion and reasoning in general, and thus there is no reasoning with such men. But in the case of those who are puzzled by the usual problems, it is easy to meet them and to reject the arguments which cause their difficulty. This becomes clear from what has been said above (943-951). ὅτι οὐκ ἐνδέχεται τὰς ἀντικειμένας φάσεις περὶ τοῦ αὐτοῦ καθ᾽ ἕνα χρόνον ἀληθεύειν, οὐδὲ τὰ ἐναντία, διὰ τὸ λέγεσθαι κατὰ στέρησιν πᾶσαν ἐναντιότητα: δῆλον δὲ τοῦτ᾽ ἐπ᾽ ἀρχὴν τοὺς λόγους ἀναλύουσι τοὺς τῶν ἐναντίων. ὁμοίως δ᾽ οὐδὲ τῶν ἀνὰ μέσον οὐδὲν οἷόν τε  κατηγορεῖσθαι καθ᾽ ἑνὸς καὶ τοῦ αὐτοῦ: λευκοῦ γὰρ ὄντος τοῦ ὑποκειμένου λέγοντες αὐτὸ εἶναι οὔτε μέλαν οὔτε λευκὸν ψευσόμεθα: συμβαίνει γὰρ εἶναι λευκὸν αὐτὸ καὶ μὴ εἶναι: θάτερον γὰρ τῶν συμπεπλεγμένων ἀληθεύσεται κατ᾽ αὐτοῦ, τοῦτο δ᾽ ἐστὶν ἀντίφασις τοῦ λευκοῦ. 953. It is evident from these considerations, then, that opposite statements cannot be verified of the same subject at one time (353; 376-377), nor can contrary ones, because every contrariety involves privation. This becomes clear if we reduce the definitions of all contraries to their principle (382). Similarly no intermediate can be predicated of one and the same subject. For if the subject is white, those who say that it is neither white nor black are wrong, for it then follows that it is white and is not white; for the second of the two terms which we have combined is true of it, and this is the contradictory of white (383-391). οὔτε δὴ καθ᾽ Ἡράκλειτον  ἐνδέχεται λέγοντας ἀληθεύειν, οὔτε κατ᾽ Ἀναξαγόραν: εἰ δὲ μή, συμβήσεται τἀναντία τοῦ αὐτοῦ κατηγορεῖν: ὅταν γὰρ ἐν παντὶ φῇ παντὸς εἶναι μοῖραν, οὐδὲν μᾶλλον εἶναί φησι γλυκὺ ἢ πικρὸν ἢ τῶν λοιπῶν ὁποιανοῦν ἐναντιώσεων, εἴπερ ἐν ἅπαντι πᾶν ὑπάρχει μὴ δυνάμει μόνον ἀλλ᾽ ἐνεργεία  ι καὶ ἀποκεκριμένον. 954. One cannot be right, then, in holding the views either of Heraclitus (940) or of Anaxagoras; and if this were not so it would follow that contraries would be predicated of the same subject. For when Anaxagoras says that there is a part of everything in everything else, he says that nothing is sweet any more than it is bitter, and so on with any of the other pairs of contraries, since everything is present in everything else, not potentially, but actually and separately. ὁμοίως δὲ οὐδὲ πάσας ψευδεῖς οὐδ᾽ ἀληθεῖς τὰς φάσεις δυνατὸν εἶναι, δι᾽ ἄλλα τε πολλὰ τῶν συναχθέντων ἂν δυσχερῶν διὰ ταύτην τὴν θέσιν, καὶ διότι ψευδῶν μὲν οὐσῶν πασῶν οὐδ᾽ αὐτὸ τοῦτό τις φάσκων ἀληθεύσει, ἀληθῶν δὲ ψευδεῖς εἶναι πάσας λέγων οὐ ψεύσεται.  955. And similarly all statements cannot be true or all false, both because of many other difficulties which might be brought forward on the basis of this position, and because, if all statements are false, anyone who says this will not speak the truth; and if all are true, it will not be false to say that all are false (392). COMMENTARY Postquam philosophus disputavit contra ponentes contradictoria simul verificari de eodem, hic ostendit quomodo haec ratio possit ab eorum mentibus removeri. Et dividitur in partes duas. In prima ostendit propositum. In secunda inducit quaedam corollaria ex dictis, ibi, quare manifestum. 2225. Having argued against those who claim that contradictories may be verified of the same subject at the same time, the Philosopher now shows how these men can be persuaded to abandon this theory. His discussion is divided into two parts. In the first (943:C 2225) he explains his thesis. In the second (953:C 2243) he draws a corollary from what has been said (“It is evident”). Prima pars dividitur in partes duas. In prima ostendit quomodo praedicta ratio in aliquibus solvi possit. In secunda ostendit in quibus possit solvi, et in quibus non, ibi, ad habentes quidem igitur. The first part is divided into two members. In the first he explains how it is possible in some cases to deal with the above-mentioned theory. In the second (952:C 2241) he indicates in what cases it can be refuted and in what not (“Hence, in the case”). Circa primum, tria facit. Primo proponit modum quo praedicta ratio in aliquibus solvi possit; dicens quod dubitatio praedicta ex qua aliqui moventur ad ponendum contradictoria simul verificari de eodem, poterit solvi, si quis consideret unde principium sumpsit haec positio. In treating the first (943) he does three things. First, he describes the way in which the foregoing theory can be disqualified in some cases. He says that the above-mentioned difficulty which led some people to adopt the position that contradictories may be verified of the same subject at the same time can. be dispelled if one considers its source. 2226. For it seems (944). Secundo ibi, videtur enim assignat duplex principium praedictae positionis: dicens quod quibusdam videtur quod principium dictae opinionis sit ex opinione naturalium philosophorum, qui posuerunt aliquid non fieri ex non ente. Aliis autem videtur quod principium sumpserit ex hoc quod non omnes eadem iudicant de eisdem. Sed quibusdam videtur hoc esse delectabile, et aliis contrarium. Ex hoc enim sequitur quod opposita sint simul vera, si quis credat quod omne quod videtur alicui sit verum. Second, he gives two sources of this position. He says that this position seems to have arisen in some cases from the opinion of the philosophers of nature, who claimed that nothing comes to be from non-being, and in others from the fact that not all men make the same judgments about the same things, but something appears pleasant to some and just the opposite to others. For if one were to believe that whatever appears is true, it would follow from this that opposites are true at the same time. 2227. For the view (945). Tertio ibi, nihil enim manifestat quomodo ex praemissis duobus principiis dicta opinio sequatur, et quomodo solvatur. Et primo quomodo sequatur ex opinione naturalium physicorum. Secundo quomodo sequatur dicta opinio ex eo quod creditur, quodcumque videtur esse verum, ibi, sed et similiter. Third, he shows how the abovementioned position might follow from the two sources just given; and he points out how it may be dealt with. First, he shows how it might follow from the opinion of the philosophers of nature; and second (946:C 2227), from the belief that every appearance is true (“But it is also foolish”). Dicit ergo primo, quod fere omnium eorum, qui de natura tractaverunt, commune dogma est, quod nihil fit ex non ente; sed omne quod fit, fit ex ente. Manifestum est etiam, quod aliquid fit non album ex eo quod est perfecte album: non autem fit album ex non albo. Ulterius etiam manifestum est, quod non album, fit ex eo, quod non est non album. Quod exinde patet, quod id quod non est non album fit non album, sicut quod non est nigrum fit nigrum. Sic igitur illud, ex quo fit non album, est album, et non est non album. Quod non potest intelligi tamquam penitus sit non ens non album; quia sic videretur sequi quod aliquid fieret simpliciter ex non ente. Sicut, si diceremus quod ignis fit ex non igne, quomodo intelligebant, quod illud, quo fit ignis, sit penitus non ignis. Sic enim videbatur eis, quod sequeretur, quod fieret aliquid ex non ente. Et propter hoc ponebant quod in eo ex quo fit ignis, erat ignis latens; ut patet ex opinione Anaxagorae, quae ponitur in primo physicorum. Similiter credebant, quod si aliquid fit non album ex eo quod non est non album, quod nihilominus non album praeexisteret in eo ex quo fit non album, ut dictum est. Sequebatur etiam secundum eos, quod illud ex quo fit non album, esset album et non album simul: nisi ponatur quod aliquid fiat ex non ente. He accordingly says, first (945), that the doctrine common to nearly all of the thinkers who have dealt with nature is that nothing comes to be from non-being, but everything from being. It is clear that something becomes not-white from what is actually white; but what is not-white does not come from what is not-white. Further, it is also evident that what is not-white comes from what is not not-white. Consequently, it is evident that what is not not-white becomes not-white, just as what is not-black becomes black. It is clear, then, that that from which the not-white comes to be is the white, and it is not not-white. This cannot be understood in the sense that the not-white is entirely non-being, because it would then seem to follow that something comes to be from non-being absolutely. For example, if we were to say that fire comes from what is not-fire, there would be the question how they think that that from which fire comes to be is entirely not-fire. For it would then seem to follow, according to them, that something comes to be from non-being. Hence they claimed that fire lay hidden in that from which fire comes to be, as is evident from the opinion of Anaxagoras, which is given in Book I of the Physics. Similarly, they believed that, if something comes to be not-white from what is not not-white, the not-white must have preexisted in that from which it comes to be, as has been explained. Thus it would follow, according to them, that that from which the not-white comes to be is both white and not-white at the same time, unless it is assumed that something comes to be from non-being. Sed hanc dubitationem, ut ait philosophus, non difficile est solvere. Expositum enim est in primo physicorum, quomodo aliquid fiat ex ente, et quomodo ex non ente. Dictum est enim quod aliquid fit ex non ente in actu, et ente in actu per accidens. Sed ex materia quae in potentia est, fit aliquid per se. Accidit enim factioni quod materia ex qua fit aliquid, fuerit subiecta formae et privationi. Et sic non oportet, quod id ex quo aliquid fit, simul sit ens et non ens in actu; sed quod de se sit potentia ad ens et non ens, idest ad formam et privationem. 2228. But this difficulty is not hard to solve, as the Philosopher points out; for it has been explained in Book I of the Physics how a thing comes to be from being and how from nonbeing; for it has been stated that something comes to be from what is a nonbeing in act, though it is incidentally a being in act. But it comes to be properly from matter, which is in potency; for it is accidental to the process of making that the matter from which a thing comes to be should be the subject of form and of privation. Thus it is not necessary that that from which a thing comes to be should be at the same time both a being and a nonbeing in act, but that it should be of itself in potency both to being and to non-being, i.e., both to form and to privation. 2229. But it is also foolish (946). Deinde cum dicit sed et similiter removet praedictam opinionem secundum quod causatur ex alio principio, quod est, opinari omne, quod videtur, esse verum. Then he rejects the foregoing opinion inasmuch as it might be derived from the other source, i.e., from the view that every appearance is judged to be true. First, he rejects this source; and second (947:C 2232), its cause (“And in general”). Et primo, removet hoc principium. Et secundo causam eius, ibi, totaliter autem. Dicit ergo primo, quod sicut stultum est propter praedicta opinari quod contradictoria simul verificantur de eodem, similiter etiam est stultum attendere, idest assentire praedictis utrisque opinionibus philosophorum dubitantium contra seipsos. Manifestum est enim quod necesse est alterum eorum mentiri. He accordingly says, first (946), that, just as it is foolish to think that contradictories may be verified of the same subject at the same time, so too “it is also foolish to occupy oneself with,” i.e., to accept, both of the foregoing opinions of the philosophers who argue against themselves; for it is obvious that one or the other of them must be in error. Et hoc palam est ex his, quae apparent secundum sensum. Nunquam enim idem videtur his quidem dulce, aliis amarum, nisi in alteris eorum sit aliqua corruptio, aut privatio secundum organum sensus, et secundum virtutem, quae iudicat de saporibus. Huiusmodi autem corruptione in alteris eorum existente, existimandum est alteros eorum esse mensuram, idest accipiendum est eorum iudicium quasi regulam et mensuram veritatis, illorum scilicet in quibus non est corruptio: non autem hoc putandum est de alteris, in quibus est corruptio. 2230. This is evident from the facts of sensory perception; for the same thing never appears sweet to some and bitter to others, unless in some the sense organ and the power which discriminates between savors, has been impaired or injured. But since this does happen in some cases, “some must be taken as the measure,” i.e., the judgment of those whose senses are not impaired in this way must be taken as the rule and measure of truth. But this should not be understood to apply to those whose senses are impaired. Et sicut hoc manifestum est in cognitione sensus, similiter dicendum est in bono et malo, in pulchro et turpi, et huiusmodi omnibus quae per intellectum cognoscuntur. Si enim quibusdam videatur secundum intellectum hoc esse bonum, aliis autem malum, standum est eorum iudicio in quibus non est aliqua corruptio secundum intellectum, nec ex prava consuetudine, neque ex prava affectione, neque ex aliqua huiusmodi causa. Nam si quis dicat quod nihil minus dignum est credere his quam illis, nihil hoc differt quam si diceret, quod ea quae apparent hominibus ponentibus sub visu digitum, idest moventibus oculum digito, et ex hoc facientibus quod id quod est unum videantur duo, quod propter hoc oporteat esse duo, quia apparent tot; et iterum oporteat esse unum, quia quando aliquis non movet oculum, apparet unum id quod est unum. Manifestum est enim, quod iudicandum est de unitate rerum, secundum id quod visus iudicat, nulla extranea passione existente in eo; non autem secundum quod iudicat ex praedicta passione. Sic autem iudicat unum esse duo, quia species unius visibilis duobus modis redditur organo visus quando movetur, et secundum utriusque dispositionem pervenit ad organum sensus communis, quasi essent duo visa. 2231. And what is evident in the case of sensory perception must also be said to apply in the case of good and evil, of beautiful and ugly, and of all attributes of this kind which are apprehended by the intellect. For if some conceive a thing to be good and others evil, the judgment of those whose intellect has not been impaired by some bad habit or by some bad influence or by some other cause of this kind must be the norm. For if someone were to hold that it is not less fitting to believe the one group rather than the other, this would not differ in any way from saying that things are as they appear “to those who push their finger under their eye,” i.e., who move their eye with their finger, and thereby make one thing appear as two, and say that it must be two because it appears to be so many, and again that it must be one because it appears to be one to those who do not move their eye with their finger. For it is obvious that we must base our judgment about the oneness of things on the judgment which the eye makes when it does not receive some strange impression, and not on the judgment which it makes when it receives such an impression. Now a man judges one visible object to be two because the form of the visible object is made to appear as two to the organ of vision when it is moved; and this double impression reaches the organ of the common sense as though there were two visible objects. 2232. And in general (947). Deinde cum dicit totaliter autem excludit causam, propter quam ponebant omne quod videtur esse verum. Hoc enim ponebant aliqui, quia existimabant res omnes esse in continuo fluxu, et quod nulla natura esset in rebus fixa et determinata. Et sic sequebatur, quod rem esse talem non erat nisi videri. Then he rejects the basis of the position that every appearance is true. For some held this because they thought that all things are in a state of continuous flux, and that there is nothing fixed and determinate in reality; and thus it would follow that a thing is such only when it is seen. Contra hoc ergo ponit quinque rationes. Quarum prima talis est, quod totaliter inconveniens est sumere iudicium de tota veritate ex hoc, quod ista sensibilia quae sunt prope, scilicet vicina nobis, permutantur et nunquam permanent. Oportet autem magis venari verum ex his, quae semper se habent eodem modo, et non patiuntur aliquam permutationem quantum ad substantiam suam, licet appareat in eis motus secundum locum. Talia enim sunt quae continent mundum, scilicet corpora caelestia; ad quae comparata haec corpora corruptibilia, quasi nullius sunt quantitatis, ut mathematici probant. Corpora autem caelestia sunt semper eadem, et non videntur quandoque talia, et alia vice alia; sed nulla permutatione participant, quae scilicet sit in eorum substantia. 2233. He therefore presents five arguments against this position. He says, first, that it is altogether unfitting to base our judgment about the whole truth on the fact that these sensible things which are near or close to us are undergoing change and are never permanent. But the truth must be based rather on those things which are always the same and never undergo any change as regards their substance, though they do appear to be subject to local motion. For such things are those “which contain the world,” i.e., the celestial bodies, to which these corruptible bodies are compared as things that have no quantity, as the mathematicians prove. Now the celestial bodies are always the same and do not at one time appear to be such and at another different, for they admit of no change which affects their substance. 2234. Further, if there (948). Secundam rationem ponit ibi, adhuc autem quae talis est. Si motus est in istis inferioribus, oportet quod id quod movetur sit aliquid; et etiam oportet, quod id quod movetur, moveatur ex aliquo, et etiam ad aliquid. Unde oportet id, quod movetur, adhuc esse in eo ex quo movetur, et nondum esse in eo ad quod movetur, sed moveri ad ipsum et continue fieri in ipso. Et sic aliqua affirmatio determinate est vera, et aliqua negatio; et non oportebit quod contradictio verificetur de eodem, quia secundum hoc nihil moveretur. Si enim idem foret esse in termino ad quem, et non esse, nulla ratio esset quare moveretur ad terminum ad quem aliquid quod nondum est in illo, quia iam esset ibi. Then he gives the second argument against this position. The argument runs thus: if there is motion in these lower bodies, there must be something that is moved, and it must also be moved from something and to something. Hence that which is moved must already be in that from which it is moved and yet not be in it, and this must be moved to something else and be continuously coming to be in it. Thus some definite affirmation, as well as some negation, must be true. And it will not be necessary that a contradiction be true of the same subject, because according to this nothing would be moved. For if the same thing might be at the extreme to which it is moved and not be at it, there would be no reason why a thing which has not yet reached an extreme should be moved thereto, because it would already be there. 2235. And if things (949). Tertiam rationem ponit ibi, et si secundum ad cuius evidentiam sciendum est, quod Heraclitus videns aliquid augeri longo tempore, puta per unum annum secundum aliquam determinatam quantitatem, et modicam, existimavit quod qualibet parte illius temporis aliquod augmentum fieret, sed insensibile propter parvitatem quantitatis, quae augetur. Et ex hoc inductus fuit ad credendum, quod omnes res, etiam quae videntur quiescentes, etiam insensibiliter moverentur continue, sed post longum tempus sensibiliter eorum motus appareret. Est autem hoc falsum quod de augmento opinabatur. Non enim continue fit augmentum, ita quod in qualibet temporis parte aliquid crescat; sed disponitur ad augmentum corpus per aliquod tempus, et tunc crescit, ut Aristoteles expressius manifestat in octavo physicorum. He gives the third argument; and with a view to making this clear it should be borne in mind that, when Heraclitus saw that a thing increased in size according to some definite and very small quantity over a long period of time (for example, a year), he thought that some addition would be made in any part of that time, and that it would be imperceptible because of the very small quantity involved. And because of this he was led to believe that all things, even those which seem to be static, are also being moved continuously by an imperceptible motion, and that after a long time their motion would become apparent to the senses. But his opinion about increase is false; for increase does not take place continuously in such a way that something grows in any part of time, but a body is disposed to increase during some time and then grows, as Aristotle makes quite clear in Book VIII of the Physics. Dicit ergo, quod si corpora praesentia hic apud nos continue fluunt et moventur secundum quantitatem, et si hoc aliquis vellet concedere, licet non verum sit, non est ratio quare non possit aliquid moveri secundum quantitatem. Videtur enim quod non parum haec opinio, quae ponit contradictiones simul esse eiusdem, procedat ex eo quod existimat quod quantum non remanet in corporibus; et sic opinantur quod id sit et non sit simul quadricubitum. Sed substantia rei determinatur secundum quale, idest secundum aliquam formam. Quale autem est determinatae naturae in rebus, etsi quantum sit indeterminatum propter motum, ut dictum est. 2236. Hence he says that, if the bodies around us here are in a continuous state of flux and motion as regards quantity, and one wishes to admit this even though it is not true, there is no reason why a thing cannot be unchanging as to its quality. For the opinion that contradictories are true of the same subject at the same time seems to be based largely on the assumption that the quantitative aspect of bodies does not remain constant; and thus some thought that the same thing is and is not four cubits long. But a thing’s substance is defined in terms of some quality, i.e., some form; and quality is of a determinate nature in things, although quantity is of an indeterminate nature because of change, as has been pointed out. 2237. Further, when a physician (950). Quartam rationem ponit ibi, adhuc propter quae talis est. Si in rebus nihil est fixum, neque quantum ad esse, neque quantum ad non esse, propter quid deferunt hunc cibum, quem medicus iubet, et non alium? Secundum enim dictam opinionem, quid magis est panis, vel non panis? Quasi diceret: non magis praedicatur de eo affirmatio quam negatio. Et sic nihil differt quod comedat vel non comedat. Sed nos videmus quod ipsi offerunt hunc cibum, quem medicus iubet, quasi habentes verum iudicium de ipso cibo, et quasi hic cibus vere sit ille cibus, de quo medicus iubet. Hoc autem non oporteret, si nulla natura sic per certitudinem maneret in sensibilibus, sed omnia semper moverentur et fluerent. Then he gives the fourth argument, which runs thus: if there is nothing fixed in the world as regards being or non-being, why do they take this kind of bread which the physician prescribes and not that? For according to the position given above, why is this bread rather than not-bread? He implies that the answer cannot be in the affirmative any more than in the negative. And thus it would make no difference whether one ate the bread or did not. But we see that they take the bread which the physician prescribes, implying that they form a true judgment about bread itself, and that this kind of bread is really the one which the physician prescribes. Yet this would not be the case if no nature remained fixed in the sensible world but all things are always in a state of motion and flux. 2238. Again, if we (951). Quintam rationem ponit ibi, adhuc si quae talis est. Cum secundum opinionem praedictam ponatur, quod propter continuam mutationem quae est in rebus, non sit aliqua veritas in rebus fixa; si sit verum esse quod est videri, necesse est dicere quod nos homines qui de rebus aliis iudicamus, aut sumus in motu, aut non. Then he presents the fifth argument: since the above-mentioned position assumes that there is no fixed truth in things because of the continuous change which they undergo, if the truth is identical with appearance it is necessary to say that we men, who make judgments about other things, are either in motion or are not. Si enim semper alteramur, et nunquam permanemus eodem modo nos habentes, non est mirabile si res non eodem modo videntur se habere nobis, sicut accidit infirmis. Quia enim transmutati sunt, et non in eadem dispositione se habent sicut quando sani erant, non videntur eis sensibilia quae percipiunt per sensum qualia videbantur eis ante infirmitatem. Nam eis, qui habent gustum infectum, etiam quae sunt dulcia videntur amara vel insipida. Et simile est in aliis sensibilibus. Non tamen propter haec sensibilia sunt permutata; sed faciunt alias impressiones infirmis, propter hoc quod sensus eorum alio modo se habent. Si ergo nos homines in continua transmutatione existentes, de rebus aliis diversimode iudicamus, non est hoc imputandum rebus, sed nobis ipsis. 2239. For if we are always undergoing change and never remain the same, it is not surprising that things never appear the same to us; and this is the case with those who are ill. For since they have been changed and are not in the same state as when they were well, the sensible qualities which they perceive by way of the senses will not seem the same to them as they did before they became ill. For to those whose sense of taste has been impaired sweet things seem bitter or tasteless; and the same is true of other sensible qualities. Yet sensible qualities themselves are not changed for this reason, but they cause different impressions in those who are ill because their senses are differently disposed. Therefore, if we men, who are continuously undergoing change, make different judgments about other things, this should not be attributed to things but to us. Si autem nos non permutamur, sed semper permanemus eodem modo nos habentes: ergo in rebus erit aliquid permanens, et per consequens aliqua veritas determinata, de qua possumus praecise diiudicare. Non enim solum iudicamus de rebus aliis, sed etiam de natura humana. 2240. However, if we are not changing but always remain the same, there will therefore be something permanent in the world and consequently some fixed truth about which we can make positive judgments. For we make judgments not only about other things but also about human nature. 2241. Hence, in the case (952). Deinde cum dicit ad habentes ostendit a quibus praedicta opinio removetur, et a quibus non; et dicit, quod si qui incidunt in praedictas opiniones non propter aliquam rationem, ita quod ex pertinacia non concedant aliquid neque inquirant rationem eorum quae dicuntur, sed pertinaciter inhaerent his, quae opinabantur, non facile est eis solvere huiusmodi opinionem. Omnis enim ratio et demonstratio fit hoc modo; scilicet concedendo et exquirendo rationem alicuius dicti. Sed illi qui nihil concedunt, interimunt disputationem et omnem argumentativam rationem. Unde ad eos non potest haberi sententia ratiocinationis, per quam a suo errore tollantur. Then he indicates who can be disabused of the above opinion and who can not. He says that, if those who adopt the foregoing opinions do so not because of any reasoning, in the sense that they do not assume anything because they are obstinate, and do not inquire into the reasons for the things that they say but stubbornly adhere to the opinions which they hold, it is not easy for them to give up an opinion of this kind. For every argument and every demonstration comes about in this way, namely, by admitting the truth of some statement and investigating the reason for it. But those who admit nothing destroy discussion and every rational argument; and thus no appeal of reason can be addressed to them whereby they can be dislodged from their error. Sed si aliqui sunt, qui dubitant propter aliquos defectus, puta, quia non bene aliqua intelligunt, facile est obviare tali errori, solvendo ea quae faciunt in eis dubitationem. Et hoc palam ex praedictis, in quibus solvit dubitationes, quae poterant ad praedictam positionem inducere. 2242. But if there are any who are perplexed because of certain deficiencies (for example, because they do not understand some things well), it is easy to dispel such an error by removing the difficulties which puzzle them. This is evident from the previous discussion in which he deals with the difficulties that could lead to the above-mentioned opinion. 2243. It is evident (953). Deinde cum dicit quare manifestum inducit tria corollaria ex dictis. Quorum primum est, quod manifestum est ex praedictis, quod oppositae propositiones non verificantur de eodem secundum unum et idem tempus. Et per consequens ex hoc patet, quod neque etiam contraria possunt simul verificari de eodem. Et hoc ideo, quia omnis contrarietas dicitur secundum privationem; semper enim alterum contrariorum est privatio. Et hoc palam est, siquis velit rationes contrariorum reducere ad primum principium. De ratione enim nigri est privatio albi. Cum igitur privatio sit quaedam negatio habens subiectum determinatum, manifestum est, quod si contraria de eodem verificarentur, oporteret quod affirmatio et negatio simul verificarentur de eodem. Then he draws three corollaries from what has been said. First, it is evident from the foregoing discussion that opposite statements cannot be verified of the same subject at one and the same time. Consequently it is clear from this that contraries cannot be verified of the same subject at the same time. And this is true because every contrariety involves privation; for one of two contraries is always a privation. This becomes evident if one wishes to reduce the definitions of contraries to their first principle; for contained in the notion of black is the privation of white. Since a privation, then, is a kind of negation having a determinate subject, it is evident that, if contraries were true of the same subject, both an affirmation and a negation would have to be true of the same subject at the same time. Non solum autem duo contraria non possunt simul verificari de eodem; sed etiam nullum medium possibile est praedicari de uno et eodem, de quo praedicatur alterum extremorum. Ex his enim quae dicta sunt in decimo, manifestum est quod medium inter contraria est habens privationem utriusque extremorum; sive sit nominatum uno nomine, sive pluribus, sive innominatum. Unde medium inter album et nigrum, ut puta rubeum vel citrinum, habet in sui ratione quod neque sit album neque nigrum. Si quis igitur, aliquo subiecto existente albo, dicat ipsum esse rubeum, simul dicit ipsum esse neque album neque nigrum. Et ita mentitur. Sequitur enim quod id subiectum, simul album sit et non sit. Quod si verum est de illo subiecto, quod sit neque album neque nigrum, oportet quod verificetur de eodem altera pars copulativae, quae contradictoria est eius quod est album esse. Et ita sequitur quod si medium et extremum verificatur de eodem, quod contradictoria de eodem verificentur. 2244. Now, it is not only impossible for two contraries to be true of the same subject at the same time, but it is also impossible for an intermediate to be predicated of one and the same subject of which one of two extremes is predicated; for from what has been said in Book X (880-86-.C 2101-10 it is evident that an intermediate between contraries involves the privation of both extremes, whether it is designated by one word or by many or is nameless. Hence an intermediate between white and black, such as red or yellow, contains in its definition the fact that it is neither white nor black. Therefore, if one says that some subject is red when it is really white, he is saying at the same time that it is neither white nor black. Hence he is in error; for it would follow that that subject is both white and not white at the same time; because if it is true that that subject is neither white nor black, the other part of the copulative proposition may be verified of the same subject, and this is the contradictory of being white. Thus it follows that, if an intermediate and an extreme are true of the same subject, contradictories must be true of the same subject. 2245. One cannot (954). Secundum corollarium ponit ibi neque enim concludit enim quod si affirmatio et negatio non sit simul vera, quod neque opinio Heracliti est vera, neque opinio Anaxagorae. Et quidem de opinione Heracliti patet ex dictis. Unde hoc manifestat de opinione Anaxagorae; dicens, quod si non sit falsa opinio Anaxagorae, sequitur contraria praedicari de eodem. Et per consequens contradictoria. Quod sic patet. Ponebat enim Anaxagoras quodlibet fieri ex quolibet, et omne quod fit, ex aliquo fit. Unde non cogebatur ponere aliquid fieri ex nihilo, et sic ponebat quodlibet esse in quolibet. Cum igitur poneret partem cuiuslibet esse in quolibet, puta partem carnis esse in osse, et partem albi in nigro, et e converso; sequitur quod totum non magis erit dulce quam amarum. Et simile est de aliis contrarietatibus. Et hoc, si pars cuiuslibet est in quolibet toto non solum in potentia, sed in actu et separatim. Hoc autem addidit, quia id quod fit ex aliquo oportet praeexistere in eo potentia, non actu. Et sic contraria praeexistunt in eodem in potentia, non in actu. Et hoc non est esse separatim contraria in aliquo, quia eadem est potentia contrariorum. Sed Anaxagoras nesciebat distinguere inter potentiam et actum. He gives the second corollary. He concludes that, if an affirmation and a negation are not true at the same time, neither the opinion of Heraclitus nor that of Anaxagoras is true. That this is so regarding the opinion of Heraclitus is evident from what has been said. Hence he shows that the same thing applies with respect to the opinion of Anaxagoras. He says that, if Anaxagoras’ opinion is not false, it follows that contraries may be predicated of the same subject, and therefore that contradictories may also be predicated of the same subject. This is shown as follows. Anaxagoras claimed that anything at all comes to be from anything at all, and everything which comes to be comes from something. Hence he was not compelled to maintain that something comes to be from nothing, and thus he claimed that everything is present in everything else. Therefore, since he posited that there is a part of everything in everything else (for example, a part of flesh in bone, and a part of whiteness in blackness, and vice versa), it follows that the whole is no more sweet than bitter. The same holds true of other contrarieties. And this is so if a part of anything is present in any whole not only potentially but actually and separately. And he added this because whatever comes to be from something else must pre-exist in it potentially and not actually. Hence contraries must preexist in the same subject potentially and not actually. This does not mean that contraries exist separately in something, because the potency for contraries is the same. But Anaxagoras did not know how to distinguish between potency and actuality. 2246. And similarly (955). Tertium corollarium ponit ibi, similiter autem. Concludit enim ex praedictis falsam esse utramque opinionem: et illorum qui dixerunt omnes propositiones esse veras; et illorum qui dixerunt omnes falsas. Et hoc manifestum est propter multa difficilia et gravia consequentia ad has opiniones quae collectae sunt, et hic, et superius in quarto. Et specialiter propter hoc, quia si omnes propositiones sunt falsae: qui autem dicit - omnis propositio est falsa - quamdam propositionem dicit. Unde non dicet verum. Et similiter, si omnes propositiones sint verae, ille qui dicit omnes esse falsas, non mentietur, sed dicet verum. Propter quod destruitur positio ponentis omnia esse vera. He gives the third corollary. He concludes from what has been said that both opinions are false, i.e., the opinion of those who said that all statements are true, and the opinion of those who said that all are false. This is evident because of the many difficult and serious conclusions which result from these opinions which have been brought together here and above in Book IV (332-402:C 611-748); and especially “because if all statements are false,” he who says that every statement is false makes a statement and thus does not speak the truth. And similarly if all statements are true, he who says that all are false will not say what is false but will speak the truth. And for this reason the position of one who claims that all statements are true is destroyed.
LESSON 7 Metaphysics Differs from All the Other Sciences
ARISTOTLE’S TEXT Chapter 7: 1063b 36-1064b 14 πᾶσα δ᾽ ἐπιστήμη ζητεῖ τινὰς ἀρχὰς καὶ αἰτίας περὶ ἕκαστον τῶν ὑφ᾽ αὑτὴν ἐπιστητῶν, [1064α]  οἷον ἰατρικὴ καὶ γυμναστικὴ καὶ τῶν λοιπῶν ἑκάστη τῶν ποιητικῶν καὶ μαθηματικῶν. ἑκάστη γὰρ τούτων περιγραψαμένη τι γένος αὑτῇ περὶ τοῦτο πραγματεύεται ὡς ὑπάρχον καὶ ὄν, οὐχ ᾗ δὲ ὄν, ἀλλ᾽ ἑτέρα τις αὕτη παρὰ ταύτας τὰς ἐπιστήμας ἐστὶν ἐπιστήμη. 956. Every science seeks certain principles and causes of each of the knowable objects which comes within its scope; for example, medicine and gymnastics do this, and so does each of the other sciences, productive as well as doctrinal. For each of these marks off for itself some class of things and occupies itself with this as with something that is real and a being, though not as being; but there is a certain other science distinct from these which does this. τῶν δὲ  λεχθεισῶν ἐπιστημῶν ἑκάστη λαβοῦσά πως τὸ τί ἐστιν ἐν ἑκάστῳ γένει πειρᾶται δεικνύναι τὰ λοιπὰ μαλακώτερον ἢ ἀκριβέστερον. λαμβάνουσι δὲ τὸ τί ἐστιν αἱ μὲν δι᾽ αἰσθήσεως αἱ δ᾽ ὑποτιθέμεναι: διὸ καὶ δῆλον ἐκ τῆς τοιαύτης ἐπαγωγῆς ὅτι τῆς οὐσίας καὶ τοῦ τί ἐστιν οὐκ ἔστιν ἀπόδειξις. 957. And each of the sciences mentioned somehow assumes the quiddity in some class of things and tries to prove the rest, with greater or lesser certainty. Some derive the quiddity from sensory perception, and some by assuming it from some other science. Hence from such a process of induction it becomes evident that there is no demonstration of the substance and of its quiddity.  ἐπεὶ δ᾽ ἔστι τις ἡ περὶ φύσεως ἐπιστήμη, δῆλον ὅτι καὶ πρακτικῆς ἑτέρα καὶ ποιητικῆς ἔσται. ποιητικῆς μὲν γὰρ ἐν τῷ ποιοῦντι καὶ οὐ τῷ ποιουμένῳ τῆς κινήσεως ἡ ἀρχή, καὶ τοῦτ᾽ ἔστιν εἴτε τέχνη τις εἴτ᾽ ἄλλη τις δύναμις: ὁμοίως δὲ καὶ τῆς πρακτικῆς οὐκ ἐν τῷ πρακτῷ μᾶλλον δ᾽ ἐν τοῖς  πράττουσιν ἡ κίνησις. ἡ δὲ τοῦ φυσικοῦ περὶ τὰ ἔχοντ᾽ ἐν ἑαυτοῖς κινήσεως ἀρχήν ἐστιν. ὅτι μὲν τοίνυν οὔτε πρακτικὴν οὔτε ποιητικὴν ἀλλὰ θεωρητικὴν ἀναγκαῖον εἶναι τὴν φυσικὴν ἐπιστήμην, δῆλον ἐκ τούτων (εἰς ἓν γάρ τι τούτων τῶν γενῶν ἀνάγκη πίπτειν): 958. Now since there is a science of nature, it is evident that it must differ from both the practical and the productive sciences. For in the case of a productive science the source of motion is in the maker and not in the thing made, and it is either the art or some kind of potency. And similarly in the case of a practical science the motion is not in the thing done but rather in the agents. But the science of the philosopher of nature is concerned with things which have a source of motion in themselves. It is evident from these considerations, then, that the philosophy of nature must be neither practical nor productive but speculative; for it must fall in one of these classes. ἐπεὶ δὲ τὸ τί ἐστιν ἀναγκαῖον  ἑκάστῃ πως τῶν ἐπιστημῶν εἰδέναι καὶ τούτῳ χρῆσθαι ἀρχῇ, δεῖ μὴ λανθάνειν πῶς ὁριστέον τῷ φυσικῷ καὶ πῶς ὁ τῆς οὐσίας λόγος ληπτέος, πότερον ὡς τὸ σιμὸν ἢ μᾶλλον ὡς τὸ κοῖλον. τούτων γὰρ ὁ μὲν τοῦ σιμοῦ λόγος μετὰ τῆς ὕλης λέγεται τῆς τοῦ πράγματος, ὁ δὲ τοῦ κοίλου χωρὶς τῆς ὕλης:  ἡ γὰρ σιμότης ἐν ῥινὶ γίγνεται, διὸ καὶ ὁ λόγος αὐτῆς μετὰ ταύτης θεωρεῖται: τὸ σιμὸν γάρ ἐστι ῥὶς κοίλη. φανερὸν οὖν ὅτι καὶ σαρκὸς καὶ ὀφθαλμοῦ καὶ τῶν λοιπῶν μορίων μετὰ τῆς ὕλης ἀεὶ τὸν λόγον ἀποδοτέον. 959. And since it is necessary that each one of the sciences have some knowledge of the quiddity and must use it as a starting point, we must not fail to consider how the philosophy of nature should define things, and how it should consider the intelligible structure of the substance: whether in the same way as the term snub or rather as the term concave. For of these the notion of snub includes the matter of the object, but that of concave is expressed without matter. For snubness comes into being in a nose, and for this reason its intelligible structure includes matter; for snub is a concave nose. It is evident, then, that the intelligible structure of flesh and of eye and of the other parts of the body must always be given along with matter. ἐπεὶ δ᾽ ἔστι τις ἐπιστήμη τοῦ ὄντος ᾗ ὂν καὶ χωριστόν, σκεπτέον πότερόν ποτε τῇ φυσικῆ  ι τὴν αὐτὴν θετέον εἶναι ταύτην ἢ μᾶλλον ἑτέραν. ἡ μὲν οὖν φυσικὴ περὶ τὰ κινήσεως ἔχοντ᾽ ἀρχὴν ἐν αὑτοῖς ἐστίν, ἡ δὲ μαθηματικὴ θεωρητικὴ μὲν καὶ περὶ μένοντά τις αὕτη, ἀλλ᾽ οὐ χωριστά. περὶ τὸ χωριστὸν ἄρα ὂν καὶ ἀκίνητον ἑτέρα τούτων ἀμφοτέρων τῶν ἐπιστημῶν ἔστι τις, εἴπερ  ὑπάρχει τις οὐσία τοιαύτη, λέγω δὲ χωριστὴ καὶ ἀκίνητος, ὅπερ πειρασόμεθα δεικνύναι. καὶ εἴπερ ἔστι τις τοιαύτη φύσις ἐν τοῖς οὖσιν, ἐνταῦθ᾽ ἂν εἴη που καὶ τὸ θεῖον, καὶ αὕτη ἂν εἴη πρώτη καὶ κυριωτάτη ἀρχή. [1064β]  δῆλον τοίνυν ὅτι τρία γένη τῶν θεωρητικῶν ἐπιστημῶν ἔστι, φυσική, μαθηματική, θεολογική. 960. And since there is a science of being as being and as separable, one must consider whether this science should be held to be the same as the philosophy of nature or rather a science distinct from it. The philosophy of nature deals with things which have a principle of motion in themselves, and mathematics is speculative and is concerned with things which are permanent but are not separable. Therefore there is a science distinct from both of these, which treats of what is separable and immovable; that is to say, if there is some such substance, and I mean one which is separable and immovable, as we shall attempt to prove (1055-76). And if there is some such nature among existing things, this will exist somewhere and will be divine, and it will be the primary and highest principle. It is evident, then, that there are three classes of speculative science: the philosophy of nature, mathematics and theology. βέλτιστον μὲν οὖν τὸ τῶν θεωρητικῶν γένος, τούτων δ᾽ αὐτῶν ἡ τελευταία λεχθεῖσα: περὶ τὸ τιμιώτατον  γάρ ἐστι τῶν ὄντων, βελτίων δὲ καὶ χείρων ἑκάστη λέγεται κατὰ τὸ οἰκεῖον ἐπιστητόν. 961. The class of speculative sciences, then, is the highest, and of these the last mentioned is highest of all. For it is concerned with the noblest of beings, and each science is said to be higher or lower by reason of its proper object. ἀπορήσειε δ᾽ ἄν τις πότερόν ποτε τὴν τοῦ ὄντος ᾗ ὂν ἐπιστήμην καθόλου δεῖ θεῖναι ἢ οὔ. τῶν μὲν γὰρ μαθηματικῶν ἑκάστη περὶ ἕν τι γένος ἀφωρισμένον ἐστίν, ἡ δὲ καθόλου κοινὴ περὶ πάντων. εἰ μὲν οὖν  αἱ φυσικαὶ οὐσίαι πρῶται τῶν ὄντων εἰσί, κἂν ἡ φυσικὴ πρώτη τῶν ἐπιστημῶν εἴη: εἰ δ᾽ ἔστιν ἑτέρα φύσις καὶ οὐσία χωριστὴ καὶ ἀκίνητος, ἑτέραν ἀνάγκη καὶ τὴν ἐπιστήμην αὐτῆς εἶναι καὶ προτέραν τῆς φυσικῆς καὶ καθόλου τῷ προτέραν.  962. However, one might raise the question whether the science of being as being is universal or not. For each of the mathematical sciences deals with some one determinate class of things, but a universal science is common to all. If, then, natural substances are the primary beings, the philosophy of nature must be the primary science. But if there is another nature and substance which is separable and immovable, the science which treats of this must be different from and prior to the philosophy of nature, and must be universal because it is prior (902). COMMENTARY Postquam philosophus ostendit de quibus sit consideratio huius scientiae, hic comparat istam scientiam ad alias. Et circa hoc tria facit. Primo ostendit quid sit proprium particularium scientiarum. Secundo ostendit differentiam particularium scientiarum adinvicem, ibi, quoniam autem est quaedam. Tertio comparat istam ad alias, ibi, quoniam autem est quaedam entis scientia. 2247. Having shown with what things this science is concerned, here the Philosopher compares this science with the others. In regard to this he does three things. First (956:C 2247), he indicates what is proper to the particular sciences. Second (958:C 2252), he shows how the particular sciences differ from one another (“Now since”). Third (960:C 2259), he compares this science with the others (“And since there is”). Circa primum duo facit, secundum duo, quae dicit pertinere ad particulares scientias. Dicit ergo primo, quod omnis scientia particularis quaerit aliqua principia et causas, circa proprium scibile quod sub ipsa continetur. Dicit autem - aliqua principia et causas,- quia non omnis scientia considerat omne genus causae. In treating the first member of this division he does two things, insofar as there are two characteristics which he says pertain to the particular sciences. He accordingly says, first (956), that every particular science seeks certain principles and causes of the proper object of knowledge which comes within its scope. He says certain principles and causes because not every science considers every class of cause. Et ponit exemplum de medicativa quae est circa sanitatem, et de exercitativa quae est circa exercitia ordinata ad bonam valetudinem corporis; et similiter de qualibet scientia alia, sive sit factiva idest practica, sive doctrinalis idest theorica; quia unaquaeque harum scientiarum particularium circumscribit et accipit sibi aliquod determinatum genus entis, circumscribens illud et dividens ab aliis entibus, et de illo solo determinans. Negociatur enim circa hoc genus entis quasi circa aliquod ens, sed non inquantum est ens. Sed hoc, scilicet considerare de ente inquantum est ens, pertinet ad quamdam scientiam quae est alia praeter omnes scientias particulares. 2248. He gives as an example the science of medicine, whose object is health, and the art of gymnastics, whose object is physical exercise directed to the well-being of the body. The same thing holds true of any of the other sciences, whether they are “productive,” i.e., practical, or “doctrinal,” i.e., theoretical; because each of these particular sciences marks off and takes as its own some determinate class of being inasmuch as it confines itself to that class and deals with it alone. For it is concerned with that class of being as a certain kind of being, though not as being. But to consider this, namely, being as being, belongs to a science which differs from all of the particular sciences. 2249. And each (957). Secundo ibi, dictarum autem ponit aliud pertinens ad particulares scientias; dicens quod unaquaeque praedictarum scientiarum particularium supponit aliqualiter quod quid est, in quocumque genere consideretur. Unde et in primo posteriorum dictum est, quod de subiecto oportet supponere, et quia est, et quid est. Et hoc supposito, scilicet quod quid est, quo quaelibet scientia utitur tamquam medio ad demonstrandum aliqua sicut passiones et huiusmodi, tentat demonstrare aut debilius aut certius, quia in quibusdam scientiis est certior modus demonstrandi sicut in mathematicis, in quibusdam autem debilior sicut in naturalibus. Second, he gives another characteristic of the particular sciences. He says that each of the above-mentioned particular sciences somehow assumes the quiddity in whatever class of things is considered. Hence it has been stated at the beginning of the Posterior Analytics that it is necessary to assume both the existence and quiddity of the subject. And having assumed this, i.e., the quiddity, which every science uses as a middle term to demonstrate certain things, such as properties and the like, it tries to demonstrate these with greater or lesser certainty; because some sciences have a more certain method of demonstrating, as the mathematical sciences, and others a less certain one, as the natural sciences. Et quia dixerat quod aliae scientiae aliqualiter supponunt quod quid est, ideo subiungit quod quaedam scientiae sumunt quod quid est per sensum, inquantum ex accidentibus sensibilibus deveniunt in cognitionem essentiae rei. Quaedam vero sumunt quod quid est, supponentes ab aliis scientiis, sicut particulares ab universalibus. 2250. And since he had said that other sciences somehow assume the quiddity, he therefore adds that some sciences derive the quiddity from sensory perception inasmuch as they acquire a knowledge of a thing’s essence from sensible accidents, and that others derive the quiddity by assuming it from other sciences, as particular sciences from universal ones. Et sic manifestum est quod in scientiis particularibus non est demonstratio de substantia rei, nec de eo quod quid est. Utrumque igitur horum de quibus particulares scientiae non se intromittunt, pertinet ad universalem scientiam, idest considerare de substantia et ente et quidditate rei. 2251. Thus it is evident that in the particular sciences there is no demonstration of the substance or the quiddity of a thing. Hence both of the things with which the particular sciences do not concern themselves, i.e., a consideration of the substance or being and its quiddity, pertain to a universal science. 2252. Now since (958). Deinde cum dicit quoniam autem ostendit differentiam particularium scientiarum abinvicem. Et primo scientiae naturalis ad scientias operativas. Secundo scientiae mathematicae ad naturalem, ibi, quoniam autem quod quid est. Then he shows how the particular sciences differ from one another. First (958:C 2252), he shows how the philosophy of nature differs from the productive sciences; and second (959:C 2256), how the mathematical sciences differ from the philosophy of nature (“And since it is necessary”). Dicit ergo primo, quod cum sit quaedam particularis scientia de natura, oportet quod sit altera a practica, idest activa et factiva. Omnis enim scientia operativa, vel est activa, vel factiva. He accordingly says, first (958), that, since there is a particular science of nature, it must be different “from the practical,” i.e., from the sciences which govern activity and from those which govern production; for every practical science is either a science of action or a science of production.
Ad quam differentiam cognoscendam sumendum est, quod supra in nono habitum est, scilicet quod agere et facere differunt. Nam agere proprie dicitur secundum operationem quae permanet in agente, et non transit in materiam exteriorem; sicut intelligere et sentire et huiusmodi. Facere autem est secundum operationem transeuntem in materiam exteriorem, quae permutatur; sicut calefacere, secare et alia. Est ergo scientia activa, ex qua instruimur ad recte exercendum operationes, quae actiones dicuntur; sicut est scientia moralis. Factiva autem scientia est, per quam recte aliquid facimus; sicut ars fabrilis, et alia huiusmodi. 2253. In order to understand this difference we must consider a distinction which was made above in Book IX (790:C 1864), namely, that to act and to make differ; for to act is said properly of an operation which remains in the agent and does not pass over into some external matter, for instance, to understand and to perceive and so on. But to make or produce is said of an operation which passes over into some external matter which is changed, for example, to heat and to cut and the like. Hence there is a science of activity by which we are instructed how to perform correctly those operations which are called actions; and moral science is such. But that science by which we make something correctly is a productive science. The art of carpentry and the like belong to this class. Ab utraque autem harum operativarum scientiarum scientia naturalis altera est; quia factivae scientiae non habent principium motus in facto, sed in faciente. Et hoc principium est sicut ars, quae est principium sicut dirigens, sive potentia aliqua quae est principium sicut exequens. Et similiter scientiae practicae, idest activae, non habent principium motus in eo in quod agitur, sed magis in agentibus. 2254. Now the philosophy of nature differs from each of these sciences which govern operations; for the productive sciences do not have a principle of motion in the thing made but in the maker, and this principle is either the art, which is a directive principle, or some potency which is the principle executing the work. Similarly “the practical sciences,” i.e., those governing activity, do not have a principle of motion in that upon which the activity is exercised but rather in the agents. Sed illa quae pertinent ad considerationem scientiae naturalis, sunt habentia principium motus in ipsis, cum natura sit principium motus in eo in quo est. Manifestum est igitur quod scientia naturalis non est activa neque factiva, sed speculativa. Necesse est enim quod scientia naturalis cadat in unum aliquod horum generum, scilicet activa vel factiva vel speculativa. Unde, si non sit activa vel factiva, sequitur quod sit speculativa. 2255. But those things which belong to the consideration of the philosophy of nature have their principles of motion in themselves, since nature is a principle of motion in the thing in which it exists. It is evident, then, that the philosophy of nature is a science neither of action nor of production but is speculative. For the philosophy of nature must fall into one of these classes, i.e., active, productive or speculative science. Hence, if it is a science neither of action nor of production, it follows that it must be speculative. 2256. And since (959). Deinde cum dicit quoniam autem ostendit differentiam mathematicae ad naturalem; et dicit, quod cum ita sit quod necessarium sit unicuique scientiarum cognoscere aliqualiter quod quid est, et uti eo quasi principio ad demonstrandum, oportet quod secundum diversum modum definitionis diversificentur scientiae. Et ita ad cognoscendum qualiter scientia naturalis differat ab aliis, oportet non latere quem modum servet naturalis in definiendo, et qualiter sit sumenda definitio in scientia naturali; utrum scilicet sicut definitur simum, aut sicut definitur concavum. Then he shows how the mathematical sciences differ from the philosophy of nature. He says that, since each of the sciences must somehow come to know the quiddity and must use this as a starting point with a view to demonstrating, the sciences must be distinguished on the basis of a different method of defining. Hence in order to understand how the philosophy of nature differs from the other sciences we must not neglect to consider the method which the philosophy of nature uses in defining things, and how the definition should be considered in the philosophy of nature; that is, whether a thing should be defined in the way that snub is or in the way that concave is. Definitio autem simi est cum materia sensibili. Sed definitio concavi est sine materia sensibili. Quia enim simitas non est nisi circa determinatam materiam sensibilem, quia non est nisi in naso: propter hoc ratio simi oportet quod accipiatur cum materia sensibili. Haec est enim definitio simi simus est nasus concavus. Sed in definitione concavi sive curvi non ponitur aliqua materia sensibilis. Sicut igitur in definitione simi ponitur materia sensibilis, ita oportet quod in definitione carnis et oculi, et aliarum partium, reddatur materia sensibilis. Et similiter est de aliis rebus naturalibus. 2257. Now the definition of snub includes sensible matter, but that of concave does not; for since snubness is found only in a definite sensible matter, because it is found only in a nose, the intelligible structure of snub must therefore include sensible matter; for snub is defined thus: snub is a concave nose. Sensible matter, however, is not included in the definition of concave or curved. Hence, just as sensible matter is included in the definition of snub, so too it must be included in the definition of flesh and of eye and of the other parts of the body. The same holds true of other natural beings. Et ex hoc accipitur differentia inter mathematicam et scientiam naturalem; quia naturalis scientia est de his in quorum definitionibus ponitur materia sensibilis. Mathematica vero est de aliis, in quorum definitionibus non ponitur materia sensibilis, licet habeant esse in materia sensibili. 2258. The difference between the philosophy of nature and mathematics is taken from this, because the philosophy of nature deals with those things whose definitions include sensible matter, whereas mathematics deals with those things whose definitions do not include sensible matter, although they have being in sensible matter. 2259. And since there is (960). Deinde cum dicit quoniam autem comparat istam scientiam ad alias scientias particulares. Et circa hoc tria facit. Primo comparat istam scientiam ad alias scientias particulares, quantum ad modum separationis. Secundo quantum ad nobilitatem, ibi, optimum quidem genus et cetera. Tertio quantum ad universalitatem, ibi, dubitabit autem. Then he compares this science with the other particular sciences; and in regard to this he does three things. First (960:C 2259), he compares this science with the different particular sciences in reference to the way in which their objects are separate from matter. Second (961:C 2265), he compares them from the viewpoint of nobility (“The class of speculative sciences”). Third (962:C 2265), he compares them from the viewpoint of universality (“However, one”). Dicit ergo primo, quod est quaedam scientia de ente inquantum est separabile; non enim solum pertinet ad hanc scientiam determinare de ente in communi, quod est determinare de ente inquantum est ens; sed etiam pertinet determinare de entibus separatis a materia secundum esse. Unde considerandum est, utrum ista scientia ad quam pertinent haec duo, sit eadem cum scientia naturali, aut altera ab ea. He accordingly says, first (960), that there is a science of being insofar as it is separable; for it is the office of this science not only to establish the truth about being in common (and this is to establish the truth about being as being) but also to establish the truth about things which are separate from matter in being. Hence it is necessary to consider whether this science whose function is to consider these two things is the same as the philosophy of nature or differs from it. Et quod sit altera, manifestat: quia scientia naturalis est circa ea quae habent in seipsis principium motus; et sic oportet quod naturalia habeant determinatam materiam, quia nihil movetur nisi quod habet materiam. Sed mathematica speculatur circa immobilia; quia ea quorum ratio accipitur sine materia sensibili, oportet quod eodem modo eorum ratio sit sine motu, cum motus non sit nisi in sensibilibus. 2260. That it differs from the philosophy of nature he makes clear as follows: the philosophy of nature is concerned with things which have a principle of motion in themselves; therefore natural things must have a definite matter, because only that which has matter is moved. But mathematics studies immovable things; for those things whose intelligible structure does not include sensible matter must likewise not have motion in their intelligible structure, since motion is found only in sensible things. Sed haec de quibus considerat mathematica, non sunt separabilia a materia et motu secundum esse, sed solum secundum rationem. Oportet igitur quod circa illud ens, quod est separatum a materia et motu secundum esse et omnino immobile, sit quaedam scientia alia, et a mathematica, et a naturali. 2261. But those things which mathematics considers are not separable from matter and motion in being but only in their intelligible structure. Hence the science which treats that kind of being which is separable from matter and from motion and is immovable in every respect must be one which differs both from mathematics and from the philosophy of nature. Et hoc dico si tamen sit aliqua talis substantia praeter sensibilia, quae sit omnino immobilis. Et hoc dicit, quia nondum est probatum aliquam talem substantiam esse. Sed hoc ostendere intendit. 2262. He says here, “if there is some such substance” apart from sensible substances which is immovable in every respect. He says this because the existence of some such substance has not yet been proved, although he intends to prove this. Si autem est aliqua talis natura in entibus, scilicet quae sit separabilis et immobilis, oportet quod talis natura sit alicubi, idest quod attribuatur alicui substantiae. Et id quod habet istam naturam erit quoddam divinum, et quoddam principalissimum omnium; quia quanto aliquid est simplicius et formalius in entibus, tanto est nobilius et prius et magis causa aliorum. Et sic patet quod haec scientia quae considerat huiusmodi entia separabilia, debet vocari scientia divina, et scientia de primis principiis. 2263. And if there is some such nature among existing things, i.e., one which is separable and immovable, it is necessary that “such a nature exist somewhere,” i.e., that it be attributed to some substance. And whatever has this nature must be something that is divine and the highest of all; because the simpler and more actual a being is, the nobler it is and the more it is prior and a cause of other things. Thus it is evident that the science which considers separate beings of this kind should be called the divine science and the science of first principles. Et ex hoc ulterius concludit, quod tria sunt genera speculativarum scientiarum: scilicet naturalis quae considerat ea mobilia, quae in sui definitione materiam sensibilem recipiunt; et mathematica quae considerat immobilia, quae non recipiunt materiam sensibilem in sui definitione, licet habeant esse in materia sensibili; et theologia quae est circa entia penitus separata. 2264. From this he again concludes that there are three classes of speculative science: the philosophy of nature, which considers things that are movable and have sensible matter in their definition; mathematics, which considers immovable things that do not have sensible matter in their definition yet exist in sensible matter; and theology, which considers beings that are entirely separate from matter. 2265. The class (961). Deinde cum dicit optimum quidem comparat istam ad alias secundum nobilitatem; et dicit, quod scientiae speculativae sunt nobilissimae inter omnes alias scientias, quia in eis quaeritur scire propter seipsum, in scientiis autem operativis quaeritur scire propter opus. Et in scientiis speculativis ultima, scilicet theologia, cum sit circa nobiliora entia, est nobilior. Tanto enim unaquaeque scientia nobilior est, quanto eius scibile nobilius fuerit. Next he compares this science with the others from the viewpoint of nobility. He says that the speculative sciences are the noblest, because of all the sciences the speculative seek knowledge for its own sake, whereas the practical seek knowledge for the sake of some work. And among the speculative sciences there is one that, is highest, namely, theology, since a science which deals with more noble beings is itself more noble; for a science is more noble in proportion to the greater nobility of its object. 2266. However, one might (962). Deinde cum dicit dubitabit autem comparat istam scientiam ad alias quantum ad universalitatem; et dicit: dubitabile est, utrum istam scientiam, quae est circa entia separabilia, oporteat poni universalem scientiam entis, inquantum est ens, aut non: et ostendit, quod sic, quasi per divisionem. Then he compares this science with the others from the viewpoint of universality. He says that one might raise the question whether or not the science which deals with separate beings must be held to be a universal science of being as being; and that it must be such he shows by a process of elimination. Manifestum est enim, quod praedictae scientiae operativae non sunt universales. Et ideo eas praetermittit. Sed inter speculativas scientias, manifestum est, quod quaelibet mathematicarum scientiarum est circa unum aliquod genus determinatum: universalis autem scientia communiter de omnibus est: unde nulla mathematicarum scientiarum est communis omnium entium. Sed de naturali manifestum est; quia si naturales substantiae, quae sunt substantiae sensibiles et mobiles, sunt primae inter entia, oportet quod naturalis scientia sit prima inter scientias; quia secundum ordinem subiectorum, est ordo scientiarum, ut iam dictum est. Si autem est alia natura et substantia praeter substantias naturales, quae sit separabilis et immobilis, necesse est alteram scientiam ipsius esse, quae sit prior naturali. Et ex eo quod est prima, oportet quod sit universalis. Eadem enim est scientia quae est de primis entibus, et quae est universalis. Nam prima entia sunt principia aliorum. 2267. For it is evident that the foregoing sciences which deal with operations are not universal sciences, and he therefore omits them. In the case of the speculative sciences it is evident that every mathematical science is concerned with some one determinate class of things. But a universal science deals with all things in common. No mathematical science, then, can be the one which treats all beings in common. Regarding the philosophy of nature it is evident that, if natural substances, which are perceptible and movable, are the primary beings, the philosophy of nature must be the primary science; because the order of the sciences corresponds with that of their subjects, as has been stated already (961:C 2265). But if there is a different nature and substance over and above natural substances, which is separable and immovable, there must be a science which differs from the philosophy of nature and is prior to it. And because it is first, it must be universal; for it is the same science which treats of primary beings and of what is universal, since the primary beings are the principles of the others.
LESSON 8 No Science of Accidental Being
ARISTOTLE’S TEXT Chapter 8: 1064b 15-1065b 4 ἐπεὶ δὲ τὸ ἁπλῶς ὂν κατὰ πλείους λέγεται τρόπους, ὧν εἷς ἐστὶν ὁ κατὰ συμβεβηκὸς εἶναι λεγόμενος, σκεπτέον πρῶτον περὶ τοῦ οὕτως ὄντος. 963. Since the term being in its unqualified sense has many meanings, and one of these is the accidental, it is first necessary to consider this sense of being. ὅτι μὲν οὖν οὐδεμία τῶν παραδεδομένων ἐπιστημῶν πραγματεύεται περὶ τὸ συμβεβηκός, δῆλον (οὔτε γὰρ οἰκοδομικὴ σκοπεῖ τὸ συμβησόμενον τοῖς τῇ  οἰκίᾳ χρησομένοις, οἷον εἰ λυπηρῶς ἢ τοὐναντίον οἰκήσουσιν, οὔθ᾽ ὑφαντικὴ οὔτε σκυτοτομικὴ οὔτε ὀψοποιική, τὸ δὲ καθ᾽ αὑτὴν ἴδιον ἑκάστη τούτων σκοπεῖ τῶν ἐπιστημῶν μόνον, τοῦτο δ᾽ ἐστὶ τὸ οἰκεῖον τέλος: 964. Now it is evident that none of the traditional sciences are concerned with the accidental. The science of building does not consider what will happen to the occupants of a house, for example, whether they will dwell there unhappily or in the opposite way; nor is the art of weaving or of shoemaking or of cooking concerned with it. But each of these sciences considers only what is proper to itself, and this is its particular end. [οὐδὲ μουσικὸν καὶ γραμματικόν,] οὐδὲ τὸν ὄντα μουσικὸν ὅτι γενόμενος γραμματικὸς ἅμα ἔσται τὰ  ἀμφότερα, πρότερον οὐκ ὤν, ὃ δὲ μὴ ἀεὶ ὂν ἔστιν, ἐγένετο τοῦτο, ὥσθ᾽ ἅμα μουσικὸς ἐγένετο καὶ γραμματικός, τοῦτο δὲ οὐδεμία ζητεῖ τῶν ὁμολογουμένως οὐσῶν ἐπιστημῶν πλὴν ἡ σοφιστική: περὶ τὸ συμβεβηκὸς γὰρ αὕτη μόνη πραγματεύεται, διὸ Πλάτων οὐ κακῶς εἴρηκε φήσας τὸν σοφιστὴν  περὶ τὸ μὴ ὂν διατρίβειν): 965. Further, no science considers a man insofar as he is a musician or also a grammarian; nor does any science consider the quibble that “when one who is a musician has become a grammarian he will be both at the same time, although he was not so before; but that which is and has not always been, must have come to be; and therefore he must have at the same time become both a musician and a grammarian.” None of the known sciences are concerned with this except sophistry, and thus Plato was not wrong in saying that sophistry is concerned with non-being. ὅτι δ᾽ οὐδ᾽ ἐνδεχόμενόν ἐστιν εἶναι τοῦ συμβεβηκότος ἐπιστήμην, φανερὸν ἔσται πειραθεῖσιν ἰδεῖν τί ποτ᾽ ἐστὶ τὸ συμβεβηκός. πᾶν δή φαμεν εἶναι τὸ μὲν ἀεὶ καὶ ἐξ ἀνάγκης (ἀνάγκης δ᾽ οὐ τῆς κατὰ τὸ βίαιον λεγομένης ἀλλ᾽ ᾗ χρώμεθα ἐν τοῖς κατὰ τὰς ἀποδείξεις),  τὸ δ᾽ ὡς ἐπὶ τὸ πολύ, τὸ δ᾽ οὔθ᾽ ὡς ἐπὶ τὸ πολὺ οὔτ᾽ ἀεὶ καὶ ἐξ ἀνάγκης ἀλλ᾽ ὅπως ἔτυχεν: οἷον ἐπὶ κυνὶ γένοιτ᾽ ἂν ψῦχος, ἀλλὰ τοῦτ᾽ οὔτ᾽ [ὡς] ἀεὶ καὶ ἐξ ἀνάγκης οὔθ᾽ ὡς ἐπὶ τὸ πολὺ γίγνεται, συμβαίη δέ ποτ᾽ ἄν. [1065α]  ἔστι δὴ τὸ συμβεβηκὸς ὃ γίγνεται μέν, οὐκ ἀεὶ δ᾽ οὐδ᾽ ἐξ ἀνάγκης οὐδ᾽ ὡς ἐπὶ τὸ πολύ. τί μὲν οὖν ἐστὶ τὸ συμβεβηκός, εἴρηται, διότι δ᾽ οὐκ ἔστιν ἐπιστήμη τοῦ τοιούτου, δῆλον: ἐπιστήμη μὲν γὰρ πᾶσα τοῦ  ἀεὶ ὄντος ἢ ὡς ἐπὶ τὸ πολύ, τὸ δὲ συμβεβηκὸς ἐν οὐδετέρῳ τούτων ἐστίν. 966. That it is impossible to have a science of the accidental will be evident to those who are trying to learn what the accidental is. Accordingly, we say of all things that some are always and of necessity (not necessity in the sense of what is done by force but with the meaning used in matters of demonstration); others are for the most part; and others are neither for the most part nor always and of necessity, but are such as occur by chance. For example, there might be cold weather during the dog days, but this occurs neither always and of necessity nor for the most part, though it might happen sometimes. Hence the accidental is what occurs, but neither always and of necessity nor for the most part. What the accidental is, then, has been stated; and it is evident that there is no science of it. For every science deals with what is always or for the most part, but the accidental belongs to neither of these. ὅτι δὲ τοῦ κατὰ συμβεβηκὸς ὄντος οὐκ εἰσὶν αἰτίαι καὶ ἀρχαὶ τοιαῦται οἷαίπερ τοῦ καθ᾽ αὑτὸ ὄντος, δῆλον: ἔσται γὰρ ἅπαντ᾽ ἐξ ἀνάγκης. εἰ γὰρ τόδε μὲν ἔστι τοῦδε ὄντος τόδε δὲ τοῦδε, τοῦτο δὲ μὴ ὅπως ἔτυχεν ἀλλ᾽ ἐξ  ἀνάγκης, ἐξ ἀνάγκης ἔσται καὶ οὗ τοῦτ᾽ ἦν αἴτιον ἕως τοῦ τελευταίου λεγομένου αἰτιατοῦ (τοῦτο δ᾽ ἦν κατὰ συμβεβηκός), ὥστ᾽ ἐξ ἀνάγκης ἅπαντ᾽ ἔσται, καὶ τὸ ὁποτέρως ἔτυχε καὶ τὸ ἐνδέχεσθαι καὶ γενέσθαι καὶ μὴ παντελῶς ἐκ τῶν γιγνομένων ἀναιρεῖται. κἂν μὴ ὂν δὲ ἀλλὰ γιγνόμενον τὸ  αἴτιον ὑποτεθῇ, ταὐτὰ συμβήσεται: πᾶν γὰρ ἐξ ἀνάγκης γενήσεται. ἡ γὰρ αὔριον ἔκλειψις γενήσεται ἂν τόδε γένηται, τοῦτο δ᾽ ἐὰν ἕτερόν τι, καὶ τοῦτ᾽ ἂν ἄλλο: καὶ τοῦτον δὴ τὸν τρόπον ἀπὸ πεπερασμένου χρόνου τοῦ ἀπὸ τοῦ νῦν μέχρι αὔριον ἀφαιρουμένου χρόνου ἥξει ποτὲ εἰς τὸ ὑπάρχον, ὥστ᾽  ἐπεὶ τοῦτ᾽ ἔστιν, ἅπαντ᾽ ἐξ ἀνάγκης τὰ μετὰ τοῦτο γενήσεται, ὥστε πάντα ἐξ ἀνάγκης γίγνεσθαι. 967. It is also evident that there are no causes and principles of accidental being such as there are of essential being; for if there were, everything would be of necessity. For if one thing exists when another does, and this again when something else does, and if this last thing is not a matter of chance but exists of necessity, then that of which it was the cause will also exist of necessity, and so on right down to the last thing said to be caused. But this was assumed to be accidental. Hence everything will be of necessity, and the possibility of anything happening by chance or being contingent and of coming to be or not coming to be will be entirely removed from the sphere of things which are generated. And if the cause is assumed not to exist but to be something which is coming to be, the same results will follow; for everything will come to be of necessity. For tomorrow’s eclipse will occur if something else does, and this again if some other thing occurs, and the latter if still another thing occurs. And if time is subtracted in this way from the limited time between the present and tomorrow, we shall at some point reach something which exists now. Therefore, since this exists, everything which comes after it will occur of necessity, so that everything will occur of necessity. τὸ δ᾽ ὡς ἀληθὲς ὂν καὶ κατὰ συμβεβηκὸς τὸ μέν ἐστιν ἐν συμπλοκῇ διανοίας καὶ πάθος ἐν ταύτῃ (διὸ περὶ μὲν τὸ οὕτως ὂν οὐ ζητοῦνται αἱ ἀρχαί, περὶ δὲ τὸ ἔξω ὂν καὶ χωριστόν): τὸ δ᾽ οὐκ  ἀναγκαῖον ἀλλ᾽ ἀόριστον, λέγω δὲ τὸ κατὰ συμβεβηκός: τοῦ τοιούτου δ᾽ ἄτακτα καὶ ἄπειρα τὰ αἴτια. 968. Regarding being in the sense of what is true and accidental being, the former depends upon the combination which the mind makes and is a modification of it. It is for this reason that it is not the principles of this kind of being that are sought but of that which exists outside the mind and is separable; and the latter kind of being is not necessary but indeterminate (and by this I mean the accidental); and the causes. of this kind of being are indeterminate and unordered (543-59). τὸ δὲ ἕνεκά του ἐν τοῖς φύσει γιγνομένοις ἢ ἀπὸ διανοίας ἐστίν, τύχη δέ ἐστιν ὅταν τι τούτων γένηται κατὰ συμβεβηκός: ὥσπερ γὰρ καὶ ὄν ἐστι τὸ μὲν καθ᾽ αὑτὸ τὸ δὲ κατὰ συμβεβηκός, οὕτω  καὶ αἴτιον. ἡ τύχη δ᾽ αἰτία κατὰ συμβεβηκὸς ἐν τοῖς κατὰ προαίρεσιν τῶν ἕνεκά του γιγνομένοις, 969. And that for the sake of which something exists is found both in things which come to be by nature and in those which are a result of mind. It is luck when one of these comes about accidentally; for just as a being is either essential or accidental, so also is a cause. And luck is an accidental cause of those things which come to be for some end as a result of choice. διὸ περὶ ταὐτὰ τύχη καὶ διάνοια: προαίρεσις γὰρ οὐ χωρὶς διανοίας. 970. And for this reason both luck and mind are concerned with the same thing; for there is no choice without mind. τὰ δ᾽ αἴτια ἀόριστα ἀφ᾽ ὧν ἂν γένοιτο τὰ ἀπὸ τύχης, διὸ ἄδηλος ἀνθρωπίνῳ λογισμῷ καὶ αἴτιον κατὰ συμβεβηκός, ἁπλῶς δ᾽  οὐδενός. 971. However, the causes from which some lucky result comes to be are indeterminate; and for this reason luck is uncertain for human knowledge and is an accidental cause, although in an absolute sense it is a cause of nothing. ἀγαθὴ δὲ τύχη καὶ κακὴ ὅταν ἀγαθὸν ἢ φαῦλον ἀποβῇ: εὐτυχία δὲ καὶ δυστυχία περὶ μέγεθος τούτων. 972. There is good or bad luck when the result is good or bad, and prosperity or misfortune when this occurs on a large scale. [1065β]  ἐπεὶ δ᾽ οὐθὲν κατὰ συμβεβηκὸς πρότερον τῶν καθ᾽ αὑτό, οὐδ᾽ ἄρ᾽ αἴτια: εἰ ἄρα τύχη ἢ τὸ αὐτόματον αἴτιον τοῦ οὐρανοῦ, πρότερον νοῦς αἴτιος καὶ φύσις.  973. And since nothing accidental is prior to things which are essential, neither are accidental causes prior. Therefore, if luck or chance is the cause of the heavens, mind and nature are prior causes. COMMENTARY Postquam philosophus recollegit ea quae praedicta erant de consideratione huius scientiae, hic incipit recolligere ea quae dicta sunt tam in sexto huius, quam in libro physicorum de ente imperfecto. Et primo de ente per accidens. Secundo de motu, ibi, est autem. 2268. After having restated in a summary way the points that were discussed before with regard to this science’s field of study, here the Philosopher begins to summarize the things that were said about imperfect being both in Book VI (543-559:C 1171-1244) of this work and in the Physics. He does this, first (963:C 2268), with regard to accidental being; and second (974:C 2289), with regard to motion (“One thing”). Circa primum duo facit. Primo ponit ea quae dicta sunt de ente per accidens. Secundo ea quae dicta sunt de causa per accidens, ibi, quod autem gratiae huius. In treating the first member of this division he does two things. First, he states the things that have been said about accidental being. Second (969:C 2284), he states those that pertain to an accidental cause (“And that for the sake”). Circa primum duo facit. Primo dicit de quo est intentio; dicens quod quia ens simpliciter, idest communiter acceptum multis modis dicitur, inter quos unus modus est secundum quod dicitur ens per accidens, ut puta cum dicimus musicum esse album, quae quidem in quinto superius manifesta sunt: prius quam dicatur de ente per se, considerandum est de ente per accidens; ut huiusmodi ente remoto, absolutior fiat sermo de ente per se. In regard to the first he does two things. First (963), he points out what he intends to do. He says that, since, “being in its unqualified sense,” i.e., taken in general, has many meanings, of which one is the accidental (as when we say, for example, that the musician is white), and these have been explained above in Book V (435-39:C 885-97), we ought to consider accidental being before we deal with essential being, so that when this kind of being has been disposed of we may speak in a more positive way of essential being. 2269. Now it is evident (964). Deinde cum dicit quod quidem secundo prosequitur quod proposuit. Et circa hoc duo facit. Primo ostendit quod ad nullam scientiam pertinet considerare de ente per accidens. Secundo removet huiusmodi ens, et ens quod significat veritatem propositionis, a consideratione huius scientiae, ibi, quod autem ut vere. Second, he proceeds to carry out his plan; and in regard to this he does two things. First (964:C 2269), he shows that the consideration of accidental being belongs to no science. Second (968:C 2283), he excludes both this kind of being and the being which signifies the truth of a proposition from this science’s field of study (“Regarding being”). Circa primum duo facit. Primo ostendit quod nulla scientia considerat de ente per accidens. Secundo, quod nec considerare potest, ibi, quod autem neque contingens. In treating the first he does two things. First, he shows that no science considers accidental being; and second (966:C 2276), that none can do so (“That it is impossible”). Circa primum duo facit. Primo inducendo manifestat quod nulla scientia considerat de ente per accidens; dicens manifestum esse quod nulla scientia tradita a nobis negociatur circa accidens. In regard to the first he does two things. First (964), he shows by a process of elimination that no science considers accidental being. He says that no one of the sciences treated by us is concerned with the accidental. Non autem accipitur hic accidens pro eo quod est in aliquo genere accidentis, sicut albedo est quoddam accidens. Sunt enim multae scientiae quae circa huiusmodi accidentia sunt; quia huiusmodi accidentia, et secundum se habent speciem quamdam et causas determinatas in subiecto; et accidentia dicuntur, quia non per se, sed in alio habent esse. Accipitur autem hic accidens pro ente per accidens; sicut album esse musicum est per accidens. Huiusmodi enim neque aliquam speciem habent in se, neque aliquam causam determinatam. Et circa huiusmodi ens non negociatur aliqua scientia. Et hoc manifestat inducendo. 2270. Now accidental here does not mean something in one of the categories of accidents, in the sense that whiteness is an accident; for there are many sciences which deal with accidents of this kind, because such accidents have a certain species of themselves and certain determinate causes in their subject. And they are called accidents because they do not have being of themselves but exist in something else.—But here accidental means what happens accidentally; for example, it is accidental that a musician is white. For accidents of this kind do not have any species or any determinate cause. And no science is concerned with this kind of being. He proves this by induction. Ars enim aedificativa non considerat quid per accidens eveniat habitantibus in domo quam facit, utrum accidat eis aliquod triste, aut habitabunt ibi contrarie, idest prospere. Hoc enim accidit domui. Similiter ars textiva non considerat quid accidat utentibus panno texto; neque coriaria quid accidat utentibus calceis; neque coquinaria de his quae per accidens se habent ad cibum, puta quis eo utatur ad superfluitatem vel ad necessitatem tantum. Sed unaquaeque harum scientiarum considerat id quod solum est proprium sibi, et subiectum, et per se accidentia eius. Et in hoc est finis considerationis cuiuslibet scientiae. 2271. For the art of building does not consider what happens accidentally to the occupants of the house which it builds, whether they happen to experience some unhappiness there or live there “in the opposite way,” i.e., happily; for this is accidental to a house. Similarly, the art of weaving does not consider what happens to those who use the cloth which has been woven; nor does the art of shoemaking consider what happens to those who use shoes; nor does the art of cooking consider what happens to the food, for example, whether someone uses too much of it or just what is necessary. But each of these sciences considers only what is proper to itself, i.e., its subject and the properties of its subject. This is the goal of any science. 2272. Further, no science (965). Secundo ibi, neque inquantum assignat causam quare nulla scientia considerat ea quae per accidens sunt. Ratio enim est, quia quod per accidens est, non est proprie ens, sed magis non ens, sicut non est per se et proprie unum. Nam unum et ens convertuntur. Omnis autem scientia est de ente. Unde relinquitur quod nulla scientia sit de eo quod est per accidens. Second, he gives the reason why no science considers things which are accidental. It is because the accidental is not a being in the proper sense but is rather a non-being inasmuch as it is not essentially and properly one; for one and being are convertible. Now every science deals with being, and therefore it follows that no science is concerned with the accidental. Dicit ergo, quod musicus est etiam grammaticus, non inquantum est musicus. Et si contingat de aliquo qui sit musicus, quod fiat grammaticus, non simul factus est ambo, grammaticus scilicet et musicus, cum prius non fuerit utrumque. Sed si aliquod ens est modo, et non fuit semper ens, oportet quod sit factum. Si igitur hoc quod dico - musicus est grammaticus - est quoddam ens, cum non semper fuerit, sequitur quod simul sit utrumque factum, scilicet musicum et album; quia cuiuslibet entis est aliqua generatio. Unde, cum non simul facta sint, manifestum est quod hoc totum quod est musicum grammaticum, non est aliquod unum et ens. 2273. Hence he says that a musician is also a grammarian, but not inasmuch as he is a musician. And if it happens that one who is a musician becomes a grammarian, he has become both at the same time, i.e., both a grammarian and a musician, although he was not so before. But if some being exists now and was not always a being, it must have come to be. Therefore, if “a musician grammarian” is a kind of being, since it did not always exist it must have become both at the same time, i.e., both a musician and a grammarian, because any being admits of some generation. Hence, since these have not come to be at the same time, it is evident that this whole—a musician-grammarian—is not one being. Nec est instantia de hoc quod in generatione substantiarum praeexistit materia, quae est ingenita; quia forma non fit proprie, sed compositum, ut in septimo probatum est. Materia autem praeexistit non quasi ens actu, sed potentia tantum. Hic autem musicus praeexistit in actu. Cum igitur ille qui erat musicus fit grammaticus, est generatio grammatici tantum, non autem totius, quod est musicum grammaticum. Unde hoc totum non est aliquid unum et ens. 2274. Nor should it be urged that matter, which is ungenerated, has existence prior to the generation of substances; for it is not the form that properly comes to be but the composite, as has been proved in Book VII (611:C 1423). Now matter does not have prior existence as an actual being but only as a potential one. But here the musician has actual prior existence. Therefore, since he who was a musician has become a grammarian, only a grammarian has come to be, and not the whole-a grammarian musician. Hence this whole is not one being. Et propter hoc, nulla scientia, quae est vere scientia, et certitudinem habet, considerat de ente per accidens. Sed sola sophistica circa ipsum negociatur, et ad decipiendum utitur eo quod est per accidens, ac si per se esset. Unde fit fallacia accidentis, quae est efficacissima ad decipiendum etiam sapientem, ut dicitur in primo elenchorum. Unde Plato non male dixit, dicens quod versatur circa non ens, quia versatur circa ens per accidens. 2275. For this reason no science that is truly a science and attains certainty is concerned with accidental being. Only sophistry deals with it; and it uses the accidental as though it were something of itself in order to deceive. From this there arises the fallacy of accident, which is most effective in deceiving even those who are wise, as is stated in Book I of the Sophistical Refutations. Hence Plato was not wrong in saying that sophistry is concerned with non-being, because it deals with the accidental. 2276. That it is impossible (966). Deinde cum dicit quod autem ostendit, quod etiam non possit esse consideratio alicuius scientiae de ente per accidens; et hoc dupliciter facit. Primo ex definitione de ente per accidens; dicens quod manifestum erit, quod non contingit esse scientiam de ente per accidens, si consideremus quid sit ens per accidens. Ad quod considerandum utitur quadam divisione trimembri: dicens quod eorum quae dicuntur esse, quaedam sunt semper et ex necessitate: non quidem secundum quod necessitas pro violentia sumitur, sed secundum quod utimur necessitate in demonstrationibus, puta dicentes necessarium esse quod triangulus habet tres angulos aequales duobus; sic enim necessarium dicimus quod impossibile est non esse. Quaedam vero sunt ut in pluribus, sicut quod homo nascatur cum quinque digitis in manibus: hoc enim non semper est ex necessitate, cum contingat aliquem nasci cum sexto digito; sed est ut in pluribus. Quaedam vero nec sunt ut in pluribus, neque semper ex necessitate, sed contingenter eveniunt; sicut si frigus fiat sub cane, idest in diebus canicularibus. Sed non semper et ex necessitate neque in pluribus, sed tamen quandoque accidit etiam huiusmodi ens. Quia autem raro accidit, et non semper et ex necessitate, neque ut in pluribus, vocatur ens per accidens. He shows that it is impossible for any science to consider accidental being, and he does this in two ways. First, he proceeds from the definition of accidental being. He says that, if we consider what accidental being is, it will be evident that there can be no science of it. With a view to proving his point he makes a tripartite division. He says that of things which are said to be there are some which are always and of necessity (not necessity in the sense of force, but in the sense used in demonstrations, as when we say that a triangle necessarily has three angles equal to two right angles; for we use the term necessary in this way to mean what cannot be otherwise). There are others which are for the most part; for example, a man is born with five fingers on each hand. This does not happen always, since it does happen that some are born with six fingers, but it does happen for the most part. And there are others which are neither always and of necessity nor for the most part but are such as occur by chance; for example, “there might be cold weather during the dog days,” i.e., during the days of the dog-star. This occurs neither always and of necessity nor for the most part, though even this kind of being sometimes occurs. But since it happens rarely, and not always and of necessity or for the most part, it is called accidental being. Quae enim semper vel in pluribus contingunt, vel ita se habent quod unum est causa alterius; vel ambo reducuntur in unam causam quae per se est causa utriusque. Et utroque modo contingunt. Si quidem causa indeficienter producit effectum suum, erit quod dicitur ex necessitate. Si autem possunt deficere propter aliquod impedimentum, erit ut in pluribus. 2277. For things which occur either always or for the most part are such that one is the cause of the other or both are referred to one cause which is the proper cause of each. And they occur in both ways. If a cause produces its effect without fail, the effect will be one that is said to be of necessity. But if a cause can fail because of some obstacle, the effect will be one that occurs for the most part. Si autem ita sit quod duorum unum non sit causa alterius, neque habeant unam causam per se communem, quae coniungat ea simul, eorum coniunctio erit raro. Sicut in hoc quod dico musicum aedificare. Nam aedificationis causa non est a musica, sed ab arte aedificativa, quae est omnino alia a musica. Similiter est in praemisso exemplo. Nam quod sit fervor caloris sub cane, est a sole appropinquante nobis. Quod autem sit frigus, est ex aliqua alia causa, puta ex Saturno, aliquo modo coniuncto soli. Unde hoc est per accidens, quod sole dies caniculares faciente, frigus sit. 2278. But if it so happens in the case of two things that one is not the cause of the other and there is no single common proper cause which links them together, they will seldom be combined. Such is the case, for example, when we say “the musician builds”; for the cause of building is not the art of music but that of building, which differs completely from the art of music. The same thing is true of the previous example; for excessive heat during the dog days is a result of the sun moving closer to the earth; but that there should be cold weather at this time is a result of some other cause, such as Saturn’s being somehow connected with the sun. Hence, if there is cold weather during the dog days, which are caused by the sun, this is accidental. Sic igitur manifestum est quod est ens per accidens; quia neque quod est in maiori parte, neque quod est semper. Omnis autem scientia est de eo quod semper, aut in plus, ut probatum est in primo posteriorum. Unde manifestum est, quod scientia non potest esse de eo quod est per accidens. 2279. It is evident, then, that the accidental is what occurs neither always nor for the most part. But every science is concerned with what occurs either always or for the most part, as has been proved in Book I of the Posterior Analytics. Thus it is clear that there can be no science of the accidental. 2280. It is also evident (967). Secundo ibi, quod autem inducit, ad idem manifestandum, quod ens per accidens non habet causas et principia talia, qualia habet ens per se; et sic de eo non potest esse scientia, cum omnis scientia sit ex principiis et causis. Quod quidem sic probat. Quia si ens per accidens haberet per se causas, omnia essent ex necessitate. Entia enim per se talem causam habent, qua posita, de necessitate sequitur effectus. Et si aliqua causa sit ad quam non de necessitate sequitur effectus, sed ut in pluribus, hoc est propter impedimentum, quod per accidens contingit. Et sic, si ens per accidens tollatur a rebus, omnis causa per se, de necessitate inducet suum effectum. Sic ergo si ens per accidens de necessitate habet causam per se, qua posita ex necessitate sequitur effectus, licet forte eam poni non sit necessarium, nihilominus tamen sequitur quod omnia ex necessitate eveniant. Quod sic patet. Second, with a view to making the same point he says that accidental being has no causes and principles such as essential being has; and thus there can be no science of it, since every science is concerned with principles and causes. He proves this as follows: if accidental being should have proper causes, everything would happen of necessity; for essential beings have a cause such that when it is placed the effect necessarily follows. And if there were some cause from which an effect did not follow of necessity but only for the most part, this would be a result of some obstacle, which can be accidental. If, then, accidental being had a necessary proper cause, so that when this cause is placed its effect necessarily follows (although perhaps it is not necessary to place it), the result would be that everything happens of necessity. He proves this as follows. Sit enim aliquid praeteritum vel praesens quod sit causa futuri effectus. Hoc quidem iam positum est. Sed posita causa, ut tu dicis, ex necessitate sequitur effectus. Si igitur hoc praesens vel praeteritum, quod iam positum est, est causa huius entis futuri, et illud alterius, non quocumque modo, sed ita quod ex necessitate sequatur effectus. Posita enim causa, ex necessitate erit illud cuius causa iam posita est, et hoc usque ad ultimum causatum. Sed hoc ponebatur esse per accidens. Et sic quod ponebatur per accidens, erit ex necessitate. Unde sequitur quod omnia sint ex necessitate, et quod a rebus auferatur, quod ad utrumque contingit, idest quod est casuale fortuitum, et accidere, idest ens per accidens. Et fieri et non fieri, idest possibile esse et non esse, vel fieri et non fieri. 2281. Let us suppose that something past or present is the cause of a future effect, and that this cause has already been placed. But when the cause has been placed, as you say, the effect necessarily follows. Therefore, if this past or present thing which has already been placed is the cause of this future effect, and this in turn is the cause of another, the effect will follow not in just any way at all but necessarily. For once the cause has been placed, that whose cause has been placed will necessarily follow, and so on right down to the last thing caused. But this was assumed to be accidental. Therefore that which was assumed to be accidental will happen of necessity. Consequently, everything will happen of necessity; and “the possibility of anything happening by chance,” i.e., any fortuitous event, “or being contingent,” i.e., being accidental, and “of coming to be or not coming to be,” i.e., the possibility of anything being or not being, or being generated or not being generated, will be completely removed from the world. Sed quia posset aliquis obviare huic rationi, dicendo, quod causa futurorum contingentium non est iam posita ut praesens et praeterita, sed adhuc est contingens ut futura, et propter hoc effectus sunt adhuc contingentes, consequenter hanc obviationem removet, ibi, et si non existens, dicens quod eadem inconvenientia accident, si ponatur quod causa futurorum contingentium non sit iam ens quasi praesens vel praeterita, sed quae in fieri et quasi futura. Sequitur enim quod omnia ex necessitate accidant sicut et prius. Si enim causa illa futura sit, oportet quod sit futura in aliquo tempore determinato, et determinate distincto a praesenti nunc; puta cras. Si ergo eclipsis, quae est per se causa quorumdam futurorum accidentium, sit futura cras, et omne quod fit, fit ex aliqua causa, oportet quod ipsa eclipsis, quae est futura cras, fiat si hoc fuerit, idest propter aliquid praeexistens, et hoc iterum propter aliud; et sic semper propter anticipationem, vel ablationem causarum, auferetur aliquid a tempore, quod est inter praesens nunc et eclipsim futuram. Unde, cum illud tempus sit finitum, et omne finitum consumatur ablato quodam, quandoque erit devenire ad aliquam causam nunc existentem. Quare, si illa iam ponitur, omnes futuri effectus consequuntur ex necessitate. Et ita omnia ex necessitate evenient. Ergo, cum hoc sit impossibile, manifestum est quod ea quae sunt per accidens, non habent causam determinatam, qua posita, ex necessitate consequantur. Ea autem omnia quae circa hoc dici possunt, supra in sexto posita sunt. 2282. But because one can meet this argument by saying that the cause of future contingent events has not yet been placed as either present or past but is still contingent and future, and that for this reason its effects are still contingent, he therefore throws out this objection (“And if the cause”). He points out that the same unreasonable conclusion follows if it is held that the cause of future contingent events is not something that already exists in the present or in the past but is something that is coming to be and is future, because it will follow that everything happens of necessity, as has been stated before. For if that cause is future, it must be going to be at some definite time, tomorrow say, and must be quite distinct from the present. Therefore, if an eclipse, which is the proper cause of certain future events, will occur tomorrow, and everything that occurs is a result of some cause, tomorrow’s eclipse must occur “if something else does,” i.e., because of something that existed before, and this in turn because of something else. Thus by always anticipating or subtracting causes some part of the time between the present moment and the future eclipse will be removed. And since that time is limited, and every limited thing is used up when some part of it is removed, we shall therefore reach at some point some cause which exists now. Hence, if that cause is already posited, all future effects will follow of necessity; and thus everything will occur of necessity. But since this is impossible, it is therefore evident that things which are accidental have no determinate cause from which they necessarily follow once it has been placed. Everything that can be said about this has been given in Book VI (543-552:C 1171-90). 2283. Regarding being (968). Deinde cum dicit quod autem ostendit, quod ens per accidens, et ens quod significat veritatem propositionis, praetermittendum est in ista scientia; dicens, quod est quoddam ens quod est ut vere ens, idest quod significat veritatem propositionis, quae in compositione consistit, et est per accidens. Sed primum consistit in compositione intellectus, et est quaedam passio circa operationem animae. Unde huiusmodi entis non quaeruntur principia in scientia, quae considerat de ente quod est extra animam, et est separabile, ut supra dictum est. Aliud autem, scilicet ens per accidens, non est necessarium, sed indeterminatum; et ideo non habet causam ordinatam; sed eius sunt infinitae causae et non habentes ordinem adinvicem. Et ideo de tali ente non considerat ista scientia. Then he shows that accidental being and the being which signifies the truth of a proposition must be omitted from this science. He says that there is one kind of being, “being in the sense of what is true,” or being as signifying the truth of a proposition, and it consists in combination; and there is accidental being.’ The first consists in the combination which the intellect makes and is a modification in the operation of the intellect. Hence the principles of this kind of being are not investigated in the science which considers the kind of being that exists outside of the mind and is separable, as has been stated. The second, i.e., accidental being, is not necessary but indeterminate. Hence it does not have a related cause but an infinite number of causes that are not related to one another. Therefore this science does not consider such being. 2284. And that for the sake (969). Deinde cum dicit quod autem colligit hoc quod dictum est de causa per accidens, scilicet de fortuna, in secundo physicorum. Et dicit hic quatuor circa fortunam. Primo quid sit. Et ad hoc investigandum praemittit, quod id quod est gratia huius, idest aliquid esse propter finem, invenitur et in his quae sunt secundum naturam, et in his quae sunt ab intellectu. Et hoc manifestum est in secundo physicorum. Et adiungit quod fortuna est in his quae fiunt propter aliquid, sed secundum accidens. Sicut enim invenitur ens per se et ens per accidens, ita et causa per se et causa per accidens. Sic igitur fortuna est causa per accidens in his quae fiunt gratia huius, idest propter finem, non quidem a natura, sed secundum electionem. Sicut si aliquis eligat fodere in agro ut plantet arborem, et invenit thesaurum, hoc dicimus esse per accidens, quia est praeter intentionem. Et hoc est a fortuna. Here he summarizes the things that have been said about an accidental cause, or luck, in Book II of the Physics. There are four points. First, he states what it is; and with a view to investigating this he prefaces his remarks with the statement, “And that for the sake of which,” i.e., what exists for the sake of some end, is found both in those things which exist by nature and in those which are a result of mind. This is evident in Book II of the Physics. He adds that luck is found in those things which occur for the sake of some end, but that it is accidental. For just as we find both essential being and accidental being, so too we find essential causes and accidental causes. Luck, then, is an accidental cause “of those things which come to be for the sake of some end,” i.e., some goal, not by nature but by choice. For example, when someone chooses to dig in a field in order to plant a tree and thereupon discovers a treasure, we say that this is accidental because it is unintended. And this happens by luck. 2285. And for this reason (970). Secundo ibi, propter quod ostendit in quibus sit fortuna; et dicit, quod cum electio non sit nisi a mente vel intellectu, oportet, quod circa eadem sit fortuna et intellectus. Unde in rebus carentibus ratione non est fortuna, sicut plantae, lapides et bruta animalia. Neque etiam est in pueris qui carent usu rationis. Second, he shows in what instances luck exists. He says that, since there is choice only where there is mind or thought, luck and thought must be concerned with the same thing. Hence luck is not found in those things which lack reason, such as plants, stones and brute animals, or in children who lack the use of reason. 2286. However, the causes (971). Tertio ibi, causae autem ostendit, quod fortuna est incerta; dicens, quod infinitae sunt causae, a quibus aliquid potest fieri a fortuna, sicut patet in exemplo posito. Potest enim aliquis invenire thesaurum fodiens in terra, vel ad plantandum, vel ad faciendum sepulchrum, et propter infinita alia. Et quia omne infinitum est ignotum, ideo fortuna est incerta humanae cognitioni. Et dicitur esse causa secundum accidens. Nullius autem est causa simpliciter et per se. Third, he shows that luck is uncertain. He says that there are an infinite number of causes by which something can happen by luck, as is evident in the examples given; for one can find a treasure by digging in the earth either to plant something or to make a grave or for an infinite number of other reasons. And since everything infinite is unknown, luck is therefore uncertain for human knowledge. And it is called an accidental cause, although absolutely and of itself it is the cause of nothing. 2287. There is good (972). Quarto ibi, bona autem ostendit qualiter fortuna dicitur bona vel mala; et dicit quod dicitur bona vel mala ex eo quod bonum et malum fortuito evenit. Sed si sit magnum bonum quod fortuito evenit, dicitur eufortunium. Si sit magnum malum, dicitur infortunium. Fourth, he explains why luck is said to be good or bad. He points out that luck is said to be good or bad because the accidental result is good or bad. And if the accidental result is a great good, it is then called prosperity; and if a great evil, it is then called misfortune. 2288. And since nothing (973). Quinto ibi, quoniam autem ostendit quod fortuna non est prima causa rerum. Nullum enim per accidens est prius his quae sunt secundum se. Unde neque causa per accidens est prior ea quae est per se. Et sic, si fortuna et casus quae sunt causae per accidens, sint causa caeli, oportet quod per prius sint causae intellectus et natura, quae sunt causae per se. Fifth, he shows that luck is not the primary cause of things; for nothing that is accidental is prior to things that are essential. Hence an accidental cause is not prior to a proper cause. Thus, if luck and chance, which are accidental causes, are the causes of the heavens, mind and nature, which are proper causes, must be prior causes.
LESSON 9 The Definition of Motion
ARISTOTLE’S TEXT Chapter 9: 1065b 5-1066a 34 1 ἔστι δὲ τὸ μὲν ἐνεργείᾳ μόνον τὸ δὲ δυνάμει τὸ δὲ δυνάμει καὶ ἐνεργείᾳ, τὸ μὲν ὂν τὸ δὲ ποσὸν τὸ δὲ τῶν λοιπῶν. οὐκ ἔστι δέ τις κίνησις παρὰ τὰ πράγματα: μεταβάλλει γὰρ ἀεὶ κατὰ τὰς τοῦ ὄντος κατηγορίας, κοινὸν δ᾽ ἐπὶ τούτων οὐδέν ἐστιν ὃ οὐδ᾽ ἐν μιᾷ κατηγορίᾳ. ἕκαστον δὲ διχῶς  ὑπάρχει πᾶσιν (οἷον τὸ τόδε—τὸ μὲν γὰρ μορφὴ αὐτοῦ τὸ δὲ στέρησις—καὶ κατὰ τὸ ποιὸν τὸ μὲν λευκὸν τὸ δὲ μέλαν, καὶ κατὰ τὸ ποσὸν τὸ μὲν τέλειον τὸ δὲ ἀτελές, καὶ κατὰ φορὰν τὸ μὲν ἄνω τὸ δὲ κάτω, ἢ κοῦφον καὶ βαρύ): ὥστε κινήσεως καὶ μεταβολῆς τοσαῦτ᾽ εἴδη ὅσα τοῦ ὄντος. 974. One thing is actual only, another potential, and others both actual and potential; and of these one is a being, another a quantity, and another one of the other categories. Motion is not something apart from things themselves; for a thing is always changed according to the categories of being, and there is nothing that is common to these and in no one category. And each belongs to all its members in a twofold way, for example, this particular thing; for sometimes this is the form of a thing and sometimes its privation. And with regard to quality, one thing is white and another black; and with regard to quantity, one is perfect and another imperfect; and with regard to motion in space, one thing tends upwards and another downwards, or one is light and another heavy. Hence there are as many kinds of motion and change as there are of being. διῃρημένου  δὲ καθ᾽ ἕκαστον γένος τοῦ μὲν δυνάμει τοῦ δ᾽ ἐντελεχείᾳ, τὴν τοῦ δυνάμει ᾗ τοιοῦτόν ἐστιν ἐνέργειαν λέγω κίνησιν. 975. Now since each class of things is divided by potentiality and actuality, I call motion the actualization of what is potential as such. ὅτι δ᾽ ἀληθῆ λέγομεν, ἐνθένδε δῆλον: ὅταν γὰρ τὸ οἰκοδομητόν, ᾗ τοιοῦτον αὐτὸ λέγομεν εἶναι, ἐνεργείᾳ ᾖ, οἰκοδομεῖται, καὶ ἔστι τοῦτο οἰκοδόμησις: ὁμοίως μάθησις, ἰάτρευσις, βάδισις,  ἅλσις, γήρανσις, ἅδρυνσις. συμβαίνει δὲ κινεῖσθαι ὅταν ἡ ἐντελέχεια ᾖ αὐτή, καὶ οὔτε πρότερον οὔθ᾽ ὕστερον. ἡ δὴ τοῦ δυνάμει ὄντος, ὅταν ἐντελεχείᾳ ὂν ἐνεργῇ, οὐχ ᾗ αὐτὸ ἀλλ᾽ ᾗ κινητόν, κίνησίς ἐστιν. 976. That our account is true becomes evident as follows: when the buildable in the sense in which we call it such actually exists, it is being built; and this is the process of building. The same is true of learning, walking, healing, dancing and bereaving. And motion occurs when something is in this very act, and neither before nor after. Motion, then, belongs to what is potential when it is actual and is engaged in activity, not inasmuch as it is itself, but inasmuch as it is movable. λέγω δὲ τὸ ᾗ ὧδε. ἔστι γὰρ ὁ χαλκὸς δυνάμει ἀνδριάς: ἀλλ᾽ ὅμως οὐχ ἡ τοῦ  χαλκοῦ ἐντελέχεια, ᾗ χαλκός, κίνησίς ἐστιν. οὐ γὰρ ταὐτὸν χαλκῷ εἶναι καὶ δυνάμει τινί, ἐπεὶ εἰ ταὐτὸν ἦν ἁπλῶς κατὰ τὸν λόγον, ἦν ἂν ἡ τοῦ χαλκοῦ ἐντελέχεια κίνησίς τις. οὐκ ἔστι δὲ ταὐτό (δῆλον δ᾽ ἐπὶ τῶν ἐναντίων: τὸ μὲν γὰρ δύνασθαι ὑγιαίνειν καὶ δύνασθαι κάμνειν οὐ ταὐτόν—καὶ γὰρ  ἂν τὸ ὑγιαίνειν καὶ τὸ κάμνειν ταὐτὸν ἦν—τὸ δ᾽ ὑποκείμενον καὶ ὑγιαῖνον καὶ νοσοῦν, εἴθ᾽ ὑγρότης εἴθ᾽ αἷμα, ταὐτὸ καὶ ἕν). ἐπεὶ δὲ οὐ τὸ αὐτό, ὥσπερ οὐδὲ χρῶμα ταὐτὸν καὶ ὁρατόν, ἡ τοῦ δυνατοῦ καὶ ᾗ δυνατὸν ἐντελέχεια κίνησίς ἐστιν. 977. And by the phrase inasmuch as I mean this: bronze is potentially a statue, but the actuality of bronze inasmuch as it is bronze is not motion; for to be bronze and to be some potentiality are not the same. If they were absolutely the same in meaning, the actuality of bronze would be a kind of motion; but they are not the same. This is evident in the case of contraries; for the potentiality of being healed and that of being ill are not the same, because being). healed would then be the same as being ill. But it is the subject which is both healed and ill, whether it be moisture or blood, that is one and the same. And since they are not the same, just as color and the visible object are not the same, it is the actualization of what is potential insofar as it is potential that is motion.  ὅτι μὲν οὖν ἐστιν αὕτη, καὶ ὅτι συμβαίνει τότε κινεῖσθαι ὅταν  ἡ ἐντελέχεια ᾖ αὐτή, καὶ οὔτε πρότερον οὔθ᾽ ὕστερον, δῆλον (ἐνδέχεται γὰρ ἕκαστον ὁτὲ μὲν ἐνεργεῖν ὁτὲ δὲ μή, [1066α]  οἷον τὸ οἰκοδομητὸν ᾗ οἰκοδομητόν, καὶ ἡ τοῦ οἰκοδομητοῦ ἐνέργεια ᾗ οἰκοδομητὸν οἰκοδόμησίς ἐστιν: ἢ γὰρ τοῦτό ἐστιν, ἡ οἰκοδόμησις, ἡ ἐνέργεια, ἢ οἰκία: ἀλλ᾽ ὅταν οἰκία ᾖ, οὐκέτι οἰκοδομητόν,  οἰκοδομεῖται δὲ τὸ οἰκοδομητόν: ἀνάγκη ἄρα οἰκοδόμησιν τὴν ἐνέργειαν εἶναι, ἡ δ᾽ οἰκοδόμησις κίνησίς τις, ὁ δ᾽ αὐτὸς λόγος καὶ ἐπὶ τῶν ἄλλων κινήσεων): 978. That motion is this, and that a thing is being moved when it is actual in this way, and neither before nor after, is evident. For each thing is capable of being at one time actual and at another not, for example, the buildable as buildable; and the actualization of the buildable as buildable is the process of building. For the actuality is either the process of building or this particular house. But when the house exists, it will no longer be buildable; but what is being built is what is buildable. Therefore the process of building must be its actualization; and the process of building is a kind of motion. The same reasoning also applies to other motions. ὅτι δὲ καλῶς εἴρηται, δῆλον ἐξ ὧν οἱ ἄλλοι λέγουσι περὶ αὐτῆς, καὶ ἐκ τοῦ μὴ ῥᾴδιον εἶναι διορίσαι ἄλλως αὐτήν. οὔτε γὰρ ἐν ἄλλῳ  τις γένει δύναιτ᾽ ἂν θεῖναι αὐτήν: 979. That this account is true is evident from what others say about motion, and because it is not easy to define it otherwise. For one cannot place it in another class. δῆλον δ᾽ ἐξ ὧν λέγουσιν: οἱ μὲν γὰρ ἑτερότητα καὶ ἀνισότητα καὶ τὸ μὴ ὄν, 980. This is evident from what some say; for they call it otherness and inequality and non-being. ὧν οὐδὲν ἀνάγκη κινεῖσθαι, ἀλλ᾽ οὐδ᾽ ἡ μεταβολὴ οὔτ᾽ εἰς ταῦτα οὔτ᾽ ἐκ τούτων μᾶλλον ἢ τῶν ἀντικειμένων. 981. However, no one of these is necessarily moved, and change is not to these or from these anymore than to or from their opposites. αἴτιον δὲ τοῦ εἰς ταῦτα τιθέναι ὅτι ἀόριστόν τι δοκεῖ εἶναι ἡ κίνησις, τῆς  δ᾽ ἑτέρας συστοιχίας αἱ ἀρχαὶ διὰ τὸ στερητικαὶ εἶναι ἀόριστοι: οὔτε γὰρ τόδε οὔτε τοιόνδε οὐδεμία αὐτῶν οὔτε τῶν λοιπῶν κατηγοριῶν. 982. The reason for putting motion in this class is that it seems to be something indefinite; and the principles in one of the columns of opposites (60) are indefinite because they are privative, for no one of them is either a this or such or any of the other categories. τοῦ δὲ δοκεῖν ἀόριστον εἶναι τὴν κίνησιν αἴτιον ὅτι οὔτ᾽ εἰς δύναμιν τῶν ὄντων οὔτ᾽ εἰς ἐνέργειαν ἔστι θεῖναι αὐτήν: οὔτε γὰρ τὸ δυνατὸν ποσὸν εἶναι κινεῖται ἐξ  ἀνάγκης, οὔτε τὸ ἐνεργείᾳ ποσόν, ἥ τε κίνησις ἐνέργεια μὲν εἶναι δοκεῖ τις, ἀτελὴς δέ: αἴτιον δ᾽ ὅτι ἀτελὲς τὸ δυνατὸν οὗ ἐστὶν ἐνέργεια. καὶ διὰ τοῦτο χαλεπὸν αὐτὴν λαβεῖν τί ἐστιν: ἢ γὰρ εἰς στέρησιν ἀνάγκη θεῖναι ἢ εἰς δύναμιν ἢ εἰς ἐνέργειαν ἁπλῆν, τούτων δ᾽ οὐδὲν φαίνεται ἐνδεχόμενον, ὥστε  λείπεται τὸ λεχθὲν εἶναι, καὶ ἐνέργειαν καὶ [μὴ] ἐνέργειαν τὴν εἰρημένην, ἰδεῖν μὲν χαλεπὴν ἐνδεχομένην δ᾽ εἶναι. 983. The reason why motion seems to be indefinite is that it cannot be identified either with the potentiality or with the actuality of existing things; for neither what is capable of having a certain quantity nor what actually has it is necessarily being moved. And motion seems to be an actuality, but an incomplete one; and the reason for this is that the potentiality of which it is the actuality is incomplete. Hence it is difficult to grasp what motion is; for it must be put under privation or under potentiality or under simple actuality; but none of these appear to be possible. It remains, then, that it must be as we have said, i.e., both an actuality and a non-actuality as explained, which is difficult to see but capable of existing.’ καὶ ὅτι ἐστὶν ἡ κίνησις ἐν τῷ κινητῷ, δῆλον: ἐντελέχεια γάρ ἐστι τούτου ὑπὸ τοῦ κινητικοῦ. 984. That motion belongs to the thing moved is evident; for it is the actualization of the thing moved by what is capable of causing motion. καὶ ἡ τοῦ κινητικοῦ ἐνέργεια οὐκ ἄλλη ἐστίν. δεῖ μὲν γὰρ εἶναι ἐντελέχειαν ἀμφοῖν: 985. And the actuality of what is capable of causing motion is no other than this; for it must be the actuality of both. κινητικὸν  μὲν γάρ ἐστι τῷ δύνασθαι, κινοῦν δὲ τῷ ἐνεργεῖν, 986. And a thing is capable of causing motion because of its power, but it is a mover because of its activity. ἀλλ᾽ ἔστιν ἐνεργητικὸν τοῦ κινητοῦ, ὥσθ᾽ ὁμοίως μία ἡ ἀμφοῖν ἐνέργεια 987. But it is on the thing moved that it is capable of acting. Thus the actuality of both alike is one. ὥσπερ τὸ αὐτὸ διάστημα ἓν πρὸς δύο καὶ δύο πρὸς ἕν, καὶ τὸ ἄναντες καὶ τὸ κάταντες, ἀλλὰ τὸ εἶναι οὐχ ἕν: ὁμοίως δὲ καὶ ἐπὶ τοῦ κινοῦντος καὶ κινουμένου.  988. And it is one just as the distance from one to two and that from two to one are the same, and just as what goes up and what comes down are the same, although their being is not one. The same applies in the case of the mover and the thing moved. COMMENTARY Postquam determinavit philosophus de ente per accidens, hic determinat de motu. Et dividitur in partes tres. In prima determinat de motu secundum se. In secunda de infinito quod est quaedam passio motus et aliorum continuorum, ibi, infinitum autem. In tertia determinat de divisione motus in suas species, ibi, praetermittatur autem. 2289. Having settled the issue about accidental being, the Philosopher now states his views about motion; and this is divided into three parts. First (974:C 2289), he deals with motion in itself; second (989:C 2314), with infinity, which is a property of motion and of other continuous things (“The infinite”); and third (1005:C 2355), with the division of motion into its species (“Everything which is changed”). Prima dividitur in partes duas. In prima ostendit quid sit motus. In secunda ostendit in quo sit, ibi, et quod est in mobili. The first is divided into two parts. First, he explains what motion is; and second (984:C 2308), he points out what the subject of motion is (“That motion”). Circa primum tria facit. Primo praemittit quaedam quasi necessaria ad definiendum motum. Secundo distinguit ipsum, ibi, diviso autem et cetera. Tertio probat definitionem bene esse assignatam, ibi, quod autem bene. In regard to the first he does three things. First, he prefaces his discussion with some points which are necessary for defining motion. Second (975:C 2294), he defines’ motion (“Now since each”). Third (979:C 2299), he proves that the definition of motion is a good one (“That this account”). Circa primum ponit quatuor, ex quibus concludit quintum. Quorum primum est, quod ens dividitur per actum et potentiam. Et hoc est quod dicit, quod entium quoddam est actu, sicut primum movens, quod Deus est; quoddam potentia tantum, ut materia prima, quoddam potentia et actu, sicut omnia intermedia. Vel esse actu tantum dicit id quod iam perfecte habet formam, puta quod perfecte iam est album. Est autem potentia tantum, quod nondum habet formam; puta, quod nullo modo est album. Actu autem et potentia est, quod etsi nondum perfecte habet formam, est tamen in moveri ad formam. In treating the first member of this division he gives four points from which he infers a fifth. The first is that being is divided by actuality and by potentiality. He says that one kind of being is actual only, such as the prime mover, which is God; another is potential only, such as prime matter; and others are both potential and actual, as all intermediate things. Or by the phrase actual only he means what already has a form completely, as what is now completely white; and by potential only, what does not have a form, as what is not white in any way; and by potential and actual, what does not yet have a form completely but is being moved to a form. Secundum est quod ens dividitur per decem praedicamenta: et hoc est quod dicit, quod entium quoddam est per se, idest substantia; quoddam est quantum, quoddam quale, et sic de aliis generibus. 2290. The second point is that being is divided by the ten categories, as is implied when he says that there is one kind of being which exists of itself, i.e., substance, and another is quantity, and another is quality, and so on for the other categories. Tertium est quod motus non habet aliquam aliam naturam separatam a rebus aliis; sed unaquaeque forma secundum quod est in fieri, est actus imperfectus qui dicitur motus. Hoc enim ipsum est moveri ad albedinem, quod est albedinem incipere actu fieri in subiecto. Sed non debet esse in actu perfecto. Et hoc est quod dicit quod motus non est aliquid praeter res; omne enim quod mutatur, mutatur secundum praedicamenta entis. Et sicut non est aliquid commune decem praedicamentis quod sit genus eorum, ita non est aliquod genus commune omnium motuum. Et propter hoc motus non est aliquod unum praedicamentum distinctum ab aliis praedicamentis; sed sequitur alia praedicamenta. 2291. The third point is that motion does not have a distinct nature separate from other things; but every form insofar as it is in a state of becoming is an imperfect actuality which is called motion. For to be moved to whiteness is the same as for whiteness to begin to become actual in a subject; but it need not be in complete actuality. This is his meaning in saying that motion is not something apart from things themselves; for everything which is being changed is being changed according to the categories of being. And just as the ten categories have nothing in common as their genus, in a similar way there is no genus common to all the kinds of motion. Hence motion is not a category distinct from the others but is a natural concomitant of the other categories. Quartum est quod in unoquoque genere invenitur aliquid dupliciter, scilicet secundum perfectionem et imperfectionem; sicut in genere substantiae unum est ut forma, et aliud ut privatio. Et in genere qualitatis hoc est, quod est perfectum, ut album quod habet perfectum colorem, et hoc est ut nigrum, quod est imperfectum in genere coloris. Et in quantitate unum est perfectum quod dicitur magnum, et aliud imperfectum quod dicitur parvum. Et in ubi in quo est locatio, idest motus localis, est sursum et deorsum, et grave et leve, secundum quod grave dicitur quod actu subsidet, et leve quod actu supereminet. Et horum unum est ut perfectum, et aliud ut imperfectum. Et ratio huius est, quia omnia genera dividuntur per contrarias differentias; contrariorum autem semper alterum est ut perfectum, alterum ut imperfectum. 2292. The fourth point is that a thing is found in any genus in two ways, namely, perfectly and imperfectly; for example, in the genus of substance one thing has the character of a form, and another the character of a privation; and in the genus of quality there is one thing which is perfect, as a white thing, which has a perfect color, and another which is imperfect, as a black thing, which is imperfect in the genus of color. And in the genus of quantity one thing is perfect, and this is called “great,” and another is imperfect, and this is called “small”; and in the genus of place, in which “motion in space” is found, i.e., local motion, one thing tends upwards and another downwards, or one is light and another heavy inasmuch as that is called light which actually rises upwards, and that heavy which actually sinks downwards; and one of these has the character of something perfect and the other the character of something imperfect. The reason is that all the categories are divided by contrary differences; and one contrary always has the character of something perfect, and the other the character of something imperfect. Ex his quatuor concludit quintum; scilicet quod tot sunt species motus et permutationis quot sunt species entis. Quod quidem non dicit eo quod in quolibet genere entis sit motus; sed quia sicut ens dividitur per actum et potentiam, per substantiam et quantitatem, et huiusmodi, et secundum perfectum et imperfectum, ita et motus. Et hoc sequitur ex eo quod dictum est, quod motus non est praeter res. Quomodo autem differant permutatio et motus, infra dicetur. 2293. From these four points he infers a fifth, namely, that there are as many kinds of motion and change as there are of being. He does not say this because there is motion in every genus of being, but because, just as being is divided by actuality and potentiality and by substance and accident and the like, and in terms of perfect and imperfect, so also is motion. This follows from his assertion that motion is not something apart from things. The way in which change and motion differ will be explained below. 2294. Now since each (975). Deinde cum dicit divisio autem definit motum. Et primo ponit definitionem ipsam, dicens, quod cum ens secundum unumquodque genus entis dividatur per potentiam et actum, motus dicitur esse actus eius, quod est in potentia inquantum huiusmodi. Next, he defines motion. First, he gives its definition, saying that, since in each genus of being, being is divided by potentiality and actuality, motion is said to be the actualization of what is potential insofar as it is such. 2295. That our account (976). Secundo ibi, quod autem exponit positam definitionem. Et circa hoc duo facit. Primo exponit id quod ponitur in definitione ex parte subiecti motus. Secundo id quod ponitur in definitione quasi genus motus, ibi, quod quidem enim est. Second, he explains the definition which has been given; and in regard to this he does two things. First (976:C 2295), he explains what was given in the definition with regard to the subject of motion; and second (978:C 2297), what was given as the genus of motion (“That motion is this”). Circa primum duo facit. Primo exponit hanc particulam eius, quod est in potentia. Secundo hanc, inquantum huiusmodi, ibi, dico autem inquantum. In regard to the first member of this division he does two things. First, he explains the part of the definition, what is potential; and second (977:C 2296), the part, insofar as it is such (“And by the phrase”). Dicit ergo primo, quod ex hoc manifestum est verum esse, motum esse hoc quod dictum est. Manifestum est enim quod aedificabile significat aliquid existens in potentia. Et ista potentia significatur esse reducta in actum per hoc quod dicitur aedificari. Et iste actus vocatur aedificatio. Et similiter in omnibus aliis motibus, ut in ambulatione et alteratione et huiusmodi. Dicitur autem aliquid moveri, cum huiusmodi fiat in actu, et huiusmodi fuerit in potentia, et non prius nec posterius. Cum ergo ita sit, sequetur, quod motus est alicuius existentis in potentia, cum sit reductum ad actum. Et hoc dico, scilicet quod sit reductum ad actum, inquantum est mobile; nam mobile dicitur aliquid per hoc, quod est in potentia ad moveri; et sic reducitur huiusmodi potentia in actum quando movetur actu: non autem habet reduci in actum per motum id quod in potentia est inquantum ipsum, idest secundum id quod actu est, et secundum seipsum. Nam hoc etiam est in actu antequam incipiat moveri. Neque etiam reducitur ad actum per motum, secundum quod est in potentia ad terminum motus, qui dum movetur adhuc remanet in potentia ad terminum motus. Sed solum per motum reducitur aliquid de potentia in actum, de illa potentia quae significatur cum dicitur aliquid esse mobile, idest potens moveri. He accordingly says, first (976), that it is evidently true from this that motion is as we have described it to be. For it is clear that the term buildable signifies something in potentiality, and that the potentiality in question is presented as being brought to actuality by what is designated as being built; and this actuality is called the process of building. The same thing is also true of other motions, such as walking, altering, and the like. And a thing is said to be being moved when it is coming to be such and such actually and has been such and such potentially, and neither before nor after. If this is so, then, it follows that motion belongs to a thing in potentiality when it is being brought to actuality; and by this I mean that it is being brought to actuality insofar as it is movable; for a thing is said to be movable because it is in potentiality to motion. Hence a potentiality of this kind is being brought to actuality when it is actually being moved; but what is potential “inasmuch as it is itself,” i.e., in reference to what it actually is and in itself, does not have to be brought to actuality by motion. For it actually is this before it begins to be moved. And neither is it being brought to actuality by motion insofar as it is in potentiality to the terminus of motion, because so long as it is being moved it still remains in potentiality to the terminus of motion. But a thing is being brought from potentiality to actuality by motion only in the case of that potentiality which is signified when a thing is said to be movable, i.e., capable of being moved. 2296. And by the phrase (977). Deinde cum dicit dico autem exponit hanc particulam positam in definitione motus; scilicet inquantum huiusmodi, vel inquantum tale. Ad cuius expositionem dicit quod aes est in potentia ad statuam. Et sic idem est subiectum aes, et aes in potentia ad statuam. Tamen non est idem ratione. Sed alia est ratio aeris inquantum aes, et alia est ratio aeris inquantum habet aliquam potentiam. Et hoc est quod dicit quod non est idem aeri esse, et alicui potentiae. Si enim esset idem simpliciter secundum rationem, tunc, sicut motus est actus aeris inquantum est aes in potentia, ita esset actus aeris inquantum est aes. Sed non est idem secundum rationem aes et potentia aeris. Et hoc manifestum est in potentia contrariorum; quia posse sanari et posse laborare, idest infirmari, non est idem secundum rationem: ratio enim potentiae sumitur ex actu. Unde, si posse sanari et posse infirmari esset idem secundum rationem, sequeretur, quod idem esset infirmari et sanari, quod est impossibile. Sic igitur non est eadem potentia ad utrumque contrariorum secundum rationem potentiae, sed est eadem subiecto; idem enim est subiectum quod potest esse sanum et languens; sive illud subiectum sit quicumque humorum in corpore animalis, sive sanguis, qui est naturalior et magis proprius vitae et animalium nutrimento, possit esse causa sanitatis et aegritudinis. Quia ergo posse sanari et posse infirmari non est idem secundum rationem, manifestum est quod neutrum horum est idem secundum rationem cum suo subiecto; quia quae uni et eidem per se sunt eadem, sibiinvicem sunt eadem per se. Quia ergo non est idem secundum rationem aes, et aes in potentia ad statuam, sicut neque color et visibile, quod est potens videri, ideo necessarium fuit quod in definitione motus, dicto quod est actus existentis in potentia, adderetur, inquantum huiusmodi. Then he explains a phrase which was given in the definition of motion, namely, insofar as it is such, or inasmuch as it is of this kind. With a view to making this clear he says that bronze is in potentiality to being a statue, and thus the subject bronze and bronze in potentiality to being a statue are the same, although they are not the same in their meaning; for the concept of bronze as bronze and that of bronze insofar as it has some potentiality are different; and this is what he means when he says that to be bronze and to be some potentiality are not the same. For if they were the same in their meaning, then just as motion is an actuality of bronze insofar as it is bronze in potentiality, in a similar way motion would be the actuality of bronze insofar as it is bronze. But bronze and the potentiality of bronze do not have the same meaning. This is evident in the case of the potentiality for contraries, because the potentiality “of being healed and that of being ill” do not have the same meaning; for the concept of a potentiality is derived from that of the actuality. Hence, if the potentiality of being healed and that of being ill were the same in meaning, it would follow that being healed and being ill are the same. But this is impossible. Therefore the potentiality for each of two contraries is not the same in meaning, although it is the same in subject. For it is the same subject which can be healed or be ill; and whether that subject is any one at all of the humors in the animal’s body, or the blood, which is more natural and proper to the life and nourishment of the animal, it can be a cause of its being healed or being ill. Since, then, the potentiality of being healed and that of being ill are not the same in meaning, it is evident that neither of these is the same as its subject in meaning, because any two things which are essentially the same as some third thing are themselves essentially the same. Hence, since bronze and bronze in potentiality to being a statue are not the same in meaning, just as color and the visible object are not the same, the phrase insofar as it is such must be added to the statement that motion is the actualization of what is potential. 2297. That motion is this (978). Deinde cum dicit quod quidem exponit id quod ponitur in definitione motus tamquam genus; dicens manifestum esse quod hoc sit motus, quia dico motus tunc est, quia tunc accidit moveri quando hic, idest actu existentis in potentia fuerit actu, et neque prius neque posterius. Manifestum est enim quod unumquodque mobilium contingit aliquando esse actu, aliquando non. Sicut aedificabile inquantum aedificabile, quandoque est in potentia, et quandoque est in actu. Dicit autem quod aedificabile inquantum aedificabile, quia materia domus est ad duo in potentia; scilicet ad formam domus et ad hoc quod aedificetur. Et quod ad utrumque contingit esse quandoque in potentia quandoque in actu. Sed potentia quae est in materia domus ad hoc quod aedificetur, significatur in hoc quod dicitur aedificabile. Tunc ergo aedificabile inquantum aedificabile fit actu, quando aedificatur. Et sic aedificatio est actus aedificabilis, inquantum aedificabile. Then he explains the term which was given as the genus in the definition of motion. That motion is this is evident, he says, because the said motion then exists “when it” (the actuality of what is potential) “is actual in this way,” and neither before nor after. For obviously every movable thing can be at one time in a state of actualization and at another not; for the buildable as buildable at one time is in a state of potentiality and at another time is in a state of actualization. He says “the buildable as buildable” because the matter of a house is in potentiality to two things, namely, to the form of a house, and to the process of being built. And it is possible for it at one time to be in a state of potentiality to both and at another to be in a state of actuality. But the potentiality which the matter of a house has for being built is signified by the term buildable. Therefore the buildable as buildable becomes actual when it is being built; and thus the process of building is the actuality of the buildable as buildable. Quod sic probat: quia materia domus non est in potentia nisi ad duos actus; scilicet ad aedificationem domus et ad formam. Aedificabile autem significat quamdam potentiam in materia domus existentem. Oportet igitur, cum omni potentiae respondeat aliquis actus, quod potentiae significatae per hoc quod dico aedificabile, respondeat alter duorum actuum; scilicet vel forma domus, vel aedificatio. Sed non est actus aedificabilis inquantum aedificabile forma domus; quia adveniente forma domus non est adhuc aedificabile, sed est iam aedificatum. Sed aedificabile est actu, quando aedificatur actu. Necesse est igitur quod aedificare sit actus aedificabilis. Aedificare autem est quidam motus; et sic motus est actus aedificabilis. Et eadem ratio est de omnibus aliis motibus. Unde manifestum est quod motus est actus existentis in potentia. 2298. He proves this as follows: the matter of a house is in potentiality to only two actualities, namely, the act of building the house and the form of the house. But the term buildable signifies a potentiality belonging to the matter of the house. Therefore, since there is some actuality corresponding to every potentiality, the potentiality signified by the term buildable must correspond to one of these two actualities, namely, either to the form of the house or to the act of building. But the form of the house is not the actuality of the buildable as buildable, because when the form of the house develops, the house is no longer buildable but is already built. But the buildable is in a state of actuality when the house is actually being built. Therefore the act of building must be the actuality of the buildable. Now the act of building is a kind of motion; and thus motion is the actuality of the buildable. The same explanation holds for all other motions. It is evident, then, that motion is the actuality of what is potential. 2299. That this account (979). Deinde cum dicit quod autem probat definitionem positam esse bene assignatam. Et primo ponit probationem in generali; dicens quod manifestum est motum esse bene definitum, ex his quae alii dixerunt de motu definientes ipsum. Et iterum ex eo quod non potest de facili aliter definiri. Non enim potest poni in alio genere nisi in genere actus. Then he proves that the definition given is a good one. First, he gives a general proof. He says that it is evident that this definition of motion is a good one if we consider what others have said about motion when they defined it; and also because it cannot easily be defined in a different way. For it cannot be put in any other class than in that of actuality. 2300. This is evident (980). Secundo ibi, palam autem ponit ea quae alii dixerunt de motu, dicens quod quidam dixerunt motum esse alteritatem, et quidam inaequalitatem, et quidam non ens. Forte ideo quia illud quod movetur recedit ab eo quod prius erat, et dum movetur semper alio et alio modo se habet, et magis appropinquat ad terminum. Second, he states what others have said about motion. He says that some have said that motion is otherness, others inequality, and others non-being. And perhaps they spoke of it thus because the thing being moved gradually loses its initial state, and so long as it is being moved it is always in different states and comes closer to its goal. 2301. However, no one (981). Tertio ibi, quorum nullum ostendit praedictas definitiones non esse convenientes. Neque enim conveniunt motui ex parte subiecti, quod movetur. Si enim motus esset non ens, vel inaequalitas, vel alteritas, sequeretur quod omne non ens, vel alterum, vel inaequale moveretur: sed nullum horum necesse est moveri: non est igitur motus quod dictum est. Idem etiam apparet ex parte terminorum motus, qui sunt terminus a quo, et terminus ad quem. Non enim magis est motus ad non ens vel inaequalitatem, vel alteritatem, quam ad opposita horum; neque magis est motus ex his, quam ex oppositis. Contingit enim moveri ex non ente ad ens, et e converso; et de alteritate ad similitudinem, et de inaequalitate ad aequalitatem et e converso. Third, he shows that the definitions given above are not suitable ones; for they do not fit motion so far as its subject is concerned, i.e., the thing moved. For if motion were non-being or inequality or otherness, it would follow that every non-being or whatever is other or unequal is moved, but it is not necessary that any of these should be moved. Hence motion is not as they have described it to be. The same thing is also apparent with regard to the termini of motion, which are the limits from which and to which there is motion. For motion is not to non-being or inequality or otherness rather than to their opposites, nor is motion from these rather than from their opposites. For there can be motion from nonbeing to being and vice versa, and from otherness to likeness, and from inequality to equality and vice versa. 2302. The reason (982). Quarto ibi, causa autem ostendit quare praedicto modo definierunt motum; dicens quod ista est causa quare posuerunt motum in praedicta quasi genera, quia motus videtur esse aliquid indeterminatum, et illa sunt indeterminata quae sunt privativa. Et ideo motum posuerunt quasi privationem quamdam. Fourth, he shows why some defined motion in the foregoing way. He says that the reason why they put motion in the above-mentioned class is that motion seems to be something indefinite, and things which are privative are indefinite. Hence they assumed that motion is a kind of privation. Et sciendum quod, sicut in primo huius dictum est, Pythagorici posuerunt duos ordines: in quorum uno quem dicebant ordinem bonorum, posuerunt illa quae videbantur perfectionem habere, sicut lucem, dextrum, masculum, quietem et huiusmodi. In alio autem ordine quem sub malo constituebant, posuerunt tenebras, sinistrum, feminam, motum et huiusmodi. Et omnia huiusmodi dicebant esse indeterminata et privativa, quia nullum istorum videbatur significare neque hoc, idest substantiam, neque tale, idest qualitatem, neque aliquod aliud praedicamentorum. 2303. It should also be noted, as has been pointed out in Book I (60:C 127) of this work, that the Pythagoreans posited two orders of things, and in one of these, which they called the order of good things, they placed things which seem to be perfect, for example, light, right, male, rest, and the like; and in the other order, which they listed under evil, they placed darkness, left, female, motion and the like. And they said that all such things are indefinite and privative because no one of them seems to signify “either a this,” i.e., substance, “or such,” i.e., quality, or any of the other categories. 2304. The reason why (983). Quinto ibi, cur autem dicit causam, quare motus inter indeterminata ponatur: et dicit, quod causa huius est, quia motus neque poterat poni in genere potentiae, neque in genere actus. Si enim esset in genere potentiae, sequeretur quod quicquid est in potentia ad aliquid, puta ad esse quantum, moveretur ad illam quantitatem: sed hoc non est necessarium, quia etiam antequam incipiat aliquid moveri ad quantitatem, est in potentia ad quantitatem illam. Neque etiam movetur quando iam actu est quantum secundum illam quantitatem, ad quam erat in potentia; sed tunc iam terminatus est motus. Fifth, he points out why motion is placed in the class of the indefinite. The reason for this, he says, is that motion can be placed neither in the class of the potential nor in that of the actual; for if it were placed in the class of the potential, it would follow that whatever is in potentiality to something, for example, to have some quantity, would be moved to that quantity. But this is not necessary, because, before a thing begins to be moved to some quantity, it is in potentiality to that quantity. Moreover, it is not being moved when it already actually has that quantity to which it was in potentiality, but the motion has then already been terminated. Sed oportet, quod motus sit actus quidam, ut supra probatum est: sed est actus imperfectus. Et huius causa est, quia illud cuius est actus, est imperfectum, et hoc est ens possibile sive ens potentia. Si enim esset actus perfectus, tolleret totam potentiam, quae est in materia ad aliquid determinatum. Unde actus perfecti non sunt actus existentis in potentia, sed existentis in actu. Motus autem ita est existentis in potentia, quod non tollit ab eo potentiam. Quamdiu enim est motus, remanet potentia in mobili ad id quod intendit per motum. Sed solum potentia quae erat ad moveri tollitur per motum; et tamen non totaliter; quia id quod movetur, adhuc in potentia est ad moveri, quia omne quod movetur, movebitur, propter divisionem motus continui, ut probatur in sexto physicorum. Unde relinquitur, quod motus est actus existentis in potentia: et sic est actus imperfectus et imperfecti. 2305. But motion must be a kind of actuality, as has been proved above (975:C 2294), although it is an imperfect one. The reason for this is that the thing of which it is the actuality is imperfect, and this is a possible or potential being; for if it were a perfect actuality, the whole potentiality for some definite actuality which is in the matter would be eliminated. Hence perfect actualities are not actualities of something in potentiality but of something in actuality. But motion belongs to something that is in potentiality, because it does not eliminate the potentiality of that thing. For so long as there is motion, the potentiality for that to which it tends by its motion remains in the thing moved. But only the previous potentiality for being moved is eliminated, though not completely; for what is being moved is still in potentiality to motion, because everything which is being moved will be moved, because of the division of continuous motion, as is proved in Book VI of the Physics. It follows, then, that motion is the actuality of what is potential; and thus it is an imperfect actuality and the actuality of something imperfect. Et propter hoc difficile est accipere quid sit motus. Videtur enim quod aut necesse sit ponere motum in genere privationis, sicut patet ex praemissis definitionibus, aut in genere potentiae, aut in genere actus simplicis et perfecti; quorum nullum contingit esse motum. Unde relinquitur quod motus sit id quod dictum est; scilicet actus; et quod non dicatur actus perfectus. Quod quidem difficile est videre, sed tamen contingens est esse, quia hoc posito nullum sequitur inconveniens. 2306. It is because of this that it is difficult to grasp what motion is; for it seems necessary to place motion either in the class of privation, as is evident from the definitions given above, or in the class of potentiality, or in that of simple and complete actuality—none of which may be moved. It follows, then, that motion is as we have described it to be, namely, an actuality, and that it is not called a perfect actuality. This is difficult to grasp, although it can nevertheless be true, because when this is admitted nothing untenable follows. Quidam autem definierunt dicentes, quod motus est exitus de potentia in actum, non subito. Sed erraverunt; quia necesse est quod in definitione exitus ponatur motus, cum sit species motus. Et similiter in definitione eius quod est subito, ponitur tempus; et in definitione temporis motus. 2307. Some have defined motion by saying that it is the gradual passage from potentiality to actuality. But they erred, because motion must be given in the definition of a passage, since it is a kind of motion. Similarly, time is placed in the definition of the gradual, and motion in the definition of time. 2308. That motion belongs (984). Deinde cum dicit et quod est ostendit in quo sit motus; et primo ostendit quod in mobili: quia omnis actus est in eo cuius est actus. Sed motus est actus mobilis a movente causatus. Unde relinquitur quod sit in mobili. Et quod sit actus mobilis, ex superioribus patet. Then he explains what the subject of motion is. First, he shows that it is the thing moved; because every actuality is found in the thing whose actuality it is. But motion is the actuality of the movable by what is capable of causing motion. Hence it follows that motion is found in the movable or thing moved; and that it is the actualization of this is clear from the above discussion. 2309. And the actuality (985). Secundo ibi, et motivi actus ostendit qualiter se habeat motus ad movens: et proponit duo: scilicet quod motus est actus motivi: et quod non est alius motus qui est actus motivi, et qui est mobilis: oportet enim motum esse actum amborum. Second, he shows how motion is related to a mover; and he gives two points, namely, that motion is the actuality of what is capable of causing motion, and that the actuality of the thing capable of causing motion and that of the thing moved do not differ; for motion must be the actuality of both. 2310. And a thing is capable (986). Tertio ibi, et motivum primum eorum duorum probat: scilicet quod motus sit motivi actus. Illud enim actus est alicuius, quo fit actu. Sed motivum dicitur ex eo quod est potens movere; movens autem in operari, idest in eo quod est esse actu; et ita, cum movens dicatur propter motum, motus erit actus motivi. Third, he proves the first of these two points, namely, that motion is the actuality of what is capable of causing motion. For the actuality of a thing is that by which it becomes actual. But a thing is said to be capable of causing motion because of its power of moving, and it is said to be a mover because of its activity, i.e., because it is actual. Hence, since a thing is said to be a mover because of motion, motion will be the actuality of what is capable of causing motion. 2311. But it is (987). Quarto ibi, sed est activum probat secundum propositorum: scilicet quod unus motus sit actus motivi et mobilis, hoc modo. Dictum est enim quod motus est actus motivi inquantum facit motum. Est autem mobilis inquantum fit in eo motus: sed motivum facit illum motum qui est in mobili et non alium. Et hoc quod est dicit quod movens est activum mobilis. Unde relinquitur quod unus motus sit actus et moventis et mobilis. Fourth, he proves the second of these points, namely, that the actuality of what is capable of causing motion and the actuality of what is capable of being moved are one and the same motion. He does this as follows: it has been stated that motion is the actuality of what is capable of causing motion inasmuch as it causes motion; and a thing is said to be movable inasmuch as motion is caused in it; but the thing capable of causing motion causes that motion which is found in the thing moved and not a different one. This is what he means when he says that it is on what is movable that the mover is capable of acting. It follows, then, that the actuality of the mover and that of the thing moved are one and the same motion. 2312. And it is one (988). Quinto ibi, quemadmodum eadem manifestat hoc per exempla: et dicit quod una est distantia duorum ad unum et unius ad duo. Sed differt ratione. Propter quod diversimode significatur: scilicet per duplum et dimidium. Similiter una est via ad ascendendum et descendendum, sed differt ratione. Et propter hoc dicuntur hi ascendentes et illi descendentes. Et ita est de movente et moto. Nam unus motus secundum substantiam est actus utriusque, sed differt ratione. Est enim actus moventis ut a quo, mobilis autem ut in quo; et non actus mobilis ut a quo, neque moventis ut in quo. Et ideo actus moventis dicitur actio, mobilis vero passio. Fifth, he clarifies this by an example. He says that the distance from one to two and from two to one are the same, although they differ conceptually; and for this reason the distance is signified differently, namely, by the terms double and half. Similarly, the path of an ascent and that of a descent are one, but they differ conceptually; and for this reason some are called ascenders and others descenders. The same applies to a mover and to the thing moved; for the actuality of both is essentially one motion, although they differ conceptually. For the actuality of a mover functions as that from which motion comes, whereas the actuality of the thing moved functions as that in which motion occurs. And the actuality of the thing moved is not that from which motion comes, nor is the actuality of the mover that in which motion occurs. Hence the actuality of the thing causing motion is called action, and that of the thing moved is called undergoing or suffering. Sed si actio et passio sunt idem secundum substantiam, videtur quod non sint diversa praedicamenta. Sed sciendum quod praedicamenta diversificantur secundum diversos modos praedicandi. Unde idem, secundum quod diversimode de diversis praedicatur, ad diversa praedicamenta pertinet. Locus enim, secundum quod praedicatur de locante, pertinet ad genus quantitatis. Secundum autem quod praedicatur denominative de locato, constituit praedicamentum ubi. Similiter motus, secundum quod praedicatur de subiecto in quo est, constituit praedicamentum passionis. Secundum autem quod praedicatur de eo a quo est, constituit praedicamentum actionis. 2313. But if action and undergoing are essentially the same thing, it seems that they should not be different categories. However, it should be borne in mind that the categories are distinguished on the basis of a different way of predicating; and thus inasmuch as the same term is differently predicated of different things, it belongs to different categories; for inasmuch as place is predicated of a thing that locates, it belongs to the genus of quantity, but inasmuch as it is predicated denominatively of the located thing it constitutes the category where. Similarly, inasmuch as motion is predicated of the subject in which it is found, it constitutes the category of undergoing; but inasmuch as it is predicated of that from which it comes, it constitutes the category of action.
LESSON 10 The Infinite
ARISTOTLE’S TEXT Chapter 10: 1066a 35-1067a 371 τὸ δ᾽ ἄπειρον ἢ τὸ ἀδύνατον διελθεῖν τῷ μὴ πεφυκέναι διιέναι, καθάπερ ἡ φωνὴ ἀόρατος, ἢ τὸ διέξοδον ἔχον ἀτελεύτητον, ἢ ὃ μόλις, ἢ ὃ πεφυκὸς ἔχειν μὴ ἔχει διέξοδον ἢ πέρας: 989. The infinite is either what cannot be spanned because it is not naturally fitted to be spanned (just as the spoken word is invisible); or what is imperfectly spanned; or what is spanned with difficulty; or what is not actually spanned, although it admits of being spanned or of having a terminus. ἔτι προσθέσει ἢ ἀφαιρέσει ἢ ἄμφω. 990. Further, a thing may be infinite either by addition or by subtraction or by both. [1066β]  χωριστὸν μὲν δὴ αὐτό τι ὂν οὐχ οἷόν τ᾽ εἶναι: εἰ γὰρ μήτε μέγεθος μήτε πλῆθος, οὐσία δ᾽ αὐτὸ τὸ ἄπειρον καὶ μὴ συμβεβηκός, ἀδιαίρετον ἔσται (τὸ γὰρ διαιρετὸν ἢ μέγεθος ἢ πλῆθος), εἰ  δὲ ἀδιαίρετον, οὐκ ἄπειρον, εἰ μὴ καθάπερ ἡ φωνὴ ἀόρατος: ἀλλ᾽ οὐχ οὕτω λέγουσιν οὐδ᾽ ἡμεῖς ζητοῦμεν, ἀλλ᾽ ὡς ἀδιέξοδον. 991. That the infinite should be a separate entity and be perceptible is impossible. For if it is neither a continuous quantity nor a plurality, and is a substance and not an accident, it will be indivisible; for what is divisible is either a continuous quantity or a plurality. But if it is indivisible, it is not infinite, except in the sense in which the spoken word is invisible. But people do not use the term in this sense, nor is this the sense of the infinite which we are investigating, but the infinite in the sense of what cannot be spanned. ἔτι πῶς ἐνδέχεται καθ᾽ αὑτὸ εἶναι ἄπειρον, εἰ μὴ καὶ ἀριθμὸς καὶ μέγεθος, ὧν πάθος τὸ ἄπειρον; 992. Further, how can the infinite exist of itself if number and continuous quantity, of which the infinite is an attribute, do not exist of themselves? ἔτι εἰ κατὰ συμβεβηκός, οὐκ ἂν εἴη στοιχεῖον τῶν ὄντων  ᾗ ἄπειρον, ὥσπερ οὐδὲ τὸ ἀόρατον τῆς διαλέκτου, καίτοι ἡ φωνὴ ἀόρατος. καὶ ὅτι οὐκ ἔστιν ἐνεργείᾳ εἶναι τὸ ἄπειρον, δῆλον. ἔσται γὰρ ὁτιοῦν αὐτοῦ ἄπειρον μέρος τὸ λαμβανόμενον (τὸ γὰρ ἀπείρῳ εἶναι καὶ ἄπειρον τὸ αὐτό, εἴπερ οὐσία τὸ ἄπειρον καὶ μὴ καθ᾽ ὑποκειμένου), ὥστε ἢ ἀδιαίρετον, ἢ εἰς  ἄπειρα διαιρετόν, εἰ μεριστόν: πολλὰ δ᾽ εἶναι τὸ αὐτὸ ἀδύνατον ἄπειρα (ὥσπερ γὰρ ἀέρος ἀὴρ μέρος, οὕτως ἄπειρον ἀπείρου, εἰ ἔστιν οὐσία καὶ ἀρχή): ἀμέριστον ἄρα καὶ ἀδιαίρετον. ἀλλὰ ἀδύνατον τὸ ἐντελεχείᾳ ὂν ἄπειρον (ποσὸν γὰρ εἶναι ἀνάγκη): κατὰ συμβεβηκὸς ἄρα ὑπάρχει. ἀλλ᾽ εἰ  οὕτως, εἴρηται ὅτι οὐκ ἐνδέχεται εἶναι ἀρχήν, ἀλλ᾽ ἐκεῖνο ᾧ συμβέβηκε, τὸν ἀέρα ἢ τὸ ἄρτιον. αὕτη μὲν οὖν ἡ ζήτησις καθόλου, 993. Again, if the infinite is an accident, it cannot, inasmuch as it is infinite, be an element of existing things, just as the invisible is not an element of speech although the spoken word is invisible.’ It is also evident that the infinite cannot be actual; for any part of it which might be taken would be infinite, since infinity and the infinite are the same if the infinite is a substance and is not predicated of a subject. Hence it is either indivisible, or if it is divisible, the parts into which it is divided are infinite in number. But it is impossible that the same thing should be many infinites; for, just as a part of air is air, so too a part of the infinite must be infinite if the infinite is a substance and principle. Therefore it cannot be divided into parts, and so is indivisible. But this cannot apply to the actually infinite, for it must be a quantity. Hence it is an accidental attribute. But if this is so, then, as we have said, it cannot be it that is a principle, but that of which it is an accident, for example, air or the even This investigation, then, is universal. ὅτι δ᾽ ἐν τοῖς αἰσθητοῖς οὐκ ἔστιν, ἐνθένδε δῆλον: εἰ γὰρ σώματος λόγος τὸ ἐπιπέδοις ὡρισμένον, οὐκ εἴη ἂν ἄπειρον σῶμα οὔτ᾽ αἰσθητὸν οὔτε νοητόν, 994. That the infinite does not exist in sensible things is made clear as follows: if it is the nature of a body to be bounded by surfaces, then no body, whether it is perceptible or intelligible, can be infinite. οὐδ᾽ ἀριθμὸς ὡς  κεχωρισμένος καὶ ἄπειρος: ἀριθμητὸν γὰρ ὁ ἀριθμὸς ἢ τὸ ἔχον ἀριθμόν. 995. Nor can there be any separate and infinite number; for a number or that which has a number is numerable. φυσικῶς δὲ ἐκ τῶνδε δῆλον: οὔτε γὰρ σύνθετον οἷόν τ᾽ εἶναι οὔθ᾽ ἁπλοῦν. σύνθετον μὲν γὰρ οὐκ ἔσται σῶμα, εἰ πεπέρανται τῷ πλήθει τὰ στοιχεῖα (δεῖ γὰρ ἰσάζειν τὰ ἐναντία καὶ μὴ εἶναι ἓν αὐτῶν ἄπειρον: εἰ γὰρ ὁτῳοῦν  λείπεται ἡ θατέρου σώματος δύναμις, φθαρήσεται ὑπὸ τοῦ ἀπείρου τὸ πεπερασμένον: ἕκαστον δ᾽ ἄπειρον εἶναι ἀδύνατον, σῶμα γάρ ἐστι τὸ πάντῃ ἔχον διάστασιν, ἄπειρον δὲ τὸ ἀπεράντως διεστηκός, ὥστ᾽ εἰ τὸ ἄπειρον σῶμα, πάντῃ ἔσται ἄπειρον): 996. This is evident from the following argument drawn from nature: the infinite can be neither composite nor simple. It cannot be a composite body if the elements are limited in number; for the contraries must be equal, and no one of them must be infinite; for if the active power of one of two elemental bodies is inferior to that of the other, the finite body will be destroyed by the infinite body. And that each should be infinite is impossible, because a body is what is extended in all directions, and the infinite is what is extended without limit; so if the infinite is a body, it must be infinite in all directions. οὐδὲ ἓν δὲ καὶ ἁπλοῦν ἐνδέχεται τὸ ἄπειρον εἶναι  σῶμα, οὔθ᾽ ὡς λέγουσί τινες, παρὰ τὰ στοιχεῖα ἐξ οὗ γεννῶσι ταῦτα (οὐκ ἔστι γὰρ τοιοῦτο σῶμα παρὰ τὰ στοιχεῖα: ἅπαν γάρ, ἐξ οὗ ἐστί, καὶ διαλύεται εἰς τοῦτο, οὐ φαίνεται δὲ τοῦτο παρὰ τὰ ἁπλᾶ σώματα), [1067α]  οὐδὲ πῦρ οὐδ᾽ ἄλλο τῶν στοιχείων οὐθέν: χωρὶς γὰρ τοῦ ἄπειρον εἶναί τι αὐτῶν, ἀδύνατον τὸ ἅπαν, κἂν ᾖ πεπερασμένον, ἢ εἶναι ἢ γίγνεσθαι ἕν τι αὐτῶν, ὥσπερ Ἡράκλειτός φησιν ἅπαντα γίγνεσθαί ποτε  πῦρ. ὁ δ᾽ αὐτὸς λόγος καὶ ἐπὶ τοῦ ἑνὸς ὃ ποιοῦσι παρὰ τὰ στοιχεῖα οἱ φυσικοί: πᾶν γὰρ μεταβάλλει ἐξ ἐναντίου, οἷον ἐκ θερμοῦ εἰς ψυχρόν. 997. Nor can the infinite be a single simple body: neither, as some say, something apart from the elements, from which they generate these (for there is no such body apart from the elements, because everything can be dissolved into that of which it is composed; but there does not appear to be anything apart from the simple bodies), nor fire, nor any of the other elements. For unless some of them are infinite, the whole, even though it is finite, could not be or become any one of them, as Heraclitus says that all things at one time become fire. The same reasoning also applies to “the one,” which the philosophers of nature posited as an entity over and above the elements (997). For everything is changed from a contrary, for example, from hot to cold. ἔτι τὸ αἰσθητὸν σῶμα πού, καὶ ὁ αὐτὸς τόπος ὅλου καὶ μορίου, οἷον τῆς γῆς, 998. Again, a sensible body is somewhere, and the place of the whole and that of a part (of the earth, for example) is the same. ὥστ᾽ εἰ μὲν ὁμοειδές, ἀκίνητον ἔσται ἢ ἀεὶ οἰσθήσεται, τοῦτο δὲ  ἀδύνατον (τί γὰρ μᾶλλον κάτω ἢ ἄνω ἢ ὁπουοῦν; οἷον εἰ βῶλος εἴη, ποῦ αὕτη κινήσεται ἢ μενεῖ; ὁ γὰρ τόπος τοῦ συγγενοῦς αὐτῇ σώματος ἄπειρος: καθέξει οὖν τὸν ὅλον τόπον; καὶ πῶς; τίς οὖν ἡ μονὴ καὶ ἡ κίνησις; ἢ πανταχοῦ μενεῖ—οὐ κινηθήσεται ἄρα, ἢ πανταχοῦ κινηθήσεται  —οὐκ ἄρα στήσεται): 999. Hence, if the infinite is composed of like parts, it will be immovable or will always be undergoing motion. But this is impossible. For why should it be moved upwards rather than downwards or in some other direction? For example, if it were a clod of earth, where would it move to or where remain at rest? For the place of the body naturally fitted to this will be infinite. Will it then occupy the whole place? And how will it do this? And what then will be its place of rest and of motion? For if it rests everywhere, it will not be in motion. And if it is moved everywhere, it will not be at rest. εἰ δ᾽ ἀνόμοιον τὸ πᾶν, ἀνόμοιοι καὶ οἱ τόποι, καὶ πρῶτον μὲν οὐχ ἓν τὸ σῶμα τοῦ παντὸς ἀλλ᾽ ἢ τῷ ἅπτεσθαι, εἶτα ἢ πεπερασμένα ταῦτ᾽ ἔσται ἢ ἄπειρα εἴδει. πεπερασμένα μὲν οὖν οὐχ οἷόν τε (ἔσται γὰρ τὰ μὲν ἄπειρα τὰ δ᾽ οὔ, εἰ τὸ πᾶν ἄπειρον, οἷον πῦρ ἢ ὕδωρ:  φθορὰ δὲ τὸ τοιοῦτον τοῖς ἐναντίοις): εἰ δ᾽ ἄπειρα καὶ ἁπλᾶ, καὶ οἱ τόποι ἄπειροι καὶ ἔσται ἄπειρα στοιχεῖα: εἰ δὲ τοῦτ᾽ ἀδύνατον καὶ οἱ τόποι πεπερασμένοι, καὶ τὸ πᾶν ἀνάγκη πεπεράνθαι. 1000. And if the whole is composed throughout of unlike parts, their places will also be unlike. And, first, the body of the whole will be one only by contact; and, second, the parts will be either finite or infinite in species. But they cannot be finite, for some would then be infinite and some not (if the whole is infinite), for example, fire or water. But such an infinite element would necessitate the destruction of contrary elements (996). But if the parts are infinite and simple, their places will be infinite, and the elements will be infinite in number. And since this is impossible, their places will be finite and the whole finite. ὅλως δ᾽ ἀδύνατον ἄπειρον εἶναι σῶμα καὶ τόπον τοῖς σώμασιν, εἰ πᾶν σῶμα αἰσθητὸν ἢ βάρος ἔχει  ἢ κουφότητα: ἢ γὰρ ἐπὶ τὸ μέσον ἢ ἄνω οἰσθήσεται, ἀδύνατον δὲ τὸ ἄπειρον ἢ πᾶν ἢ τὸ ἥμισυ ὁποτερονοῦν πεπονθέναι: πῶς γὰρ διελεῖς; ἢ πῶς τοῦ ἀπείρου ἔσται τὸ μὲν κάτω τὸ δ᾽ ἄνω, ἢ ἔσχατον καὶ μέσον; 1001. And in general there cannot be an infinite body and a place for bodies if every sensible body has either heaviness or lightness; for it will tend either to the center or upwards. But the infinite-either the whole or a half of it-is incapable of any of these motions. For how can you divide it? Or how can one part tend upwards and another downwards, or one part tend to the extreme and another to the center? ἔτι πᾶν σῶμα αἰσθητὸν ἐν τόπῳ, τόπου δὲ εἴδη ἕξ, ἀδύνατον δ᾽ ἐν τῷ  ἀπείρῳ σώματι ταῦτ᾽ εἶναι. 1002. Further, every sensible body is in a place, and there are six kinds of place, but these cannot pertain to an infinite body. ὅλως δ᾽ εἰ ἀδύνατον τόπον ἄπειρον εἶναι, καὶ σῶμα ἀδύνατον: τὸ γὰρ ἐν τόπῳ πού, τοῦτο δὲ σημαίνει ἢ ἄνω ἢ κάτω ἢ τῶν λοιπῶν τι, τούτων δ᾽ ἕκαστον πέρας τι. 1003. And in general if a place cannot be infinite, neither can a body be infinite; for to be in a place is to be somewhere, and this means to be either down or up or in some one of the other places, and each of these is a limit. τὸ δ᾽ ἄπειρον οὐ ταὐτὸν ἐν μεγέθει καὶ κινήσει καὶ χρόνῳ ὡς μία τις φύσις, ἀλλὰ τὸ ὕστερον  λέγεται κατὰ τὸ πρότερον, οἷον κίνησις κατὰ τὸ μέγεθος ἐφ᾽ οὗ κινεῖται ἢ ἀλλοιοῦται ἢ αὔξεται, χρόνος δὲ διὰ τὴν κίνησιν. [1067β]  1004. And the infinite is not the same in the case of continuous quantity, of motion, and of time, as though it were a single reality; but the secondary member is said to be infinite inasmuch as the primary one is; for example, motion is said to be infinite in reference to the continuous quantity in which it is moved or altered or increased, and time is said to be such in reference to motion. COMMENTARY Postquam philosophus determinavit de motu, hic determinat de infinito, quod est passio motus et cuiuslibet quanti universalis. Et circa hoc tria facit. Primo distinguit quot modis dicitur infinitum. Secundo ostendit quod non est infinitum actu, ibi, separabile quidem. Tertio quomodo infinitum invenitur in diversis, ibi, infinitum autem. 2314. Having given his views about motion, here the Philosopher deals with the infinite, which is an attribute of motion and of any quantity in general. In regard to this he does three things. First (989:C 2314), he distinguishes the various senses in which the term infinite is used. Second (991:C 2322), he shows that the actually infinite does not exist (“That the infinite”). Third (1004:C 2354), he explains how the infinite is found in different things (“And the infinite”). Circa primum duo facit. Primo ostendit quot modis dicitur infinitum in actu. Secundo quot modus dicitur infinitum in potentia, ibi, adhuc autem appositione. In regard to the first he does two things. First, he explains the different senses in which the term infinite is used; and second (990:C 2319), the various senses in which things are said to be potentially infinite (“Further, a thing”). Circa primum considerandum est, quod omne finitum dividendo pertransitur. Unde infinitum proprie est, quod mensurando pertransiri non potest. Tot ergo modis dicitur infinitum, quot modis dicitur intransibile. In regard to the first (989) part it should be borne in mind that every finite thing may be spanned by division. Hence the infinite, properly speaking, is what cannot be spanned by measurement; and therefore the term infinite is used in the same number of senses as the term untraversable. Utrumque autem dicitur quatuor modis: quorum primus est secundum quod infinitum sive intransibile dicitur quod non potest transiri mensurando, eo quod non est natum secundum suum genus pertransiri, sicut dicimus punctum, aut unitatem, aut aliquid quod non est quantum et mensurabile, esse infinitum seu intransibile; per quem modum vox dicitur invisibilis, quia non est de genere visibilium. 2315. Now each of these is used in four ways. First, the infinite or untraversable means what cannot be spanned by measurement because it does not belong to the class of things which are naturally fitted to be spanned; for example, we say that the point or the unit or something which is not a quantity and is not measurable is infinite or untraversable; and in this sense the spoken word is said to be invisible because it does not belong to the class of things which are visible. Secundo modo dicitur infinitum vel intransibile quod nondum est pertransitum, licet inceptum sit pertransiri: hoc enim est quod dicit habens transitionem imperfectam. 2316. Second, the infinite or untraversable means what has not yet been spanned although it has begun to be spanned. This is his meaning in saying “what is imperfectly spanned.” Tertius modus est secundum quod dicitur infinitum vel intransibile quod vix transitur. Ut si dicamus profunditatem maris infinitam, vel altitudinem caeli, vel aliquam viam longam immensurabilem seu intransibilem seu infinitam: quia excedit vires mensurantis, licet in se sit transibilis. 2317. Third, the infinite or untraversable means what is spanned with difficulty. Thus we may say that the depth of the sea or the height of the sky is infinite, or that any long distance is immeasurable or untraversable or infinite, because it surpasses our powers of measurement although in itself it is capable of being spanned. Quartus modus est secundum quod dicitur infinitum illud quod natum est habere transitionem aut terminum secundum suum genus, sed non habet. Puta si sit linea aliqua interminata. Et hoc est vere et proprie infinitum. 2318. Fourth, the infinite or untraversable means what belongs to the class of things which are naturally fitted to be spanned, or to have some limit set to them, but are not actually spanned; for example, if a line is limitless. This sense of the infinite is the true and proper one. 2319. Further, a thing (990). Secundo ibi, adhuc appositione ostendit quot modis dicitur infinitum in potentia; et dicit quod dicitur infinitum uno modo appositione sicut numerus. Semper enim cuilibet numero dato est apponere unitatem, et sic numerus est augmentabilis in infinitum. Second, he explains the various senses in which things are said to be potentially infinite. He says that in one sense a thing is said to be infinite by addition, as a number; for it is always possible to add a unit to any number, and in this respect number is capable of infinite increase. Alius modus secundum quod infinitum dicitur ablatione et divisione, secundum quod magnitudo dicitur divisibilis in infinitum. 2320. In another sense a thing is said to be infinite by subtraction or division inasmuch as a continuous quantity is said to be infinitely divisible. Tertius modus contingit utrinque; sicut tempus dicitur infinitum et divisione, quia continuum est, et appositione, quia numerus est. Et similiter etiam in motu infinitum est. 2321. In a third sense it is possible for a thing to be infinite from both points of view; for example, time is said to be infinite both as regards division, because it is continuous, and as regards addition, because it is a number. It is in a similar way that the infinite is found in motion. 2322. That the infinite (991). Deinde cum dicit separabile quidem ostendit, quod non sit infinitum in actu. Circa quod sciendum est, quod Platonici posuerunt infinitum separatum a sensibilibus, et posuerunt ipsum esse principium. Naturales autem philosophi posuerunt infinitum in rebus sensibilibus; non ita quod ipsum infinitum esset substantia, sed quod esset accidens alicui corpori sensibili. Primo ergo ostendit quod non est infinitum separatum. Secundo, quod non est infinitum actu in sensibilibus, ibi, quod autem in sensibilibus. Then he shows that the actually infinite does not exist; and in regard to this it should be noted that the Platonists held that the infinite is separate from sensible things and is a principle of them, whereas the philosophers of nature held that the infinite exists in sensible things, not in the sense that it is a substance, but rather in the sense that it is an accident of some sensible body. He therefore shows, first (991:C 2322), that the infinite is not a separate entity; and second (994:C 2327), that the actually infinite does not exist in sensible things (“That the infinite does not”). Circa primum ponit tres rationes. Quarum prima est: quod si ipsum infinitum est quaedam substantia per se existens, et non accidens alicui subiecto, oportet quod ipsum infinitum sit absque magnitudine et multitudine, quia magnitudo et numerus sunt subiectum infiniti. Si autem est sine magnitudine et multitudine, oportet quod sit indivisibile; quia omne divisibile, aut est magnitudo, aut multitudo. Si autem est indivisibile, non est infinitum nisi primo modo, sicut vox dicitur invisibilis: quo modo non inquirimus nos nunc, nec ipsi; sed de infinito intransibili secundum quartum modum. Ergo, de primo ad ultimum, si infinitum sit substantia separata per se existens, non erit vere infinitum. Et sic ista positio destruit seipsam. In treating the first member of this division he gives three arguments. The first is as follows: if the infinite is a substance which exists of itself and is not an accident of some subject, the infinite must lack continuous quantity and plurality, because continuous quantity and number constitute the subject of the infinite. But if it lacks continuous quantity and plurality, it must be indivisible, because everything divisible is either a continuous quantity or a plurality. But if it is indivisible, it is infinite only in the first sense of the term, as a spoken word is said to be invisible. However, we are not investigating this sense of the term here, nor did they use the term in this sense; but we are considering the fourth sense, i.e., what is untraversable. Therefore, all things considered, if the infinite were an independently existing substance, it would not be truly infinite. This position destroys itself in this way. 2323. Further, how can (992). Secundam rationem ponit ibi, adhuc quomodo quae talis est. Infinitum est passio numeri et magnitudinis. Sed numerus et magnitudo non sunt per se existentia separata, ut in primo ostensum est, et infra ostendetur: ergo multo minus infinitum separatum est. Then he gives the second argument, which runs thus: infinity is an attribute of number and of continuous quantity. But number and continuous quantity are not things which have separate existence, as has been shown in Book I (122:C 239) and will be shown below (993:C 2324). Therefore much less is the infinite a separate substance. 2324. Again, if the infinite (993). Tertiam rationem ponit ibi, adhuc si quae talis est. Si infinitum ponitur separatum a sensibilibus, aut ponitur ut substantia per se existens, aut ut accidens inhaerens alicui subiecto separato, puta magnitudini, aut numero, quae sunt separata secundum Platonicos. Si autem ponatur esse accidens, tunc ipsum infinitum non erit principium entium inquantum hoc est infinitum, sed magis subiectum infiniti. Sicut principium locutionis non dicitur invisibile, sed vox, quamvis vox sit sic invisibilis. Here he gives the third argument, which runs as follows. Let us suppose that the infinite is either a substance which is separate from sensible things or an accident belonging to some separate subject, for example, to continuous quantity or to number-which are separate according to the Platonists. Now if the infinite is assumed to be an accident, it cannot be the infinite as infinite that is a principle of existing things, but rather the subject of the infinite; just as what is invisible is not said to be a principle of speech, but the spoken word, although the spoken word is invisible in this sense. Si autem infinitum sit substantia, et non praedicetur de aliquo subiecto, etiam manifestum est quod non potest esse actu infinitum. Aut enim est divisibile, aut indivisibile. Si autem est divisibile, et infinitum hoc ipsum quod est infinitum est substantia, oportet quod quaelibet pars eius accepta sit infinita, quia idem est infinito esse et infinitum, si infinitum est substantia, id est si infinitum praedicat propriam rationem eius quod est infinitum. Unde, sicut quaelibet pars aquae est aqua, et quaelibet pars aeris est aer, ita quaelibet pars infiniti est infinita, si infinitum est substantia divisibilis. Quare oportet dicere, quod aut sit indivisibile infinitum, aut sit divisibile in multa infinita. Sed hoc est impossibile, quod multa infinita constituant unum infinitum: quia infinitum non est maius infinito: omne autem totum maius est sua parte. 2325. And if the infinite is assumed to be a substance and is not predicated of a subject, it is also evident that it cannot be actually infinite; for it is either divisible or indivisible. But if the infinite itself as infinite is a substance and is divisible, any part of it which might be taken would necessarily be infinite; because infinity and the infinite are the same “if the infinite is a substance,” i.e., if infinity expresses the proper intelligible structure of the infinite. Hence, just as a part of water is water and a part of air is air, so too any part of the infinite is infinite if the infinite is a divisible substance. We must say, then, that the infinite is either indivisible or divisible into many infinites. But many infinite things cannot possibly constitute one finite thing; for the infinite is not greater than the infinite, but every whole is greater than any of its parts. Relinquitur igitur, quod infinitum sit indivisibile. Sed impossibile est quod id quod est indivisibile sit actu infinitum, quia infinitum oportet esse quantum. Relinquitur igitur quod non sit substantia, sed accidens. Sed si est accidens, non est principium ipsum infinitum, sed illud cui accidit, ut dictum est, sive sit aer, ut quidam naturales posuerunt, sive sit par, ut posuerunt Pythagorici. Relinquitur igitur quod infinitum non possit esse substantia simul et principium entium. Et ultimo concludit quod haec inquisitio est universalis excedens naturalium considerationem. 2326. It follows, then, that the infinite is indivisible. But that any indivisible thing should be actually infinite is impossible, because the infinite must be a quantity. Therefore it remains that it is not a substance but an accident. But if the infinite is an accident, it is not the infinite that is a principle, but the subject of which it is an accident (as was said above), whether it be air, as some of the natural philosophers claimed, or the even, as the Pythagoreans claimed. Thus it follows that the infinite cannot be both a substance and a principle of beings at the same time. Last, he concludes that this investigation is a general one which goes beyond the study of natural things. 2327. That the infinite does not exist (994). Deinde cum dicit quod autem probat quod infinitum actu non sit in sensibilibus. Et primo probat hoc per rationes probabiles. Secundo per rationes naturales, ibi, naturaliter autem. Then he proves that the actually infinite does not exist in sensible things. First (994:C 2327), he proves this by probable arguments; and second (996:C 2330), by arguments drawn from nature (“This is evident”). Dicit ergo primo, quod manifestum est quod infinitum actu non est in sensibilibus. Et ostendit duo. Dicit ergo primo, quod in sensibilibus non est corpus infinitum. De ratione enim corporis est, quod sit superficie determinatum. Sed nullum corpus determinatum superficie est infinitum: ergo nullum corpus est infinitum, neque sensibile, idest naturale, neque intellectuale, idest mathematicum. He accordingly says, first (994), that it is obvious that the actually infinite is not found in sensible things; and he proves two points. First, he says that there is no infinite body in the sensible world, for it is the nature of a body to be bounded by surfaces. But no body with a definite surface is infinite. Therefore no body is infinite, “whether it be perceptible,” i.e., a natural body, “or intelligible,” i.e., a mathematical one. 2328. Nor can there be (995). Secundo ibi, neque numerus dicit quod in sensibilibus non est numerus infinitus hoc modo. Omnis numerus et omne habens numerum est numerale. Sed nullum numerale est infinitum, quia numerale est pertransibile numerando: ergo nullus numerus est infinitus. Second, he shows in the following way that there is no infinite number in sensible things. Every number and everything which has a number is numerable. But nothing numerable is infinite, because what is numerable can be spanned by numeration. Therefore no number is infinite. Hae autem rationes non sunt naturales, quia non sumuntur ex principiis corporis naturalis, sed ex quibusdam principiis communibus et probabilibus, non ex necessariis: quia qui poneret corpus infinitum, non poneret ipsum terminari superficie. Hoc enim est de ratione corporis finiti. Et qui poneret multitudinem infinitorum, non poneret eam numerum, quia numerus est multitudo mensurata per unum, ut in decimo habitum est. Nullum autem mensuratum infinitum est. 2329. Now these arguments do not pertain to natural philosophy, because they are not based on the principles of a natural body but on certain principles which are common and probable and not necessary. For anyone who would claim that a body is infinite would not maintain that its surface has limits, for this characteristic belongs to the nature of a finite body. And anyone who would claim that there is an infinite multitude would not hold that it is a number, because number is multitude measured by one, as has been explained in Book X (875-C 2090). But nothing measured is infinite. 2330. This is evident (996). Deinde cum dicit naturaliter autem ostendit quod non sit infinitum in actu in sensibilibus, per rationes naturales. Et primo ex parte activi et passivi. Secundo ex parte loci et locati, ibi, adhuc sensibile. Next, he proves that the actually infinite does not exist within sensible things, by using arguments drawn from nature. He does this, first (996:C 2330), with reference to the active and passive powers of bodies; and second (998:C 2339), with reference to place and the thing in place (“Again, a sensible body”). Activum autem et passivum, locus et locatum sunt proprietates corporis naturalis, inquantum huiusmodi. Et ideo dicit, quod istae rationes sunt naturales. Dicit ergo primo, quod si corpus aliquod sensibile et infinitum, aut erit corpus simplex, aut erit corpus compositum, sive mixtum. Now active and passive powers, Place and thing in place are proper to natural bodies as such; and therefore he says that these arguments are drawn from nature. He accordingly says, first (996), that, if a body is perceptible and infinite, it wilt be either a simple body or a composite body or compound. Et primo ostendit, quod corpus compositum non possit esse infinitum, supposito quod corpora simplicia, quae sunt elementa corporum compositorum, sunt finita multitudine. Quod ita probat: quia oportebit quod vel omnia sint infinita in quantitate, aut quod unum sit infinitum, alia finita. Aliter enim non posset componi corpus infinitum ex elementis multitudine finitis. 2331. First, he shows that a composite body cannot be infinite, if we assume that simple bodies, which are the elements of composite bodies, are finite in number. He proves this as follows: either all the elements must be infinite in quantity, or one must be infinite and the others finite, otherwise an infinite body could not be composed of elements which are finite in number. Non autem potest esse quod unum eorum sit infinitum et alia finita; quia in corpore mixto oportebit aliqualiter adaequari contraria, ad hoc, quod corpus mixtum conservetur. Aliter enim unum eorum quod esset excedens, corrumperet alia. Si autem unum sit infinitum, et alia finita, non est aequalitas, cum non sit proportio infiniti ad finitum. Unde corpus mixtum non poterit consistere, sed infinitum corrumpet alia. 2332. But that one of the elements should be infinite and the rest finite is impossible; because in the case of a compound contraries must somehow be equalized in order that the compound may be preserved in being, for otherwise that contrary which exceeds the others will destroy them. But if one contrary is infinite and the rest finite, no equality will be established, since there is no proportion between the infinite and the finite. A compound, then, could not exist, for the infinite element would destroy the others. Sed quia posset aliquis dicere, quod corpus quod est finitum quantitate est potentius virtute, et ita fit aequalitas; puta si quis dicat quod in corpore mixto sit aer infinitus et ignis finitus: ideo subiungit, quod quamvis virtus unius corporis quod ponitur infinitum, deficiat a virtute alterius cuiuscumque, quod ponitur finitum, nihilominus finitum corrumperetur ab infinito. Corporis enim finiti necesse est esse virtutem finitam; et ita ignis finitus habebit virtutem finitam. Si ergo abscindatur ab aere infinito, aer aequalis igni habebit minorem virtutem, quam habeat totus aer infinitus, proportionatam tamen virtuti ignis. Sit ergo virtus ignis centupla virtuti aeris. Si ergo accipiamus centuplum de aere ab aere infinito, habebit aequalem virtutem cum igne; et ita totus aer infinitus habebit maiorem virtutem infinitam quam ignis, et corrumpet ipsum. Non est ergo possibile quod in corpore mixto sit unum elementum infinitum, et alia finita. 2333. And since someone might say that a body which is finite in quantity has greater power, and that equality is achieved in this way (for example, if someone were to say that in a compound air is infinite and fire finite), he therefore adds that, even if we suppose that the active power of one body which is assumed to be infinite falls short of the active power of any one of the others, because these are assumed to be finite, the finite element will be destroyed by the infinite one; for a finite body must have a finite power, and then finite fire will have a finite power. Hence, if from infinite air a portion of air equal to the fire is taken out, its power will be less than that of the whole infinite air, but proportioned to the power of fire. Let us suppose, then, that the power of fire is a hundred times greater than that of air. Hence, if we take away a hundredfold of air from infinite air it will be equal to fire in power; and thus the whole infinite air will have a greater infinite power than fire and will destroy it. It is impossible, then, that one element of a compound should be infinite and the rest finite. Similiter non est possibile quod omnia sint infinita; quia corpus est quod distenditur in omnem dimensionem. Infinitum autem est quod habet dimensionem infinitam. Unde oportet quod corpus infinitum habeat ex omni parte dimensionem infinitam. Duo autem corpora non possunt esse simul. Sic ergo duo infinita non possunt coniungi in unum. 2334. Similarly, it is impossible that all should be infinite, because a body is what is extended in every dimension. But the infinite is what is infinite in dimension. Hence an infinite body must have an infinite dimension in every direction. But two bodies cannot be in the same place. Therefore two infinite bodies cannot be combined into one. 2335. Nor can the infinite (997). Secundo ibi, neque unum ostendit, quod non potest esse aliquod corpus simplex infinitum. Non enim est possibile, quod sit corpus simplex praeter elementa, ex quo omnia generantur, sicut quidam posuerunt vaporem: quia unumquodque resolvitur in ea ex quibus componitur: in nullis autem videmus resolvi corpora mixta nisi in quatuor elementa: non est ergo aliquod corpus simplex praeter quatuor elementa. Second, he proves that the infinite cannot be a simple body. There cannot be a simple body apart from the elements, from which all of them are generated, as some claimed air to be, because each thing is dissolved into the elements of which it is composed. But we see that compounds are dissolved only into the four elements; and therefore there cannot be a simple body apart from the four elements. Sed neque ignis, neque aliquod aliud elementorum potest esse infinitum: quia impossibile esset aliquod elementorum esse, praeter id quod esset infinitum, quia illud repleret totum undique. Et etiam si esset aliquod finitum, oporteret quod converteretur in illud infinitum, propter excessum ipsius virtutis; sicut Heraclitus manifeste posuit quod aliquando omnia sint convertenda in elementum ignis, propter nimium excessum virtutis eius. 2336. Nor can fire or any of the other elements be infinite, because no element could possibly exist except the one which is infinite, since it would fill every place. Again, if there were some finite element it would have to be changed into that infinite element because of the very great power of the latter; just as Heraclitus claimed that at some time all things must be changed into the element fire because of its very great power. Et eadem ergo ratio est de uno corpore simplici, quod quidem faciunt naturales praeter ipsa elementa. Oportet enim quod habeat quamdam contrariam repugnantiam in ordine ad alia elementa, cum permutatio fiat ex illo uno solo corpore ad alia. Omnis autem rerum permutatio fit ex contrario in contrarium. Cum igitur unum contrariorum corrumpat alterum, sequitur quod si illud corpus quod ponitur praeter elementa sit infinitum, quod corrumpat alia. 2337. And the same argument therefore applies to the one simple body which the natural philosophers posited as an entity over and above the elements themselves; for it would have to be opposed to the other elements as a kind of contrary, since according to them there is change from that one body alone into the others. But every change in things is from one contrary to another. Therefore, since one of two contraries destroys the other, it follows that, if that body which is supposed to exist apart from the elements is infinite, it will destroy the others. Praetermittit autem hic philosophus de corpore caelesti, quod est praeter ipsa quatuor elementa, non tamen habet aliquam contrarietatem sive repugnantiam ad ea, nec constituuntur ex eo naturaliter corpora. Non enim naturales philosophi ponentes corpus infinitum actu, pervenerunt in notitiam huius quintae essentiae vel naturae. Sed tamen in libro de caelo Aristoteles probat etiam de corpore caeli quod circulariter movetur, quod non sit infinitum actu. 2338. The philosopher omits the celestial body here, because, while it is something apart from the four elements, it is not contrary or repugnant to them in any way, nor are these bodies naturally derived from it. For the philosophers of nature who posited an actually infinite body did not attain any knowledge of this fifth essence or nature. Yet in The Heavens Aristotle proves that even a celestial body, which moves circularly, is not actually infinite. 2339. Again, a sensible body (998). Deinde cum dicit adhuc sensibile ostendit quod non est corpus sensibile infinitum, rationibus acceptis ex parte ipsius loci et locati: et ponit tres. Circa quarum primam praemittit duo necessaria. Quorum primum est, quod omne corpus sensibile est in loco. Et dicit notanter, sensibile, ad differentiam corporis mathematici, cui non attribuitur locus et tactus nisi per similitudinem. Then he proves that a sensible body is not infinite; and he does this by means of arguments based upon place and a thing in place. He gives three arguments. As a sort of preamble to the first he considers two points necessary for its development. The first is that every sensible body is in a place. He emphasizes sensible in order to distinguish this kind of body from a mathematical one, to which place and contact are attributed only figuratively. Aliud est quod idem est locus naturalis totius et partis, scilicet in quo naturaliter quiescit, et ad quod, scilicet naturaliter movetur. Sicut patet de terra et parte terrae. Utriusque enim locus naturalis est deorsum. 2340. The second point is that the natural place of a whole and that of a part are the same, i.e., the place in which it naturally rests and to which it is naturally moved. This is clear, for instance, in the case of earth and of any part of it, for the natural place of each is down. 2341. Hence, if the infinite (999). His autem duobus positis proponit rationem, ibi, quare siquidem. Et est ratio talis. Si ponatur corpus sensibile infinitum, aut est totum unius speciei, sicut corpora similium partium, sicut aer et terra et sanguis et huiusmodi. Aut erit diversarum specierum in partibus. After giving these two points he states his argument, which runs as follows. If a sensible body is assumed to be infinite, either its parts will all be specifically the same, as is the case with bodies having like parts, such as air, earth, blood, and so on, or they will be specifically different. Si autem est eiusdem speciei quantum ad omnes partes, sequetur, quod aut totum erit immobile et semper quiescens, aut totum semper movebitur. Quorum utrumque est impossibile et repugnans sensui. 2342. But if all of its parts are specifically the same, it will follow that the whole will always be at rest or always in motion. Each one of these is impossible and incompatible with the facts of sensory perception. 2343. For why should it (ibid.). Sed quod oporteat alterum sequi, ostendit cum dicit, quid enim magis deorsum. Iam enim suppositum est quod idem est locus naturalis totius et partis. Manifestum est etiam quod unumquodque corpus, cum est in loco suo naturali, quiescit. Cum autem est extra naturalem locum suum, naturaliter movetur ad ipsum. Si igitur totus locus in quo est corpus similium partium infinitum, est ei naturalis, oportet quod sit naturalis cuilibet parti; et ita ipsum totum et quaelibet pars quiescit. Si vero non est ei naturalis, ergo et totum et pars erunt extra proprium locum. Et ita totum et quaelibet pars eius movebitur semper. Then he shows that the other alternative has to be accepted; for it has already been assumed that the natural place of a whole and that of a part are the same. And it is evident that every body is at rest when it is in its natural place, and that it naturally moves to its natural place when it is outside of it. If, then, the whole place occupied by a body having an infinite number of like parts is natural to it, this place must be natural to each part, and thus the whole and each of its parts will be at rest. But if it is not natural to it, the whole and each of its parts will then be outside their proper place; and thus the whole and any part of it will always be in motion. Non enim potest dici quod aliqua pars loci sit naturalis toti et partibus eius, et aliqua pars innaturalis: quia si corpus esset infinitum, et omne corpus esset in loco, oportet quod locus etiam sit infinitus. In loco autem infinito non potest inveniri ratio divisionis, quare aliquid eius sit naturalis locus corporis, et aliud non naturalis locus: quia oportet esse aliquam determinatam proportionem et distantiam loci naturalis ad non naturalem: quod in loco infinito non potest inveniri. Hoc est ergo quod dicit, quod non magis movebitur corpus infinitum aut pars eius, deorsum quam sursum, vel versus quamcumque aliam partem; quia in loco infinito non potest sumi aliqua determinata proportio harum partium. 2344. For it cannot be said that some part of a place is natural to the whole and to its parts, and that some part of a place is not; because, if a body were infinite and every body were in a place, its place would also have to be infinite. But in infinite place there is no dividedness by reason of which one part of it is the natural place of the body and another is not, because there must be some fixed proportion and distance between a place which is natural and one which is not, and this cannot apply to an infinite place. This is what he means when he says that an infinite body or one of its parts will not be moved downwards rather than upwards or in some other direction, because in an infinite place it is impossible to find any fixed proportion between these parts. Et ponit exemplum: ut si ponamus terram esse infinitam, non erit assignare rationem, quare magis moveatur vel quiescat hic quam ibi: quia totus locus infinitus est connaturalis similiter ipsius corporis infiniti, quod est in loco. Unde si aliqua pars loci est connaturalis glebae, et similiter alia pars; et si una non est connaturalis, nec alia. Si igitur corpus infinitum sit in loco, obtinebit totum locum infinitum. Et quomodo poterit simul esse quies et motus? Quia si ubique quiescit, non movebitur; aut si movebitur ubique, sequitur quod nihil quiescat. 2345. He gives an example of this. If we assume that the earth is infinite, it will be impossible to give any reason why it should be in motion or at rest in one place rather than in another, because the whole infinite place will be equally fitted by nature to the infinite body which occupies this place. Hence, if some part of a place is naturally fitted to a clod of earth, the same will apply to another part; and if one part is not naturally fitted to a Place, neither will another be. If, then, an infinite body is in a place, it will fill the whole of that infinite place. Yet how can it be at rest and in motion at the same time? For if it rests everywhere, it will not be in motion ; or if it is in motion everywhere, it follows that no part of it will be at rest. 2346. And if the whole (1000). Deinde cum dicit si autem prosequitur philosophus alteram partem disiunctivae, scilicet si totum non est similium partium: dicens, quod primo sequitur, quod corpus omnis, idest totius, si sit partium dissimilium specie, non sit unum nisi in tangendo, sicut acervus lapidum est unus. Quae autem sunt diversarum specierum, non possunt esse continua, sicut ignis et aer et aqua. Et hoc non est esse unum simpliciter. Then the Philosopher examines the other alternative, namely, the supposition that the whole is not composed of like parts. He says that it follows, first, that, if “the body of the whole,” i.e., of the universe, is composed of specifically unlike parts, it will be one only by contact, as a pile of stones is one. But things specifically different, such as fire, air and water, cannot be continuous; and this is not to be one in an absolute sense. Item si istud totum constat ex dissimilibus partibus specie, aut essent infinita specie, ita scilicet quod sint infinitae species diversae partes totius; aut essent finita specie, ita scilicet quod diversitas specierum quae est in partibus, aliquo certo numero concludatur. 2347. Again, if this whole is composed of parts which are specifically unlike, they will be either infinite in species, i.e., so that the different parts of the whole are infinite in species; or they will be finite in species, i.e., so that the diversity of species found among the parts amount to some fixed number. Sed quod impossibile sit esse finita elementa secundum speciem, patet ex eo quod in praecedenti ratione est positum. Non enim esset possibile ex partibus numero finitis constitui totum infinitum, nisi vel omnes partes essent infinitae quantitate, quod est impossibile, cum corpus infinitum oporteat ad quamlibet partem infinitum esse, vel saltem quod aliqua pars vel aliquae partes infinitatem habeant. Sequitur igitur quod, si totum est infinitum et partes specie diversae infinitae numero, quod quaedam earum sint infinitae in quantitate, et quaedam finitae: puta si poneretur quod aqua esset infinita, et ignis finitus. Sed hoc ponere inducit corruptionem in contrariis: quia id quod est infinitum, corrumpet alia, ut supra ostensum est. Non est igitur possibile, quod sint finita numero. 2348. But that the elements cannot be finite in species is clear from what was proposed in the preceding argument; for it would be impossible for an infinite whole to be composed of parts which are finite in number, unless either all parts were infinite in quantity, which is impossible, since an infinite body must be infinite in any of its parts, or at least unless some part or parts were infinite. Therefore, if a whole were infinite and its parts were different species infinite in number, it would follow that some of them would be infinite and some finite in quantity—for example, if one were to assume that water is infinite and fire finite. But this position introduces corruption among contraries, because an infinite contrary would destroy other contraries, as has been shown above (996:C 2332). Therefore they cannot be finite in number. Sed si sunt infinitae secundum speciem primae partes universi, quas oportet ponere partes simplices, sequitur quod loca erunt infinita, et quod elementa erunt infinita. Quorum utrumque est impossibile. Cum enim unumquodque corpus simplex habeat locum sibi connaturalem diversum a loco corporis alterius secundum speciem, si sint infinita corpora simplicia secundum speciem diversa, sequitur quod etiam sint infinita loca diversa specie. Quod patet esse falsum. Nam species locorum sunt sub aliquo numero determinato, quae sunt sursum et deorsum et huiusmodi. Elementa etiam esse infinita impossibile est; quia sic sequeretur quod essent ignota, et eis ignotis omnia ignorarentur. Si ergo impossibile est elementa esse infinita, necesse est quod loca sint finita, et per consequens quod totum sit finitum. 2349. But if the parts of the universe were infinite in species, and these must be assumed to be simple, it would follow that places would be infinite and that the elements would be infinite. But both of these are impossible; for since each simple body has a place naturally fitted to it which is specifically different from the place of another body, if there were an infinite number of simple bodies which are different in species, it would also follow that there are an infinite number of places which are different in species. This is obviously false; for the species of places are limited in number, and these are up and down, and so on. It is also impossible that the elements should be infinite in number, because it would then follow that they would remain unknown; and if they were unknown, all things would be unknown. Therefore, if the elements cannot be infinite, places must be finite, and consequently the whole must be finite. 2350. And in general (1001). Deinde cum dicit totaliter autem secundam rationem ponit; dicens, quod cum omne corpus sensibile habeat locum, impossibile est quod aliquod corpus sensibile sit infinitum: hac positione facta, quod omne corpus sensibile habeat gravitatem aut levitatem. Quod quidem verum erat secundum opinionem antiquorum naturalium ponentium corpus infinitum actu: sed ipse opinatur quod sit aliquod corpus sensibile, non habens gravitatem neque levitatem, scilicet corpus caeleste, ut probavit in libro de caelo et mundo. Et ideo hoc induxit sub conditione, quasi ab adversariis concessum, sed non simpliciter verum. Si ergo omne corpus sensibile est grave vel leve, et est aliquod corpus sensibile infinitum, oportet quod sit grave vel leve, et per consequens quod feratur sursum vel ad medium. Definitur enim leve quod fertur sursum, et grave quod fertur ad medium. Sed hoc est impossibile invenire in infinito, neque in toto neque in parte. Non enim invenitur medium in aliquo corpore nisi proportione habita ad extrema in dividendo totum. Infinitum vero non potest dividi secundum aliquam proportionem. Unde non potest ibi inveniri sursum et deorsum, nec extremum et medium. Here he gives the second argument. He says that, since every sensible body has a place, it is impossible for any sensible body to be infinite, granted the assumption that every sensible body has heaviness and lightness-which would be true according to the opinion of the ancient natural philosophers, who claimed that bodies are actually infinite. Aristotle, however, is of the opinion that there is a sensible body which does not have heaviness or lightness, namely, a celestial body, as he proved in The Heavens. He introduces this circumstantially, as admitted by his opponents, but not in the sense that it is unqualifiedly true. If every sensible body, then, is either heavy or light and some sensible body is infinite, it must be heavy or light; and therefore it must be moved upwards or towards the center; for a light thing is defined as one that rises upwards, and a heavy thing as one that tends towards the center. But this cannot apply to the infinite, either to the whole of it or to a part; for the center of a body is found only when a proportion is established between the boundaries by dividing the whole. But the infinite cannot be divided according to any proportion; and therefore neither up and down nor boundary and center can be found there. Considerandum autem quod haec ratio valet etiam si ponatur corpus tertium, quod neque est grave neque leve. Tale enim corpus naturaliter movetur circa medium, quod non potest in corpore infinito inveniri. 2351. This argument must be understood to apply even if one assumes that there is a third kind of body which is neither heavy nor light; for such a body is naturally moved around the center, and this could not be the case with an infinite body. 2352. Further, every sensible body (1002). Deinde cum dicit adhuc omne hic philosophus ponit tertiam rationem, quae talis est. Omne corpus sensibile est in loco. Sed loci species sunt sex; scilicet sursum, deorsum, dextrum, sinistrum, ante et retro. Quae quidem impossibile est attribui corpori infinito, cum sint quaedam extrema distantiarum; et sic corpori infinito impossibile est attribuere locum. Non est igitur aliquod corpus sensibile infinitum. Non autem dicit quod sint sex species loci, asserere intendens quod ista loca distinguantur in elementis; quia motus eorum non distinguunt nisi sursum et deorsum; sed quia, sicut ab infinito corpore removentur sursum et deorsum, ita omnes aliae differentiae loci. The Philosopher now gives the third argument, which runs thus: every sensible body is in a place. But there are six kinds of place: up and down, right and left, before and behind; and it is impossible to attribute these to an infinite body, since they are the limits of distances. Thus it. is impossible that a place should be attributed to an infinite body; and therefore no sensible body is infinite. However, in saying that there are six kinds of place he does not mean that these places are distinguished because of the elements (for their motions are distinguished merely in terms of up and down) but only because, just as up and down are out of the question so far as an infinite body is concerned, so are all the other differences of place. 2353. And in general if (1003). Quartam rationem ponit ibi totaliter autem. Quae talis est. Omne corpus sensibile est in loco. Sed impossibile est esse locum infinitum; ergo impossibile est esse corpus infinitum. Quomodo autem impossibile sit locum esse infinitum, ex hoc probatur. De quocumque enim praedicatur commune aliquod, oportet praedicari aliquod eorum quae sunt sub illo communi; sicut quod est animal, oportebit quod sit in aliqua specie animalis. Et quod est homo, oportet quod sit aliquis homo. Et similiter quod est in infinito loco oportet quod sit alicubi, idest in aliquo loco. Esse autem in aliquo loco, est esse vel sursum vel deorsum, vel secundum aliquam aliam speciem: quarum nullam possibile est esse infinitam, quia unumquodque horum est terminus alicuius distantiae; ergo impossibile est esse locum infinitum et similiter corpus. He gives the fourth argument, which is as follows. Every sensible body is in a place; but it is impossible for a place to be infinite; and therefore it is impossible for a body to be infinite. The way in which it is impossible for a place to be infinite he proves thus: whatever has a common term predicated of it must also have predicated of it any of the things which fall under that common term; for example, whatever is an animal must belong to some particular species of animal, and whatever is man must be some particular man. Similarly, whatever occupies an infinite place must be “somewhere,” i.e., it must occupy some place. But to occupy some place is to be up or down or to be in some one of the other kinds of place. However, none of these can be infinite because each is the limit of some distance. It is impossible, then, that a place should be infinite, and the same applies to a body. 2354. And the infinite (1004). Deinde cum dicit infinitum autem ostendit quomodo infinitum in potentia in diversis inveniatur; et dicit quod invenitur in magnitudine et motu et tempore; et non univoce praedicatur de eis, sed per prius et posterius. Et semper quod est in eis posterius, dicitur infinitum, secundum quod id quod est prius est infinitum, sicut motus secundum magnitudinem, in quam aliquid movetur localiter, aut augetur, aut alteratur. Et tempus dicitur infinitum secundum motum: quod sic intelligendum est. Infinitum enim divisione, attribuitur continuo, quod primo attribuitur magnitudini, ex qua motus habet continuitatem. Quod manifestum est in motu locali; quia partes in motu locali accipiuntur secundum partes magnitudinis. Et similiter manifestum est in motu augmenti; quia secundum additionem magnitudinis, augmentum attenditur. Sed in alteratione non est ita manifestum. Sed tamen etiam ibi aliqualiter verum est; quia qualitas secundum quam fit alteratio, per accidens dividitur ad divisionem magnitudinis. Et iterum intensio et remissio qualitatis attenditur secundum quod subiectum in magnitudine existens, aliquo modo vel perfectiori vel minus perfecto participat qualitatem. Then he shows how the potentially infinite is found in different things. He says that it is found in continuous quantity, in motion, and in time, and it is not predicated of them univocally but in a primary and a secondary way. And the secondary member among them is always said to be infinite inasmuch as the primary member is; for example, motion is said to be infinite in reference to the continuous quantity in which something is moved locally or increased or altered; and time is said to be infinite in reference to motion. This must be understood as follows: infinite divisibility is attributed to what is continuous, and this is done first with reference to continuous quantity, from which motion derives its continuity. This is evident in the case of local motion because the parts of local motion are considered in relation to the parts of continuous quantity. The same thing is evident in the case of the motion of increase, because increase is noted in terms of the addition of continuous quantity. However, this is not as evident in the case of alteration, although in a sense it also applies there; because quality, which is the realm of alteration, is divided accidentally upon the division of continuous quantity. Again, the intensification and abatement of a quality is also noted inasmuch as its subject, which has continuous quantity, participates in some quality to a greater or lesser degree. Ad continuitatem autem motus, est et tempus continuum. Nam tempus secundum se, cum sit numerus, non habet continuitatem, sed solum in subiecto. Sicut decem mensurae panni continuae sunt, eo quod pannus quoddam continuum est. Eodem igitur ordine oportet quod infinitum de istis tribus dicatur sicut et continuum. And motion is referred to continuity, and so is a continuous time; for since time in itself is a number, it is continuous only in a subject, just as ten measures of cloth are continuous because the cloth is continuous. The term infinite, then, must be used of these three things in the same order of priority as the term continuous is.
LESSON 11 Motion and Change
ARISTOTLE’S TEXT Chapter it: 1067b 1-1068a 7 μεταβάλλει δὲ τὸ μεταβάλλον τὸ μὲν κατὰ συμβεβηκός,  ὡς τὸ μουσικὸν βαδίζει, τὸ δὲ τῷ τούτου τι μεταβάλλειν ἁπλῶς λέγεται μεταβάλλειν, οἷον ὅσα κατὰ μέρη (ὑγιάζεται γὰρ τὸ σῶμα, ὅτι ὁ ὀφθαλμός), ἔστι δέ  τι ὃ καθ᾽ αὑτὸ πρῶτον κινεῖται, καὶ τοῦτ᾽ ἔστι τὸ καθ᾽ αὑτὸ κινητόν. 1005. Everything which is changed is changed either accidentally, as when we say that a musician walks; or it is changed without qualification because something belonging to it is changed, as what is changed in some of its parts; for example, the body is said to be healed because the eye is. And there is some primary thing which is moved of itself, and this is what is essentially movable. ἔστι δέ [τι] καὶ ἐπὶ τοῦ κινοῦντος ὡσαύτως: κινεῖ γὰρ κατὰ συμβεβηκὸς τὸ δὲ κατὰ μέρος τὸ δὲ καθ᾽ αὑτό: 1006. The same division applies to a mover, for it causes motion either accidentally or in some part of itself or essentially. ἔστι δέ τι τὸ κινοῦν πρῶτον: ἔστι δέ τι τὸ κινούμενον, ἔτι ἐν ᾧ χρόνῳ καὶ ἐξ οὗ καὶ εἰς ὅ. τὰ δ᾽ εἴδη καὶ τὰ πάθη καὶ  ὁ τόπος, εἰς ἃ κινοῦνται τὰ κινούμενα, ἀκίνητά ἐστιν, οἷον ἐπιστήμη καὶ θερμότης: ἔστι δ᾽ οὐχ ἡ θερμότης κίνησις ἀλλ᾽ ἡ θέρμανσις. 1007. And there is a primary mover and something which is moved. And there is also a time in which it is moved, and something from which it is moved, and something to which it is moved. But the forms and modifications and place to which things in motion are moved are immovable, as science and heat. Heat is not motion, but heating is. ἡ δὲ μὴ κατὰ συμβεβηκὸς μεταβολὴ οὐκ ἐν ἅπασιν ὑπάρχει ἀλλ᾽ ἐν τοῖς ἐναντίοις καὶ μεταξὺ καὶ ἐν ἀντιφάσει: τούτου δὲ πίστις ἐκ τῆς ἐπαγωγῆς. μεταβάλλει  δὲ τὸ μεταβάλλον ἢ ἐξ ὑποκειμένου εἰς ὑποκείμενον, ἢ οὐκ ἐξ ὑποκειμένου εἰς οὐχ ὑποκείμενον, ἢ ἐξ ὑποκειμένου εἰς οὐχ ὑποκείμενον, ἢ οὐκ ἐξ ὑποκειμένου εἰς ὑποκείμενον (λέγω δὲ ὑποκείμενον τὸ καταφάσει δηλούμενον), ὥστ᾽ ἀνάγκη τρεῖς εἶναι μεταβολάς: ἡ γὰρ ἐξ οὐχ ὑποκειμένου  εἰς μὴ ὑποκείμενον οὐκ ἔστι μεταβολή: οὔτε γὰρ ἐναντία οὔτε ἀντίφασίς ἐστιν, ὅτι οὐκ ἀντίθεσις. 1008. Now change which is not accidental is not found in all things, but between contraries and between their intermediates and between contradictories. We may be convinced of this by induction. Whatever is changed is changed either from a subject to a subject, or from a non-subject to a non-subject, or from a subject to a non-subject, or from a non-subject to a subject. And by subject I mean what is expressed by an affirmative term. Hence there must be three changes; for to go from a non-subject to a non-subject is not change, because, since the limits are neither contraries nor contradictories, there is no opposition (1008). ἡ μὲν οὖν οὐκ ἐξ ὑποκειμένου εἰς ὑποκείμενον κατ᾽ ἀντίφασιν γένεσίς ἐστιν, ἡ μὲν ἁπλῶς ἁπλῆ, ἡ δὲ τινὸς τίς: ἡ δ᾽ ἐξ ὑποκειμένου εἰς μὴ ὑποκείμενον φθορά, ἡ μὲν ἁπλῶς ἁπλῆ, ἡ δὲ τινὸς  τίς. 1009. The change from a non-subject to a subject which is its contradictory is generation; and if it is unqualified, it is generation in an unqualified sense, and if in a part, partial generation; and the change from a subject to a non-subject is destruction. εἰ δὴ τὸ μὴ ὂν λέγεται πλεοναχῶς, καὶ μήτε τὸ κατὰ σύνθεσιν ἢ διαίρεσιν ἐνδέχεται κινεῖσθαι μήτε τὸ κατὰ δύναμιν τὸ τῷ ἁπλῶς ὄντι ἀντικείμενον (τὸ γὰρ μὴ λευκὸν ἢ μὴ ἀγαθὸν ὅμως ἐνδέχεται κινεῖσθαι κατὰ συμβεβηκός, εἴη γὰρ ἂν ἄνθρωπος τὸ μὴ λευκόν: τὸ δ᾽ ἁπλῶς  μὴ τόδε οὐδαμῶς), ἀδύνατον τὸ μὴ ὂν κινεῖσθαι (εἰ δὲ τοῦτο, καὶ τὴν γένεσιν κίνησιν εἶναι: γίγνεται γὰρ τὸ μὴ ὄν: εἰ γὰρ καὶ ὅτι μάλιστα κατὰ συμβεβηκὸς γίγνεται, ἀλλ᾽ ὅμως ἀληθὲς εἰπεῖν ὅτι ὑπάρχει τὸ μὴ ὂν κατὰ τοῦ γιγνομένου ἁπλῶς): ὁμοίως δὲ καὶ τὸ ἠρεμεῖν. ταῦτά  τε δὴ συμβαίνει δυσχερῆ, καὶ εἰ πᾶν τὸ κινούμενον ἐν τόπῳ, τὸ δὲ μὴ ὂν οὐκ ἔστιν ἐν τόπῳ: εἴη γὰρ ἂν πού. οὐδὲ δὴ ἡ φθορὰ κίνησις: ἐναντίον γὰρ κινήσει κίνησις ἢ ἠρεμία, φθορὰ δὲ γενέσει. 1010. If non-being has several different meanings, then neither that which involves a combination or separation of terms, nor that which refers to potentiality and is opposed to being in an unqualified sense, is capable of being moved (for what is not-white or not-good can be moved only accidentally, since what is not-white may be a man). But non-being in an unqualified sense cannot be moved in any way, because it is impossible for non-being to be moved. And if this is so, generation cannot be motion, because non-being is generated. For even if it is most certainly generated accidentally, it will still be true to say that what is generated in an unqualified sense is non-being. The same argument applies to rest. These are the difficulties, then, which result from this view. And if everything moved is in a place, though non-being is not in a place, it would have to be somewhere. Nor is destruction motion; for the contrary of motion is motion or rest, but the contrary of destruction is generation. [1068α]  ἐπεὶ δὲ πᾶσα κίνησις μεταβολή τις, μεταβολαὶ δὲ τρεῖς αἱ εἰρημέναι, τούτων δ᾽ αἱ κατὰ γένεσιν καὶ φθορὰν οὐ κινήσεις, αὗται δ᾽ εἰσὶν αἱ κατ᾽ ἀντίφασιν, ἀνάγκη τὴν ἐξ ὑποκειμένου εἰς ὑποκείμενον κίνησιν εἶναι  μόνην. τὰ δ᾽ ὑποκείμενα ἢ ἐναντία ἢ μεταξύ (καὶ γὰρ ἡ στέρησις κείσθω ἐναντίον), καὶ δηλοῦται καταφάσει, οἷον τὸ γυμνὸν καὶ νωδὸν καὶ μέλαν. 1011. And since every motion is a kind of change, and the three changes are those described (1008), and of these those which refer to generation and destruction are not motions, and these are changes between contradictories, only change from a subject to a subject must be motion. And the subjects are either contraries or their intermediates—for privation is given as a contrary—and they are expressed by an affirmative term, for example, naked or toothless or black. COMMENTARY Postquam philosophus ostendit quid est motus, et determinavit de infinito quod est passio quaedam motus, hic determinat de partibus motus; et dividitur in duas partes. In prima dividit motum in suas partes. In secunda manifestat concomitantia motum et partes eius, ibi, simul secundum locum. 2355. Having explained what motion is, and having dealt with the infinite, which is a certain attribute of motion, here the Philosopher establishes the truth about the parts of motion. This is divided into two parts. In the first (1005:C 2355) he distinguishes the parts of motion; and in the second (1021:C :2404) he explains the connection between motion and its parts (“Things which are”). Prima dividitur in partes tres, secundum tres divisiones motus, quarum tamen una sub altera accipitur, utpote dividens aliquod membrum praecedentis divisionis. The first is divided into three members, corresponding to the three divisions which he makes in motion, although one of these is included under the other as a subdivision of the preceding division. Circa primum duo facit. Primo dividit motum ex parte mobilis. Secundo ex parte moventis, ibi, est autem aliquid. In regard to the first he does two things. First, he divides motion with regard to the thing moved; and second (1006:C 2358), with regard to a mover (“The same division”). Dicit ergo primo, quod tribus modis aliquid permutatur. Uno modo permutatur aliquid per accidens tantum, quando scilicet aliquid dicitur permutari ex quo illud in quo est, permutatur: sive sit in eo ut accidens in subiecto, sicut musicum dicimus ambulare, sive sit forma substantialis in materia ut anima in moto corpore, sive quaecumque pars moto toto, sive etiam contentum moto continente, ut nauta mota navi. He accordingly says, first (1005), that a thing may be changed in three ways. In one way a thing may be changed only accidentally, as when something is said to be changed because the thing to which it belongs is changed, whether it belongs to it as an accident to a subject, as when we say that a musician walks, or as a substantial form to matter, as the soul belongs to the body which is moved; or as a part is said to be moved when the whole is moved, or also as something contained is moved when its container is moved, as a sailor is said to be in motion when his ship is in motion. Secundo modo dicitur aliquid permutari simpliciter eo quod aliquid eius permutatur, sicut ea quae moventur secundum partem. Sicut corpus hominis dicitur sanari, quia sanatur oculus. Et hoc quidem est per se moveri, sed non primo modo. 2356. In a second way a thing is said to be changed without qualification because some part of it is changed, as those things which are moved in some part; for example, the body of a man is said to be healed because the eye is; and this is to be moved essentially but not in the first instance. Tertio modo dicitur aliquid moveri primo et per se, sicut si aliquod totum moveatur secundum totum, ut si lapis deorsum feratur. 2357. In a third way a thing is said to be moved primarily and of itself; as when some whole is moved in its totality, for example, when a stone is moved downwards. 2358. The same division (1006). Deinde cum dicit est autem ponit eamdem divisionem ex parte moventis. Dicitur enim movens tripliciter. Uno modo movens secundum accidens, sicut musicus aedificat. He then gives the same division with regard to a mover; for a thing is said to be a mover in three ways. First, a thing is said to cause motion accidentally; as when a musician builds. Alio modo secundum partem, sicut homo manu vulnerat et percutit. 2359. Second, a thing is said to be a mover in regard to some one of its parts; as when a man strikes and injures someone with his hand. Tertio modo per se, sicut ignis calefacit, et medicus sanat. 2360. Third, a thing is said to be a mover essentially; as when fire heats and a physician heals. 2361. And there is (1007). Deinde cum dicit est autem ponit secundam divisionem motus, seu mutationis. Et circa hoc tria facit. Primo praemittit quaedam quae sunt necessaria ad divisionem motus accipiendam. Secundo dividit motionem, ibi, quae autem non secundum accidens. Tertio manifestat divisionem mutationis, ibi, quae quidem igitur non ex subiecto. Then he gives a second division of motion or change, and in regard to this he does three things. First (1007:C 2361), he prefaces his discussion with certain points which are necessary for an understanding of the division of motion. Second (1008:C 2363), he divides motion (“Now change”). Third (1009:C 2366), he explains the division of change (“The change”). Dicit ergo primo, quod in qualibet mutatione inveniuntur quinque. Est enim in omni mutatione aliquid quod est primum movens. Secundo est aliquid quod movetur. Tertio est tempus in quo fit mutatio: quia omnis motus est in tempore. Quarto est terminus ex quo incipit motus. Quinto est terminus in quem motus tendit. Non autem dividitur motus sive mutatio in suas species, secundum movens, neque secundum id quod movetur, neque secundum tempus: quia ista sunt communia omni mutationi. Sed dividitur secundum terminos, ex quo, et in quem est motus. He says, first, that there are five things found in every change. First, there is a primary mover; second, something which is moved; third, a time during which the motion takes place, because every motion occurs in time; fourth, a starting point from which motion begins; and fifth, a terminus to which the motion proceeds. However, motion or change is not divided into species either on the basis of the mover or of the thing moved or of time, because these are common to every change; but it is divided on the basis of the starting point from which it begins and the terminus to which it proceeds. Et ideo duo ultimo posita manifestat, dicens, quod species, idest formae et passiones, idest qualitates et locus, sunt termini motuum, quia in ea moventur ea quae mobilia sunt. Et dicit species, propter generationem et corruptionem. Passiones, propter alterationes. Et locum, propter loci mutationem. Et exemplificat de passionibus per scientiam et caliditatem. Sed quia quibusdam videbatur quod caliditas esset idem quod alteratio, et sic sequeretur quod caliditas esset motus et non terminus motus, ideo dicit quod caliditas non est motus, sed calefactio. 2362. He therefore explains the last two, saying that “the forms,” i.e., specifying principles, “modifications,” i.e., qualities, and “place,” are limits of motion, because those things which are movable are moved with respect to these. He uses the term forms, because of generation; modifications, because of alterations; and place, because of local motion. He gives examples of modifications by using science and heat. And because it might seem to some that heat is the same as alteration, and then it would follow that heat is motion and not a limit or terminus of motion, he therefore says that heat is not motion but heating is. 2363. Now change (1008). Deinde cum dicit quae autem praetermissis duabus partibus primae divisionis, accipit tertiam; et eam subdividit secundum terminos, scilicet mutationem, quae non est per accidens, neque secundum partem: dicens, quod permutatio quae non est secundum accidens, non existit inter quoscumque terminos; sed oportet, quod termini eius sint vel contraria, sicut est mutatio de albo in nigrum; vel intermedia, sicut mutatio de nigro in rubeum et de rubeo in pallidum; aut est mutatio inter contradictoria, sicut de albo in non album, aut e converso. Tacet autem de privative oppositis, quia media sunt inter contradictoria et contraria, et sub eis intelliguntur. Then, passing over two parts of the first division, he takes the third, namely, change which is neither accidental nor in a part, and subdivides it according to its limits. He says that change which is not accidental is not found between just any limits whatever; but its limits must either be contraries, as change from white to black, or intermediates, as change from black to red and from red to gray; or there is change between contradictories, as from white to not-white, and vice versa. He says nothing of privative opposites because they are found between contradictories and contraries and are understood to come under these. Et quod solum inter praedictos terminos fiat permutatio, ostendit per inductionem. Quatuor enim modis possunt variari termini mutationis. Aut ita, quod uterque sit affirmativus, ut si aliquid dicatur mutari ex albo in nigrum; et hoc est quod dicit, ex subiecto in subiectum. Aut ita, quod uterque sit negativus, ut si aliquid dicatur mutari de non albo in non nigrum: et hoc est quod dicitur, ex non subiecto in non subiectum. Aut ita quod terminus a quo sit affirmativus, et terminus ad quem sit negativus, ut si dicatur mutari de albo in non album: et hoc est quod dicit, ex subiecto in non subiectum. Aut ita, quod terminus a quo sit negativus et terminus ad quem affirmativus, ut si dicatur aliquid mutari de non albo in album: et hoc est quod dicit, ex non subiecto in subiectum. Exponit autem quod dixerat subiectum, scilicet id quod affirmative significatur. 2364. He shows by induction that change takes place only between the above-mentioned limits; for the limits of change admit of four possible combinations: first, when both limits are affirmative or positive terms, as when something is said to be changed from white to black, and this change he describes as one from subject to subject; second, when both limits are negative terms, as when something is said to be changed from not-white to not-black, or in his words, from non-subject to non-subject; third, when the starting point from which change begins is a positive term and the terminus to which it proceeds is a negative one, as when a thing is said to be changed from white to not-white, or as he says, from subject to non-subject; fourth, when the starting point of change is a negative term and the terminus to which it proceeds is a positive one, as when a thing is said to be changed from not-white to white, or as he says, from a non-subject to a subject. He explains the meaning of the term subject which he had used, as what is signified by an affirmative or positive term. Harum autem quatuor combinationum, una est inutilis. Non enim est aliqua permutatio de non subiecto in non subiectum. Duae enim negationes, sicut non album, et non nigrum, neque sunt contraria, neque contradictoria, quia non sunt opposita. Possunt enim verificari de eodem. Multa enim sunt, quae neque alba neque nigra sunt. Unde, cum mutatio sit inter opposita, ut in primo physicorum probatum est, relinquitur quod de non subiecto in non subiectum, non sit permutatio. Et sic est necesse solum tres esse permutationes; scilicet duas secundum contradictionem, et unam secundum contrarietatem. 2365. Now one of these four combinations is useless; for there is no change from a non-subject to a non-subject, because two negative terms, such as not-white and not-black, are neither contraries nor contradictories since they are not opposites; for they can be affirmed truly of the same subject because there are many things which are neither white nor black. Hence, since change is between opposites, as is proved in Book I of the Physics, it follows that there is no change from a non-subject to a non-subject. Therefore there must be three kinds of change, two of which relate to contradiction and the other to contrariety. 2366. The change (1009). Deinde cum dicit quae quidem manifestat quid sint praedictae tres mutationes; et circa hoc tria facit. Primo ostendit quod duae earum sunt generatio et corruptio. Secundo ostendit quod neutra earum est motus, ibi, si itaque non ens. Tertio concludit quae mutatio dicatur motus, ibi, quoniam autem omnis motus et cetera. Then he shows what these three changes are; and in regard to this he does three things. First, he shows that generation and destruction are two of these. Second (1010:C 2368), he shows that neither of these is motion (“If non-being”). Third (1011:C 2375), he draws his conclusion as to which change is called motion (“And since every”). Dicit ergo primo, quod trium praedictarum mutationum illa quae est de non subiecto in subiectum, existens inter contradictorios terminos, vocatur generatio. Sed hoc contingit dupliciter. Quia aut est mutatio de non ente simpliciter in ens simpliciter, et tunc est generatio simpliciter. Et hoc quando mutabile subiectum mutatur secundum substantiam. Aut est de non ente in ens non simpliciter, sed secundum quid, sicut de eo quod non est album, in albo: et haec est generatio quaedam et secundum quid. He accordingly says, first (1009), that of the three changes mentioned above, that which is from a non-subject to a subject, or between contradictory terms, is called generation. And this is twofold; for there is change either from non-being in an unqualified sense to being in an unqualified sense (generation in an unqualified sense), and this occurs when a movable subject is changed substantially; or there is change from non-being to being, not in an unqualified sense but in a qualified one, for example, change from not-white to white (generation in a qualified sense). Illa vero mutatio, quae est de subiecto in non subiectum, dicitur corruptio. Et similiter in hac distinguitur simpliciter et secundum quid sicut in generatione. 2367. But that change which proceeds from a subject to a non-subject is called destruction; and in this change we also distinguish between destruction in an unqualified sense and in a qualified one, just as we did in the case of generation. 2368. If non-being (1010). Deinde cum dicit si itaque ostendit philosophus quod neutra harum mutationum est motus. Et primo ostendit hoc de generatione. Secundo de corruptione, ibi, neque itaque corruptio motus. Then the Philosopher shows that neither of these changes is motion. First (1010:C 2368), he shows that this is true of generation; and second (ibid.), that it is true of destruction (“Nor is destruction”). Dicit ergo primo, quod non ens dicitur multipliciter sicut et ens. Uno enim modo dicitur quod est secundum compositionem et divisionem propositionis. Et hoc, cum non sit in rebus, sed in mente, non potest moveri. He accordingly says, first (1010), that the term non-bring is used in the same number of senses as being is. One meaning is the combination and separation found in a proposition; and since this does not exist in reality but only in the mind, it cannot be moved. Alio modo dicitur ens et non ens secundum potentiam et actum. Et id quod est actu, est simpliciter ens. Quod autem est secundum potentiam tantum, est non ens. Dicit ergo, quod neque contingit moveri hoc non ens, quod quidem est secundum potentiam ens, sed non ens actu, quod est quasi oppositum enti in actu simpliciter. 2369. Being and non-being are used in another sense with reference to actuality and potentiality. That which is actual is a being in an unqualified sense, but that which is potential only is a non-being. He therefore says that even that sort of non-being which is a being potentially but not actually cannot be moved. Sed quare dixerit quod est oppositum enti simpliciter, manifestat, cum subdit: quod enim non album. Ens enim in potentia, quod opponitur enti in actu, quod non est ens simpliciter, contingit moveri; quia quod non est non album in actu, aut non bonum in actu, contingit moveri, sed tamen secundum accidens. Non enim ipsum non album movetur, sed subiectum in quo est haec privatio, quod est ens actu. Quod enim est non album, potest esse homo. Sed quod est non ens in actu simpliciter, idest secundum substantiam, nequaquam contingit moveri. Si, inquam, haec omnia vera sunt, impossibile est non ens moveri. Et si hoc verum est, impossibile est generationem esse motum, quia non ens generatur. Est enim generatio, ut dictum est, de non ente in ens. Unde, si generatio simpliciter esset motus, sequeretur quod non ens simpliciter moveretur. 2370. He explains why he had said that actual non-being is opposed to being in an unqualified sense, when he adds “for what is not-white.” For potential being, which is opposed to actual being and is not being in an unqualified sense, can be moved, because what is not not-white actually or not-good actually can be moved, but only accidentally. For what is moved is not the not-white itself, but the subject in which this privation is found, and this is an actual being. For that which is not white may be a man, but that which is an actual non-being in an unqualified sense, i.e., in substance, cannot be moved at all. Now if all of these statements are true, I say, it is impossible for non-being to be moved. And if this is the case, generation cannot be motion, because non-being is generated. For generation, as has been pointed out (1009:C 2366), proceeds from non-being to being. Hence, if generation in an unqualified sense were motion, it would follow that non-being in an unqualified sense would be moved. Sed huic processui posset aliquis obviare, dicens, quod non ens non generatur nisi per accidens: per se enim generatur id quod est subiectum generationis, idest ens in potentia. Non ens autem significat privationem in materia. Unde non generatur nisi per accidens. 2371. But one can raise an objection to this process of reasoning by saying that non-being is generated only accidentally; for “the subject of generation,” i.e., a being in potentiality, is generated essentially. But non-being signifies privation in a matter. Hence it is generated only accidentally. 2372. For even if (ibid.). Sed hanc obviationem excludit, ibi, si enim et quam maxime. Dicens, quod licet ens non generetur nisi secundum accidens, tamen de eo quod generatur simpliciter, verum est dicere, quod est non ens. Et de quocumque est hoc verum dicere, impossibile est id moveri. Ergo subiectum mutationis impossibile est moveri. Et similiter impossibile est ipsum quiescere, quia non ens simpliciter non movetur neque quiescit. Haec enim inconvenientia accidunt, si quis ponit generationem esse motum. Then he refutes this objection. He says that, even if a being is generated only accidentally, nevertheless it is true to say that what is generated in an unqualified sense is non-being. And of each of these it is true to say that it cannot be moved. Similarly it cannot be at rest, because non-being in an unqualified sense is neither in motion nor at rest. These are the untenable results if one maintains that generation is motion. Ad ostendendum autem quod non ens non movetur, subiungit quod omne quod movetur, est in loco, quia motus localis est prior motuum. Non ens autem simpliciter, non est in loco, quia alicubi esset non ens. Igitur non potest moveri: et sic generatio non est motus. 2373. In order to show that nonbeing is not moved, he adds that everything which is moved is in a place because local motion is the first of all motions, whereas non-being in an unqualified sense is not in a place; for [were it moved] it would then be somewhere. Hence it cannot be moved; and therefore generation is not motion. 2374. Nor is destruction (ibid.). Et ex hoc ulterius ostendit quod neque corruptio est motus, ibi, neque itaque corruptio. Quia motui non contrariatur nisi motus vel quies. Sed corruptioni contrariatur generatio. Si ergo corruptio sit motus, oportet quod generatio sit vel motus vel quies. Quod non potest esse, ut ostensum est. From these considerations he further shows that destruction is not motion; for the only thing that is opposed to motion is motion or rest. But destruction is opposed to generation. Therefore, if destruction were motion, generation would have to be either motion or rest. But this cannot be true, as has been shown. 2375. And since every motion (1011). Deinde cum dicit quoniam autem ostendit quae mutatio dicatur motus; dicens quod omnis motus est aliqua permutatio. Permutationes autem sunt solum tres: quarum duae, quae sunt secundum contradictionem, scilicet generatio et corruptio, non sunt motus. Relinquitur ergo quod sola mutatio, scilicet de subiecto in subiectum, sit motus. Et cum subiecta ista inter quae est motus oporteat esse opposita, necesse est quod sint contraria vel intermedia; quia privatio, licet affirmativa monstretur, sicut nudum, edentulum et nigrum, tamen ad contrarium reducitur, quia privatio est prima contrarietas, ut in decimo ostensum est. Dicit autem nigrum esse privationem non simpliciter, sed inquantum defective participat generis naturam. Next he shows which change is said to be motion. He says that every motion is a kind of change. But there are only three changes, and two of these, which involve contradictories, i.e., generation and destruction, are not motion. It follows, then, that only change from a subject to a subject is motion. And since the subjects between which motion takes place must be opposed to each other, they must be contraries or intermediates; for even though a privation is expressed by an affirmative term, such as naked, toothless, and black, it is regarded as a contrary, because privation is the primary contrariety, as has been pointed out in Book X (852:C 2049). And he says that black is a privation not in an unqualified sense but inasmuch as it participates deficiently in the nature of its genus.
LESSON 12 Motion Pertains to Quantity, Quality and Place
ARISTOTLE’S TEXT Chapter 12: 1068a 8-1068b 25 εἰ οὖν αἱ κατηγορίαι διῄρηνται οὐσίᾳ, ποιότητι, τόπῳ, τῷ ποιεῖν ἢ πάσχειν, τῷ πρός τι, τῷ ποσῷ, ἀνάγκη τρεῖς  εἶναι κινήσεις, ποιοῦ ποσοῦ τόπου: 1012. If the categories are divided into substance, quality, place, action, passion, relation and quantity, there must be three kinds of motion, namely, of quality, of quantity and of place. κατ᾽ οὐσίαν δ᾽ οὔ, διὰ τὸ μηθὲν εἶναι οὐσίᾳ ἐναντίον, 1013. There is no motion of substance, because substance has no contrary. οὐδὲ τοῦ πρός τι (ἔστι γὰρ θατέρου μεταβάλλοντος μὴ ἀληθεύεσθαι θάτερον μηδὲν μεταβάλλον, ὥστε κατὰ συμβεβηκὸς ἡ κίνησις αὐτῶν), 1014. Nor is there motion of relation; for it is possible that, when one of two relative things has undergone a change, the other may be truly referred to under a new term even though it has not been changed in any way. Hence the motion of these relative things will be accidental. οὐδὲ ποιοῦντος καὶ πάσχοντος, ἢ κινοῦντος καὶ κινουμένου, ὅτι οὐκ ἔστι  κινήσεως κίνησις οὐδὲ γενέσεως γένεσις, οὐδ᾽ ὅλως μεταβολῆς μεταβολή. διχῶς γὰρ ἐνδέχεται κινήσεως εἶναι κίνησιν, ἢ ὡς ὑποκειμένου (οἷον ὁ ἄνθρωπος κινεῖται ὅτι ἐκ λευκοῦ εἰς μέλαν μεταβάλλει, ὥστε οὕτω καὶ ἡ κίνησις ἢ θερμαίνεται ἢ ψύχεται ἢ τόπον ἀλλάττει ἢ αὔξεται: τοῦτο  δὲ ἀδύνατον: οὐ γὰρ τῶν ὑποκειμένων τι ἡ μεταβολή), ἢ τῷ ἕτερόν τι ὑποκείμενον ἐκ μεταβολῆς μεταβάλλειν εἰς ἄλλο εἶδος, οἷον ἄνθρωπον ἐκ νόσου εἰς ὑγίειαν. ἀλλ᾽ οὐδὲ τοῦτο δυνατὸν πλὴν κατὰ συμβεβηκός. πᾶσα γὰρ κίνησις ἐξ ἄλλου εἰς ἄλλο ἐστὶ μεταβολή, καὶ γένεσις καὶ φθορὰ  ὡσαύτως: πλὴν αἱ μὲν εἰς ἀντικείμενα ὡδί, ἡ δ᾽ ὡδί, ἡ κίνησις. ἅμα οὖν μεταβάλλει ἐξ ὑγιείας εἰς νόσον, καὶ ἐξ αὐτῆς ταύτης τῆς μεταβολῆς εἰς ἄλλην. δῆλον δὴ ὅτι ἂν νοσήσῃ, μεταβεβληκὸς ἔσται εἰς ὁποιανοῦν (ἐνδέχεται γὰρ ἠρεμεῖν) καὶ ἔτι εἰς μὴ τὴν τυχοῦσαν ἀεί: κἀκείνη ἔκ τινος εἴς  τι ἄλλο ἔσται: ὥσθ᾽ ἡ ἀντικειμένη ἔσται, ὑγίανσις, ἀλλὰ τῷ συμβεβηκέναι, οἷον ἐξ ἀναμνήσεως εἰς λήθην μεταβάλλει ὅτι ᾧ ὑπάρχει ἐκεῖνο μεταβάλλει, ὁτὲ μὲν εἰς ἐπιστήμην ὁτὲ δὲ εἰς ἄγνοιαν. 1015. Nor is there motion of agent or of patient as of mover and thing moved, because there is no motion of motion or generation of generation. There are two ways in which there might be motion of motion. First, motion might be of the subject moved, as a man is moved because he is changed from white to black. Thus motion might be heated or cooled or might change its place or might increase. But this is impossible, for change is not a subject. Or, second, some other subject might be changed from change to some other form of being, as a man might be changed from sickness to health. But this is possible only accidentally; for every motion is a change from one thing to something else. The same applies to generation and destruction; although the opposites involved in these changes are different from those of motion. Therefore a man changes at the same time from health to sickness, and from this change itself to another. And it is evident that, if a man has become ill, he will be changed into something else whatever it may be (for he can come to rest); and further this will always be to some opposite which is not contingent; and that change will be from something to something else. Hence, its opposite will be becoming healthy; but this will happen accidentally; for example, there is a change from recollection to forgetting, because the subject to which forgetting belongs is changed, sometimes to a state of knowledge and sometimes to one of ignorance. ἔτι εἰς ἄπειρον βαδιεῖται, εἰ ἔσται μεταβολῆς μεταβολὴ καὶ γενέσεως γένεσις. ἀνάγκη  δὴ καὶ τὴν προτέραν, εἰ ἡ ὑστέρα: οἷον εἰ ἡ ἁπλῆ γένεσις ἐγίγνετό ποτε, καὶ τὸ γιγνόμενον ἐγίγνετο: [1068β]  ὥστε οὔπω ἦν τὸ γιγνόμενον ἁπλῶς, ἀλλά τι γιγνόμενον [ἢ] γιγνόμενον ἤδη. καὶ τοῦτ᾽ ἐγίγνετό ποτε, ὥστ᾽ οὐκ ἦν πω τότε γιγνόμενον. ἐπεὶ δὲ τῶν ἀπείρων οὐκ ἔστι τι πρῶτον, οὐκ  ἔσται τὸ πρῶτον, ὥστ᾽ οὐδὲ τὸ ἐχόμενον. οὔτε γίγνεσθαι οὖν οὔτε κινεῖσθαι οἷόν τε οὔτε μεταβάλλειν οὐδέν. 1016. Further, the process will go on to infinity if there is change of change and generation of generation. Therefore, if the latter comes to be, the former must also; for example, if generation in an unqualified sense at one time was coming to be, that which is coming to be something was also coming to be. Hence that which was coming to be in an unqualified sense did not yet exist, but there was something which was coming to be, or which has already come to be. Therefore, if this also at one time was coming to be, then at that time it was not coming to be something. However, since there is no first term in infinite things, neither will there be a subsequent one. Hence it is impossible for anything to come to be or be moved or be changed in any way. ἔτι τοῦ αὐτοῦ κίνησις ἡ ἐναντία καὶ ἠρέμησις, καὶ γένεσις καὶ φθορά, ὥστε τὸ γιγνόμενον, ὅταν γένηται γιγνόμενον, τότε φθείρεται: οὔτε γὰρ εὐθὺς γιγνόμενον οὔθ᾽ ὕστερον: εἶναι γὰρ δεῖ  τὸ φθειρόμενον. 1017. Further, of the same thing of which there is contrary motion and rest there is also generation and destruction. Hence when that which is coming to be becomes that which is coming to be, it is then being destroyed; for it is not destroyed as soon as it is generated or afterwards; for that which is being destroyed must be. ἔτι δεῖ ὕλην ὑπεῖναι τῷ γιγνομένῳ καὶ μεταβάλλοντι. τίς οὖν ἔσται ὥσπερ τὸ ἀλλοιωτὸν σῶμα ἢ ψυχή—οὕτω τί τὸ γιγνόμενον κίνησις ἢ γένεσις; καὶ ἔτι τί εἰς ὃ κινοῦνται; δεῖ γὰρ εἶναι τὴν τοῦδε ἐκ τοῦδε εἰς τόδε κίνησιν ἢ γένεσιν. πῶς οὖν; οὐ γὰρ ἔσται μάθησις τῆς  μαθήσεως, ὥστ᾽ οὐδὲ γένεσις γενέσεως. 1018. Further, there must be some matter underlying the thing which is coming to be or being changed. What then will it be that becomes motion or generation in the same way that a body or a soul or something else of this kind is alterable? Further, what is the thing to which motion proceeds; for motion must be of this particular thing from this to that, and yet the latter should not be a motion at all. In what way then is this to take place? For there can be no learning of learning, and therefore no generation of generation (1008-9). ἐπεὶ δ᾽ οὔτ᾽ οὐσίας οὔτε τοῦ πρός τι οὔτε τοῦ ποιεῖν καὶ πάσχειν, λείπεται κατὰ τὸ ποιὸν καὶ ποσὸν καὶ τόπον κίνησιν εἶναι (τούτων γὰρ ἑκάστῳ ἐναντίωσις ἔστιν), λέγω δὲ τὸ ποιὸν οὐ τὸ ἐν τῇ οὐσίᾳ (καὶ γὰρ ἡ διαφορὰ ποιόν) ἀλλὰ τὸ παθητικόν, καθ᾽ ὃ  λέγεται πάσχειν ἢ ἀπαθὲς εἶναι. 1019. And since there is no motion of substance or of relation or of action or of passion, it follows that there is motion of quality, of quantity and of location; for each of these admits of contrariety. By quality I mean, not that which comes under the category of substance (for even difference is quality), but the passive power in virtue of which a thing is said to be acted upon or to be incapable of being acted upon. τὸ δὲ ἀκίνητον τό τε ὅλως ἀδύνατον κινηθῆναι καὶ τὸ μόλις ἐν χρόνῳ πολλῷ ἢ βραδέως ἀρχόμενον, καὶ τὸ πεφυκὸς μὲν κινεῖσθαι καὶ δυνάμενον <μὴ κινούμενον> δὲ ὅτε πέφυκε καὶ οὗ καὶ ὥς: ὃ καλῶ ἠρεμεῖν τῶν ἀκινήτων μόνον: ἐναντίον γὰρ ἠρεμία  κινήσει, ὥστε στέρησις ἂν εἴη τοῦ δεκτικοῦ. 1020. The immovable is what is totally incapable of being moved, or what is moved with difficulty over a long period of time or begins to be moved slowly, or what is naturally fit to be moved but is not capable of being moved when it is so fit, and where, and in the way in which it would naturally be moved. And this is the only kind of immobility which I call rest; for rest is contrary to motion. Hence it will be the privation of what is receptive of motion. COMMENTARY Postquam divisit transmutationes in generationem et corruptionem et motum, hic subdividit alterum membrum divisionis, scilicet motum, secundum genera in quibus potest esse motus. Et circa hoc duo facit. Primo ostendit in quibus generibus possit esse motus. Secundo ostendit quot modis dicitur immobile, ibi, immobile autem quod. 2376. Having divided change into generation, destruction and motion, here he subdivides the other member of this division, Le, motion, on the basis of the categories in which it takes place. In regard to this he does two things. First (1012:C 2376), he indicates the categories in which motion can be found. Second (1020:C 2401), he explains the different senses in which the term immovable is used (“The immovable”). Circa primum tria facit. Primo proponit quod intendit. Secundo probat propositum, ibi, secundum substantiam autem. Tertio concludit principalem intentionem, ibi, quoniam autem neque. In regard to the first he does three things. First, he sets forth his thesis. Second (1013:C 2378), he proves this (“There is no motion”). Third (1019:C 2399), he draws his main conclusion (“And since”). Dicit ergo primo, quod cum praedicamenta dividantur per substantiam, qualitatem, et huiusmodi; et in aliis generibus non possit esse motus; erunt igitur tria genera entis in quibus potest esse motus: quae sunt qualitas, quantitas et ubi: loco cuius ponit locum, quia nihil aliud significat esse ubi, nisi esse in loco; et moveri secundum locum, nihil est aliud quam moveri secundum ubi. Non enim motus secundum locum attribuitur subiecto loco, in quo est locus, sed ei quod est in loco. He accordingly says, first (1012), that, since the categories are divided into substance, quality and so on, and since there cannot be motion in the other categories, there are therefore three categories of being in which motion can be found; that is, quality, quantity and location, for which he substitutes the term place, because location merely signifies being in a place; and to be moved with respect to place is merely to be moved with respect to one’s location. For motion with respect to place is not attributed to a subject in which place inheres but to the thing in place. Attendendum est autem quod praetermittere videtur tria genera, scilicet quando, situm et habere. Cum enim quando significet esse in tempore, tempus autem sit numerus motus, eiusdem rationis est non esse motum in genere quando, et non esse motum in genere actionis et passionis, quae significant aliqualiter ipsum motum. Positio vero non addit supra ubi, nisi ordinem partium determinatum, qui nihil aliud est quam determinata relatio partium adinvicem. Habitus etiam importat habitudinem indumenti ad indutum. Et sic eiusdem rationis videtur esse quod non sit motus in situ et habere, et quod non sit in ad aliquid. 2377. Now it should be noted that he seems to omit three categories, namely, temporal situation (quando), posture and accoutrement; for since temporal situation signifies being in time, and time is the measure of motion, the reason why there is no motion in the category of temporal situation or in that of action and of passion, which signify motion itself under special aspects, is the same. And posture adds nothing to location except a definite arrangement of parts, which is nothing else than a definite relationship of parts to each other. And accoutrement implies the relation of one clothed to his clothing. Hence the reason why there does not seem to be motion with respect to posture and to accoutrement and to relation seems to be the same. 2378. There is no motion (1013). Deinde cum dicit secundum substantiam probat propositum. Et circa hoc tria facit. Primo ostendit quod non sit motus in substantia. Secundo quod non sit motus in ad aliquid, ibi, neque ad aliquid. Tertio quod non est motus in agere et pati, ibi, neque facientis et patientis. Next, he proves his thesis; and in regard to this he does three things. First (1013:C 2378) he shows that there is no motion with respect to substance; second (8014:C 2385), that there is no motion with respect to relation (“Nor is there motion”); and third (1015:C 2386), that there is no motion with respect to action and passion (“Nor is there motion of agent”). Ostendit ergo primo, quod secundum substantiam non potest esse motus, quia motus est mutatio de subiecto in subiectum. Duo ergo subiecta inter quae est motus, sunt contraria aut media. Cum igitur substantiae nihil sit contrarium, relinquitur quod secundum substantiam non possit esse motus, sed generatio et corruptio tantum, quorum termini sunt oppositi secundum contradictionem, et non secundum contrarietatem, ut supra dictum est. He accordingly proves, first (1013), that there cannot be motion with respect to substance because motion is a change from subject to subject. Therefore the two subjects between which there is motion are either contraries or intermediates. Hence, since nothing is contrary to substance, it follows that there cannot be motion with respect to substance, but only generation and destruction, whose limits are opposed to each other as contradictories and not as contraries, as has been stated above (1009:C 2366). Videtur autem hoc quod dictum est substantiae nihil est contrarium, falsum esse, cum ignis manifeste appareat contrarius aquae: et cum Aristoteles in primo de caelo probaverit quod caelum non est corruptibile, quia non habet contrarium; alia vero corpora quae sunt corruptibilia, contrarium habent. 2379. Now it seems that his statement that “substance has no contrary” is false, because fire clearly appears to be contrary to water, and because Aristotle had proved in Book I of The Heavens that the heavens are not destructible since they do not have a contrary, whereas other bodies, which are corruptible, have a contrary. Dixerunt igitur quidam, quod toti substantiae compositae, non est aliquid contrarium, quia oportet contrariorum esse unum subiectum; sed formae substantiali nihil prohibet esse contrarium. Dicebant enim quod calor est forma substantialis ignis. Hoc autem non potest esse verum, quia formae substantiales non sunt sensibiles per se. Et iterum manifestum est quod calor et frigus in aliis corporibus sunt accidentia. Quod autem est in genere substantiae, nulli potest accidens esse. 2380. Hence some said that there is nothing contrary to the whole composite substance because the subject of contraries must be one; but nothing prevents a substantial form from having a contrary. For they said that heat is the substantial form of fire. But this cannot be true, because substantial forms are not perceptible of themselves. And again it is evident that in other bodies heat and cold are accidents. But what belongs to the category of substance cannot be an accident in anything. Unde alii dixerunt, quod calor et frigus non sunt formae substantiales ignis et aquae, sed tamen eorum formae substantiales sunt contrariae, et recipiunt magis et minus, et sunt quasi mediae inter substantiam et accidens. Sed hoc omnino irrationabiliter dicitur. Nam, cum forma sit principium speciei, si formae ignis et aquae non sunt vere substantiales, neque ignis et aqua sunt verae species in genere substantiae. Non est igitur possibile quod inter substantiam et accidens sit aliquod medium: tum quia sunt diversorum generum, inter huiusmodi autem non cadit medium, ut supra in decimo ostensum est: tum quia etiam definitiones substantiae et accidentis immediatae sunt. Est enim substantia ens per se; accidens vero ens per se non est, sed in alio. 2381. Others have said that heat and cold are not the substantial forms of fire and water, but that their substantial forms are contraries differing in degree, and are, so to speak, intermediate between substance and accidents. But this is wholly unreasonable; for, since form is the principle of a species, if the forms of fire and of water are not truly substantial, neither are fire and water true species in the category of substance. It is impossible, then, that there should be an intermediate between substance and accidents, because they belong to different categories, and between such things an intermediate does not fall, as has been shown above in Book X (881:C 2102); and also because the definitions of substance and accident have no intermediate. For a substance is a being of itself, whereas an accident is not a being of itself but has being in something else. Dicendum est ergo quod nec formae substantiales possunt esse contrariae, quia contraria sunt extrema quaedam cuiusdam determinatae distantiae, et quodammodo continuae, cum sit motus de uno contrario in aliud contrarium. Unde in illis generibus in quibus talis distantia continua et determinata non invenitur, non potest contrarium inveniri. Sicut patet in numeris. Distantia enim numerorum adinvicem non intelligitur secundum aliquam continuitatem, sed secundum additionem unitatum. Unde numerus numero non est contrarius. Et similiter nec figura figurae. 2382. It is necessary then to say that substantial forms cannot be contraries, because contraries are extremes of a certain definite distance, and in a sense they are continuous, since motion is from one contrary to another. In those categories, then, in which no such continuous and definite distance is found, it is impossible to find a contrary, as is clear in the case of numbers. For the distance between one number and another does not mean continuity but the addition of units. Hence number is not contrary to number, nor similarly is figure contrary to figure. Eodem autem modo est in substantiis; quia ratio cuiuslibet speciei constituitur in quodam determinato indivisibili. Sed cum forma sit differentiae principium; si formae substantiales non sunt adinvicem contrariae, sequitur quod non sit contrarietas in differentiis; cum tamen supra ostensum sit, quod genus dividitur in contrarias differentias. 2383. The same thing applies to substances because the intelligible structure of each species consists in a definite unity. But since form is the basis of difference, if substantial forms are not contrary to each other, it follows that contrariety cannot be found between differences. Dicendum est igitur quod forma substantialis secundum quod in se consideratur, constituit speciem in genere substantiae: secundum autem quod una forma habet sibi intellectam privationem alterius formae, sic diversae formae sunt contrariarum differentiarum principia. Nam privatio quodammodo contrarium est. Et per hunc modum opponuntur animatum et inanimatum, rationale et irrationale et huiusmodi. 2384. It is necessary to say, then, that a substantial form, considered in itself, constitutes a species in the category of substance; but according as one form implies the privation of another, different forms are the principles of contrary differences. For in one respect a privation is a contrary, and living and non-living, rational and irrational, and the like are opposed in this way. 2385. Nor is there motion of relation (1014). Deinde cum dicit neque ad ostendit non per se esse motum in genere ad aliquid, sed solum per accidens. Sicuti enim aliquid movetur per accidens, quando non fit motus in eo, nisi quodam altero moto; ita et in aliquo dicitur esse motus per accidens, quando non fit motus in eo, nisi quodam altero moto. Hoc autem invenimus in genere ad aliquid; quod nisi aliquid alterum permutetur, non verum est dicere quod in eo fiat permutatio, sicut non fit de aequali inaequale, non facta permutatione secundum quantitatem. Et similiter non fit de dissimili simile, nisi facta permutatione secundum qualitatem. Videmus etiam quod unum relativorum dicitur permutari facta permutatione circa alterum; sicut alterum per se manens de sinistro fit dextrum, altero secundum locum permutato. Relinquitur igitur quod in ad aliquid non est motus nisi per accidens. Next, he shows that there is no motion in the proper sense in the category of relation except accidentally. For just as a thing is moved accidentally when motion takes place in it only as a result of something else being moved, in a similar way motion is said to be accidental to a thing when it takes place in it only because something else is moved. Now we find this in the category of relation; for unless something else is changed, it is not true to say that change occurs in relation; for example, the unequal comes from the equal only when there has been change in quantity. Similarly the like comes from the unlike only when there has been a change in quality. Thus we see that one of two relative things is said to be changed when change affects the other one of them; for example, a thing which is unmoved of itself changes from left to right when some other thing changes its place. Hence it follows that there is motion in the category of relation only accidentally. 2386. Nor is there motion of agent (1015). Deinde cum dicit neque facientis ostendit, quod neque in agere et pati sit motus: et hoc quatuor rationibus: quarum prima talis est. Agere et pati sunt motus, et significant motum. Si igitur in agere et pati esset motus, sequeretur, quod motus sit alicuius motus, et generatio generationis, et permutatio permutationis. Sed hoc est impossibile; ergo, et hoc quod in agere et pati sit motus. Quod autem impossibile sit motum esse motus, sic ostendit. Motum enim esse motus contingit dupliciter: aut ut eius quod movetur, aut ut termini. Eius quidem quod movetur: sicut dicimus motum esse hominis, quia homo movetur, quia ex albo in nigrum permutatur. Unde et similiter motus movebitur, et aut calefiet, aut infrigidabitur, aut mutabitur secundum locum, aut augebitur. Hoc autem est impossibile; quia motus non potest esse subiectum caloris aut frigoris, aut alicuius huiusmodi. Relinquitur igitur quod non contingat motum esse motus sicut subiecti. Here he shows that motion does not occur with respect to either action or passion. He proves this by four arguments, of which the first is as follows: action and passion constitute motion and designate it. If, then, motion were to occur in action and in passion, it would follow that there would be motion of motion and generation of generation and change of change. But this is impossible. Therefore it is also impossible that there should be motion in action and in passion. That it is impossible for motion to be moved he proves thus: there are two ways in which there might be motion of motion: first, there might be motion of motion as of a subject which is moved, or, second, as of the limit of motion. And motion might be the subject of motion, as we say that there is motion of a man because a man is moved since he is changed from white to black. In a similar way motion would be moved, and would either be heated or cooled, or changed with respect to place, or increase. But this is impossible; because motion cannot be the subject of heat or of cold or of similar attributes. It follows, then, that there cannot be motion of motion if motion is regarded as a subject. Sed neque etiam sicut termini; ita scilicet quod aliquod subiectum alterum permutetur de una specie permutationis in aliam, sicut homo permutatur de languore in sanitatem. Hoc enim est impossibile nisi per accidens. 2387. But neither can there be motion of motion as of a limit, some other subject being changed from one species of change to another, as a man might be changed from sickness to health; for this is possible only accidentally. Unde consequenter ostendit quod est impossibile per se, quia omnis motus est permutatio de uno in aliud. Et similiter generatio et corruptio est mutatio de uno in aliud, licet termini permutationis non sic opponantur in generatione et corruptione sicut in motu, ut supra dictum est. Si igitur sit aliqua permutatio de una permutatione in aliam, puta de sanatione in quamdam aliam permutationem, sequetur quod simul dum aliquid permutatur de sanitate in aegritudinem, permutetur de illa permutatione in aliam permutationem; quia adhuc uno extremorum permutationis existente, fit transmutatio de illo extremo in aliud. Et sic, si duae transmutationes sunt extrema unius permutationis, sequetur, quod durante prima transmutatione, fiat transmutatio in aliam. Et sic simul, dum aliquod movetur de sanitate in aegritudinem, transmutabitur de sanatione in aliam transmutationem. 2388. Hence he shows next that it is impossible for motion to be moved essentially because every motion is a change from one thing to something else. Similarly generation and destruction are a change from one thing to something else, even though in their case the limits of change are not opposed to each other as they are in that of motion, as has been said above (1008:C 2363). If, then, there is change from one change to another, as from becoming sick to some other process of change, it will follow that, while a thing is being changed from health to sickness, it is being changed at the same time from that change to another; because, while one of the limits of a change is arising, a change from one limit to another occurs. Thus if two processes of change are the limits of one change, it follows that while the original change is occurring, a change into another takes place. And so at the same time that a thing is being moved from health to sickness it will be being changed from becoming healthy to some other change. Sed hoc non videtur, nisi inquantum una mutatio succedit alteri. Contingit autem quod ad hanc mutationem qua aliquid movetur de sanitate in aegritudinem, succedat quaevis alia mutatio; puta dealbatio, vel denigratio, mutatio secundum locum, vel quaecumque alia. Unde manifestum est, quod si aliquis languet per hoc quod movetur de sanitate in aegritudinem, quod ex hac mutatione permutari poterit in quamcumque aliam mutationem. Neque est mirum, quia poterit ex hac mutatione mutari ut in quiete. Contingit enim post hanc mutationem aliquem quiescere. 2389. But this seems to be true only inasmuch as one change succeeds another. And it is possible that any other change may succeed this one by which something is being moved from health to sickness, for example, becoming white or becoming black or change of place or any other change. Hence it is evident that, if someone is becoming ill because he is being moved from health to sickness, he can be changed from this change to any other. Nor is this surprising, because he can even be changed from this change to a state of repose; for it is possible that someone might come to rest after this change. Sed cum omnis mutatio sit in non contingens, idest in oppositum, quod non contingit simul verum esse cum suo opposito, sequitur quod si permutatio sit de mutatione in mutationem, quod semper sit in oppositam mutationem quam appellat non contingentem. Et illa transmutatio in quam fit transitus, oportet quod sit de aliquo in aliquid. Quare non fiet transitus de permutatione languoris, nisi in oppositam mutationem quae dicitur sanatio. 2390. But since every change is “always to an opposite which is not contingent,” i.e., an opposite which cannot be true at the same time as the opposed term, it follows that, if there is a change from change to change, it will always be to an opposite change, which he calls not contingent. And that change in which the transition takes place will have to be from one thing to something else. Hence the transition from a change of becoming ill will only be to the opposite change, which is called becoming healthy. Et sic videntur duo contraria sequi: scilicet quod opposita permutatio fiat de una permutatione in quamcumque aliam, et quod non nisi in oppositam. Ex quo sequitur ulterius, quod simul dum mutatur aliquid ad unum oppositorum, mutetur in mutationem tamquam in aliud oppositum. Quod videtur impossibile: sequitur enim, quod simul intentio naturae tendat in opposita. Non igitur est possibile, quod per se mutetur aliquid de una permutatione in aliam. 2391. And so two contrary positions seem to follow, namely, that an opposite change passes from one change to any other, and only to its opposite. And from this it further follows that, at the same time that something is being changed to one of its opposites, it is also being changed to a change as if it were another opposite. This seems to be impossible, for it would follow that nature inclines to opposite effects at the same time. Hence it cannot be that anything is changed essentially from one change to another. Sed per accidens hoc contingit; sicut aliquis permutatur ex reminiscentia in oblivionem, quia subiectum permutatur, quandoque ad unum terminum, quandoque ad alium: non quod sit intentio moventis ad hoc, quod simul dum permutatur in unum, intendat tendere in aliud. 2392. But this can happen accidentally; for example, a person may change from recollection to forgetfulness because the subject is changed, sometimes in relation to one extreme and sometimes to the other-not that it may be the mover’s intention that at the same time that he is being changed to one extreme he is at the same time intending to move to the other. 2393. Further, the process (1016). Deinde cum dicit et adhuc secundam rationem ponit, quae talis est. Si permutatio sit permutationis, sicut terminus termini, vel generatio generationis, necesse erit quod ad permutationem non perveniatur nisi per aliam permutationem, sicut ad qualitatem non pervenitur nisi per alterationem praecedentem: et sic ad illam mutationem praecedentem non pervenitur, nisi per aliquam priorem mutationem: et ita procedetur in infinitum. Then he gives the second argument, which runs thus: if there is change of change, as limit of limit, or generation of generation, one change must be reached only by another change, as one quality is reached only by a preceding alteration; and thus it will be possible to reach that preceding change only by a prior change, and so on to infinity. Quod esse non potest: quia si ponantur infinitae permutationes hoc modo ordinatae, quod una inducat ad aliam, necesse est priorem esse si posterior sit. Ponamus enim quod generationis simpliciter, quae est generatio substantiae, sit quaedam generatio. Si ergo generatio simpliciter fiat quandoque et iterum ipsum fieri generationis simpliciter aliquando fiebat, sequetur, quod nondum erat quod fit simpliciter: sed erat generatio secundum aliquid, secundum quod fit ipsa generatio generationis. Si itaque et haec generatio aliquando fiebat, cum non sit abire in infinitum, et in infinitis non sit accipere primum, non erit devenire ad primum fieri. Si autem prius non est, neque posterius, ut supra dictum est: quare sequetur quod non sit habitum, idest, id quod consequenter est. Et inde sequitur, quod nihil possit fieri neque moveri neque mutari: quod est impossibile. Non igitur possibile est quod mutationis sit mutatio. 2394. But this cannot be the case, because, if it is assumed that there are an infinite number of changes related in such a way that one leads to the other, the preceding must exist if the following does. Let us suppose that there is a particular instance of the generation of a generation in an unqualified sense, which is the generation of substance. Then, if the generation in an unqualified sense sometimes comes to be, and again if the coming to be of generation in an unqualified sense itself at one time came to be, it will follow that that which is coming to be in an unqualified sense did not yet exist, but there was generation in one respect, namely, the very generation of the process of generation. And if this generation also came to be at some time, since it is not possible to have either an infinite regress or any first term among infinite things, it is impossible ever to come to any first process of generation. But if the preceding member in a series does not exist, there will be no succeeding member, as has been pointed out above, and the consequence will be that “there will not be a subsequent one,” i.e., one which follows it. It follows, then, that nothing can come to be or be moved or be changed. But this is impossible. Hence change of change is impossible. 2395. Further, of the same thing (1017) Deinde cum dicit adhuc eiusdem tertiam rationem ponit, quae talis est. Motus contrarii sunt eiusdem subiecti, etiam quies et motus, et etiam generatio et corruptio; quia opposita nata sunt fieri circa idem. Si igitur aliquod subiectum transmutetur de generatione in corruptionem, simul dum generatur, transmutabitur ad corruptionem; quod est transmutari ad non esse; nam corruptionis terminus est non esse. Quod autem transmutatur ad non esse, corrumpitur. Sequitur igitur, quod aliquid simul dum fit corrumpatur. Then he gives the third argument, which is as follows. Contrary motions, and rest and motion, and generation and destruction, belong to the same subject, because opposites are suited by nature to come to be in the same subject. Therefore, if some subject is being changed from generation to destruction, at the same time that it is being generated it will be undergoing change leading to destruction, which is to be changed into non-being; for the terminus of destruction is non-being, Now what is being changed into non-being is being destroyed. Hence it follows that a thing is being destroyed at the same time that it is being generated. Sed hoc non potest esse. Neque enim dum aliquid fit corrumpitur, neque statim postea corrumpitur. Cum enim corruptio sit de esse in non esse, oportebit id quod corrumpitur esse. Et sic oportet inter generationem quae est mutatio ad esse, et corruptionem quae est mutatio ad non esse, invenire quietem mediam. Et sic non est mutatio de generatione in corruptionem. 2396. But this cannot be true; for while a thing is coming to be it is not being destroyed, nor is it corrupted immediately afterwards. For since destruction is a process from being to nonbeing, that which is being destroyed must be. And thus there will have to be an intermediate state of rest between generation, which is a change to being, and destruction, which is a change to non-being. Hence there is no change from generation to destruction. 2397. Further, there must be (1018). Deinde cum dicit adhuc oportet quartam rationem ponit; quae talis est. In omni, quod generatur, oportet duo inveniri, quorum unum est materia eius quod fit, et aliud ad quod terminatur generatio. Si ergo generetur generatio, oportet quod generatio et motus habeant materiam talem, quale est alterabile corpus, aut anima, aut aliquid huiusmodi: sed huius materiam non est assignare generationi et motui. Then he gives the fourth argument, which runs as follows. In everything that is being generated two things must be present: first, the matter of the thing which is generated, and, second, that in which the generation is terminated. If, then, there is generation of generation, both generation and motion will have to have some matter, such as an alterable body or a soul or something of this kind. But it is impossible to assign matter of this kind to generation and to motion. Similiter etiam oportet in generatione esse aliquid ad quod terminatur mutatio; quia oportet aliquam partem, scilicet materiam eius quod generatur, esse motam ex hoc in hoc: et hoc in quod terminatur motus, non contingit esse motum sed terminum motus. Non enim huiusmodi permutationis quae est disciplinatio, est aliqua alia disciplinatio quae ad eam terminetur, quae sit disciplina disciplinationis. Quare relinquitur quod non sit generatio generationis. 2398. Similarly, there must also be something in which the process of change is terminated, because some part, namely, the matter of the thing generated, must be moved from one attribute to another, and that in which motion is terminated cannot be motion but is the terminus of motion. For of the kind of change which we call learning there is not some other learning which is terminated in it, which is a learning of learning. Hence there is nothing to conclude but that there is no generation of generation. 2399. And since (1019). Deinde cum dicit quoniam autem concludit principale intentum; dicens, quod quia motus non potest esse neque in genere substantiae, neque in ad aliquid, neque in agere et pati, relinquitur quod motus sit secundum quale et quantum et ubi. In his enim generibus contingit esse contrarietatem quae est inter terminos motus, ut ostensum est. Here he draws as his conclusion his main thesis. He says that, since there cannot be motion either in the category of substance or in that of relation or in that of action and passion, it follows that motion belongs to quality, quantity and location; for in these categories there can be contrariety, which stands between the termini of motion, as has been pointed out. Sed quia qualitas quandoque dicitur de forma substantiali, subiungitur quod cum motus dicitur esse in quali, non intelligitur significare substantiam secundum quod differentia substantialis praedicatur in eo quod quale; sed de quali secundum quod dicitur aliquid pati, vel impassibile esse. Non enim est proprie alteratio nisi secundum passibiles qualitates, ut in septimo physicorum probatur. 2400. But since quality is sometimes used to mean substantial form, he adds that, when there is said to be motion in quality, it is not understood to signify substance, in view of the fact that substantial difference is predicated as something qualitative; but it refers to the kind of quality by which something is said to be acted upon or to be incapable of this. For there is alteration, properly speaking, only in terms of susceptible qualities, as is proved in Book VII of the Physics. 2401. The immovable (1020). Deinde cum dicit immobile autem ostendit quot modis dicitur immobile. Et ponit tres modos: quorum primus est, quod immobile dicitur id quod omnino est impossibile moveri, sicut Deus est immobilis. Then he explains the different senses in which the term immovable is used; and he gives three of these. First, the immovable means what is completely incapable of being moved; for example, God is immovable. Secundus modus est secundum quod dicitur immobile, id quod vix non potest moveri, sicut saxum magnum. 2402. Second, it means what can be moved with difficulty, as a huge boulder. Tertius modus est secundum quod dicitur immobile id quod natum est moveri, sed tunc non possit moveri, quando natum est, et ubi natum est moveri, et sicut natum est moveri. Et hoc solum immobile dicitur proprie quiescere, quia quies est contraria motui. Unde oportet quod quies sit privatio motus in susceptivo motus. 2403. Third, it means what is naturally fit to be moved but cannot be moved when it is fit, and where, and in the way in which it is fit to be moved. And only this kind of immobility is properly called rest, because rest is contrary to motion. Hence rest must be the privation of motion in what is susceptible of motion.
LESSON 13 Concepts Related to Motion
ARISTOTLE’S TEXT Chapter 12: 1068b 26-1069a 14 ἅμα κατὰ τόπον ὅσα ἐν ἑνὶ τόπῳ πρώτῳ, καὶ χωρὶς ὅσα ἐν ἄλλῳ: ἅπτεσθαι δὲ ὧν τὰ ἄκρα ἅμα: μεταξὺ δ᾽ εἰς ὃ πέφυκε πρότερον ἀφικνεῖσθαι τὸ μεταβάλλον ἢ εἰς ὃ ἔσχατον μεταβάλλει κατὰ φύσιν τὸ συνεχῶς μεταβάλλον.  ἐναντίον κατὰ τόπον τὸ κατ᾽ εὐθεῖαν ἀπέχον πλεῖστον: ἑξῆς δὲ οὗ μετὰ τὴν ἀρχὴν ὄντος, θέσει ἢ εἴδει ἢ ἄλλως πως ἀφορισθέντος, μηθὲν μεταξύ ἐστι τῶν ἐν ταὐτῷ γένει καὶ οὗ ἐφεξῆς ἐστίν, οἷον γραμμαὶ γραμμῆς ἢ μονάδες μονάδος ἢ οἰκίας οἰκία (ἄλλο δ᾽ οὐθὲν κωλύει μεταξὺ  εἶναι). τὸ γὰρ ἑξῆς τινὸς ἐφεξῆς καὶ ὕστερόν τι: οὐ γὰρ τὸ ἓν ἑξῆς τῶν δύο οὐδ᾽ ἡ νουμηνία τῆς δευτέρας. [1069α]  ἐχόμενον δὲ ὃ ἂν ἑξῆς ὂν ἅπτηται. ἐπεὶ δὲ πᾶσα μεταβολὴ ἐν τοῖς ἀντικειμένοις, ταῦτα δὲ τὰ ἐναντία καὶ ἀντίφασις, ἀντιφάσεως δ᾽ οὐδὲν ἀνὰ μέσον, δῆλον ὡς ἐν τοῖς ἐναντίοις τὸ  μεταξύ. τὸ δὲ συνεχὲς ὅπερ ἐχόμενόν τι. λέγω δὲ συνεχὲς ὅταν ταὐτὸ γένηται καὶ ἓν τὸ ἑκατέρου πέρας οἷς ἅπτονται καὶ συνέχονται, 1021. Things which are in one primary place are together in place, and those which are in different places are separate, and those whose extremities are together are in contact. And an intermediate is that at which something continuously changing according to its nature naturally arrives before it reaches the limit to which it is changing. That is contrary in place which is most distant in a straight line. That is subsequent which comes after a starting point (the order being determined by position or form or in some other way) and has nothing in the same genus between itself and that which it follows; for example, lines in the case of a line, and units in the case of a unit, or a house in the case of a house. But there is nothing to prevent something else from coming between. For that which follows something is subsequent and comes after something else; for one does not follow two, nor does [the first day of] the new moon follow the second. Again, what is subsequent and in contact is contiguous. And since every change is between opposites, and these are contraries and contradictories, and since there is no intermediate between contradictories, it is evident that an intermediate is between contraries. The continuous has something of the nature of the contiguous; and I call two things continuous when both have the same extremity in which they are in contact and are uninterrupted. ὥστε δῆλον ὅτι τὸ συνεχὲς ἐν τούτοις ἐξ ὧν ἕν τι πέφυκε γίγνεσθαι κατὰ τὴν σύναψιν. καὶ ὅτι πρῶτον τὸ ἐφεξῆς, δῆλον (τὸ γὰρ ἐφεξῆς οὐχ ἅπτεται,  τοῦτο δ᾽ ἐφεξῆς: καὶ εἰ συνεχές, ἅπτεται, εἰ δ᾽ ἅπτεται, οὔπω συνεχές: ἐν οἷς δὲ μὴ ἔστιν ἁφή, οὐκ ἔστι σύμφυσις ἐν τούτοις): ὥστ᾽ οὐκ ἔστι στιγμὴ μονάδι ταὐτόν: ταῖς μὲν γὰρ ὑπάρχει τὸ ἅπτεσθαι, ταῖς δ᾽ οὔ, ἀλλὰ τὸ ἐφεξῆς: καὶ τῶν μὲν μεταξύ τι τῶν δ᾽ οὔ. 1022. It is evident, then, that the continuous belongs to those things from which one thing results in virtue of their contact. And it is evident that the subsequent is the first of these; for things which are subsequent are not necessarily in contact, but what is in contact is subsequent. But if it is in contact it is not necessarily continuous. And in things in which there is no contact there is no natural coherence. The point, then, is not the same as the unit; for contact belongs to the former but not to the latter, but only successiveness, and there is an intermediate between the former but not between the latter. COMMENTARY Notificat quae circumstant motum, et praecipue motum localem. Et primo notificat ea. Secundo inducit quaedam corollaria ex dictis, ibi, quare palam. 2404. He explains the terms which apply to motion, especially local motion. First (2021:C 2404), he explains them. Second (1022:C 2413), he draws a corollary from his remarks (“It is evident”). Dicit ergo primo, quod simul secundum locum dicuntur quaecumque sunt in uno loco primo, idest proprio. Si enim aliqua sunt in uno loco communi, non propter hoc dicuntur esse simul: sic enim omnia, quae continentur caeli ambitu, dicerentur esse simul. He accordingly says, first (1021), that things which are “in one primary place,” i.e., a proper place, are said to be together in place; for if some things are in one common place, they are not for this reason said to be together, for then all things which are contained in the circumference of the heavens would be said to be together. Seorsum autem dicuntur quaecumque sunt in alio et alio loco. 2405. Things which are in different places are said to be separate. Tangi autem adinvicem dicuntur, quorum ultima sunt simul; puta duo corpora quorum superficies coniunguntur. 2406. And those whose extremities are said to touch one another are said to be in contact; for example, two bodies whose surfaces are joined. Medium autem inter duo est, in quod id quod continuo permutatur, natum est prius pervenire quam in ultimum. Sicut si motus continuus de a in c, prius veniet in b, id quod mutatur, quam in c. 2407. And an intermediate between two things is that at which it is natural for something that continuously changes to arrive before it reaches its limit; for example, if there is continuous motion from a to c, the thing being changed first arrives at b before it reaches c. Contrarium vero secundum locum est, quod est plurimum distans secundum rectam lineam. Non enim distantia plurima potest mensurari secundum lineam curvam, eo quod inter duo puncta possunt designari infinitae decisiones circulorum dissimiles. Sed inter duo puncta non potest esse nisi una linea recta. Mensuram autem oportet esse certam et determinatam. Plurimum autem distans in locis invenitur secundum naturam sursum et deorsum, quae sunt medium et extremum mundi. 2408. Again, that which is most distant in a straight line is contrary in place; for that which is most distant cannot be measured by a curved line, because an infinite number of unlike sections of circles can be drawn between two points, but there can be only one straight line between two points. Now a measure must be definite and fixed. And that which is most distant as to place admits of being above and below, which are the extremity and the center of the universe. Consequenter autem dicitur quod est post aliquod primum principium; sive attendatur ordo secundum positionem, sive secundum speciem, sicut binarius est post unitatem, sive qualitercumque aliter. Adhuc autem oportet quod nihil eiusdem generis sit medium inter id quod est consequenter et id cui consequenter est. Sicut lineae sunt consequenter alicui lineae, et unitates alicui unitati, et domus alicui domui consequenter. Sed nihil prohibet inter duo, quorum unum se habet consequenter ad alterum, esse aliquid medium alterius generis; puta si inter duas domus sit unus equus medius. Et ad manifestandum praemissam divisionem subiungit, quod illud quod dicitur consequenter, oportet quod sit consequenter respectu alicuius, et quod sit aliquod posterius. Unum enim non se habet consequenter ad duo, cum sit prius, neque nova luna ad secundam, sed e converso. 2409. That is said to be subsequent which comes after some starting point, whether the order is determined by position or by form or in some other way; for example, two comes after one. And there must also be nothing of the same genus between that which is subsequent and that which it follows, as lines are subsequent to a line and units to a unit and a house to a house. But nothing prevents something of another genus from being an intermediate between two things one of which follows the other; for example, there may be one intermediate horse between two houses. In order to make the above distinction clear he adds that what is said to follow something must be subsequent and come after something. For one does not come after two, since it is first; nor does the first day of the new moon follow the second, but the other way around. Deinde dicit quod habitum dicitur illud quod est consequenter et tangit; puta si duo corpora sint ordinata, quorum unum alterum tangat. 2410. Then he says that the contiguous means what is subsequent and in contact with something else-for example, if two bodies are so related that one touches the other. Deinde dicit quod, cum omnis permutatio sit inter opposita, et opposita inter quae est permutatio sint contraria et contradictoria, ut ostensum est; et cum contradictionis nullum sit medium: manifestum est quod inter sola contraria oportet esse medium, cum medium sit inter extrema motus, ut ex definitione superius posita patet. Hoc autem bene inducit. Quia enim dixerat quod consequenter sunt, inter quae non est medium, conveniens fuit ut ostenderetur inter quae potest esse medium. 2411. Then he says that, since every change is between opposites, and the opposites between which there is change are either contraries or contradictories, as has been shown (1008:C 2363), and since there is no intermediate between contradictories, it is evident that there is an intermediate only between contraries; for that which is intermediate is between the limits of a motion, as is clear from the definition given above. His introduction of this is timely; for since he said that those things are subsequent between which there is no intermediate, it was fitting that he should indicate between what things it is possible to have an intermediate. Deinde ostendit quid sit continuum: et dicit, quod continuum addit aliquid supra habitum. Et dicit quod continuum est cum utriusque eorum, quae se tangunt, et quae simul sunt, sit unus et idem terminus, sicut partes lineae continuantur ad punctum. 2412. Then he shows what the continuous is. He says that the continuous adds something to the contiguous; for there is continuity when both of those things which are in contact and together have one and the same extremity, as the parts of a line are continuous in relation to a point. 2413. It is evident (1022). Deinde cum dicit quare palam inducit tria corollaria ex praemissis. Quorum primum est, quod continuum est in illis ex quibus natum est fieri unum secundum contactum. Et hoc ideo est, quia continuum requirit identitatem termini. Then he draws three corollaries from what has been said. The first is that continuity belongs to those things from which one thing naturally results in virtue of their contact; and this is because the continuous requires identical extremities. Secundum corollarium est, quod inter ista tria, consequenter, contactum et continuum, prius et communius est quod est consequenter. Non enim omne quod est consequenter tangit, sed omne quod tangit est consequenter. Oportet enim contacta secundum positionem esse ordinata, et nihil eorum esse medium. Et similiter tangens est prius et communius ens quod continuum; quia si est continuum, est necesse quod tangat. Quod enim est unum, necesse est esse simul; nisi forte intelligatur in hoc, quod est esse simul, pluralitas. Sic enim continuum non esset contactum. Sed eo modo quo id quod est unum est simul, necesse est continuum esse tangens. Sed non sequitur, si tangit, quod sit continuum; sicut non sequitur quod si aliqua sunt simul, quod sint unum. Sed in quibus non est contactus non est nascentia, idest naturalis coniunctio, quae est proprie continuorum. 2414. The second corollary is that, of these three things—the subsequent, the contiguous and the continuous—the first and most common is the subsequent; for not everything that is subsequent is in contact, but everything which is in contact is subsequent or consecutive. For things which are in contact are arranged according to their position, and no one of them is an intermediate. Similarly, the contiguous is prior to and more common than the continuous, because, if a thing is continuous, there must be contact. For what is one must be together, unless perhaps plurality is understood in the phrase being together. For in that case the continuous would not involve being in contact. But the continuous must involve contact in the way in which something one is together. Yet if there is contact it does not follow that there is continuity; for example, if certain things are together it does not follow that they are one. But in things in which there is no contact “there is no natural coherence,” i.e., natural union, which is a property of the continuous. Tertium corollarium est, quod punctus et unitas non sunt idem, ut Platonici posuerunt, dicentes quod punctum est unitas habens positionem. Et quod non sint idem, patet ex duobus. Primo quidem, quia secundum puncta est contactus, non autem secundum unitates, sed consequenter se habent adinvicem. Secundo, quia inter duo puncta semper est aliquid medium, ut probatur in sexto physicorum. Sed inter duas unitates necesse non est aliquid esse medium. 2415. The third corollary is that the point and the unit are not the same, as the Platonists claimed when they said that the point is the unit having position. That they are not the same is evident for two reasons: first, because there is contact between points but not between units, which only follow each other; second, because there is always some intermediate between two points, as is proved in Book V of the Physics. But it is not necessary that there should be an intermediate between two units.