PhD. Protokol November the 5th. 1rst Part.

November the 5th.

Minutes.

ON Topics I.

(I use the english translation of the Loeb edition)

The main subject the Topica deals with is syllogistic reasoning, i.e. its main features and constituting elements. He (Aristotle?) starts immediately by drawing a distinction between dialectical and contentious reasoning (ἐριστικὸς συλλογισμός). Συλλογισμός and συλλογίζεσθαι are compound words formed through assimilation: συν- and -λογισμός and συν- and λογίζεσθαι. They mean reasoning. A reasoning can be identified when it finishes. When someone says something we do not quite fully understand we might ask how he came to that conclusion. He could have jumped or rushed into it. He could also have thought about it thoroughly. 

A reasoning is a way of applying certain rules to combine more elemental structures. These elemental structures are phrases or declarative sentences which are either affirmative or negative, existential or universally formulated. 

Take for instance A and B in the “modus ponens” (A implies B. A. Therefore, B) and in the “modus tollens” (A implies B. Not B. Therefore not A) and take A, B and C in the hypothetical syllogism (If A, then B. If B, then C. Therefore, if A then C). A, B and C can be premises. B and C can be conclusions. B can be both a premise and a conclusion. 

A, B and C isolated are however the elemental structures, each of which may be represented through a phrase or a declarative sentence. If A, B and C are sentences of the type “S is P”, “S is not P”, “Some S’s are P”, “Some S’s are not P”, “Every single S is P” or “There is no S that is P”, we need to know how they arrive at? their meaning, their reasoning basis, and whether they are true sentences or false ones. 

Before we can move on to investigating how we formally deduce  a true conclusion from some premises, the proper function of the  συλλογισμός and συλλογίζεσθαι, we need to isolate the λόγος structure as its elementary and basic feature. The ΣΥΝ does not apply if we do not arrive first at a sentence, the elementary logical meaning structure.

Aristotle begins his investigation about what our opinions of (or thoughts about) things are grounded upon. 

Text 1: 

So “[in order to grasp dialectical reasoning] we need to find a method of investigation (μέθοδον) whereby we shall be able to reason from 

opinions that are generally accepted (ἐξ ἐνδόξων) about every problem propounded to us (περὶ παντὸς τοῦ προτεθέντος προβλήματος). When we hold to a λόγος, there is nothing we can say that will contradict it (μηθὲν ἐροῦμεν ὑπεναντίον.)” Top. 100a18-242

Our concern is with the logical elementary structure, the λόγος. So we skip to A. IV.  

Text 2. “First, then, we must see the parts of which our inquiry consists. Now if we were to grasp (a) with reference to how many, and what kind of, things οἱ λόγοι take place, and with what materials they start, and (h) how we can become well supplied with these, we should have sufficiently won our goal. Now the materials with which οἱ λόγοι start are equal in number, and are identical, with the subjects on which reasonings, συλλογισμοί, take place. For arguments start with 'propositions' (γὰρ οἱ λόγοι ἐκ τῶν προτάσεων) while the subjects on which reasonings take place are 'problems' (περὶ ὧν δὲ οἱ συλλογισμοί, τὰ προβλήματά ἐστι.). Now every proposition and every problem let us know (πᾶσα δὲ πρότασις καὶ πᾶν πρόβλημα δηλοῖ) either a peculiarity (ἴδιον) or genus (γένος) or an accident (συμβεβηκός).” Top. 101b11-19.

Text 3. 

“The specific generic difference (διαφορά γενική) should be ranked (τακτέον) together with the genus (ὁμοῦ τῷ γένει).” Top. 101b18-19.

Aristotle is now ready to state the elementary formal features that constitute a λόγος. These are: “definition, ὅρος, peculiarities?, ἴδιον, genus, γένος, and incident (accident?), συμβεβηκός.” Before getting into a detailed analysis, let us briefly sketch the path Aristotle takes. His aim is to define what syllogistic reasoning is. He presents several ways of how reasoning takes place. He then zooms in on λόγος as the elemental structure of meaning. A λόγος may be a πρότασις, a sentence, S is p, which can be modified to a problem: whether S is p or not or whether it is or is not the case that S is p. It can also be the conclusion of a reasoning, a combination of several προτάσεις. 

 The terminus technicus λόγος is a sentence of the type: S is p. The question is how soundly S is thereby defined. The issue is not only to determine what are the grounds for us understanding that this is the case. A) It is the opinion of the majority. B) It is the opinion expressed by the experts. C) it is an axiom. D it is the result of a demonstration. What we are trying to determine is the kind of statement that catches the essence of something. Catching the “what it means to be the sort of thing this thing is”

To define something is to say what is particularly idiosyncratic about it. Now this something may for sure have some idiosyncratic characteristics which do not necessarily define it. They serve to momentarily help us identify this something or someone out of many others things that are very similar. We will go into this later. For the time being let us say that this is a property something or someone has at a particular time and in relation to others. This property is circumstantial, depending upon either time or a given relationship or connexion with others. So when I want to get someone’s attention, I tell another person to call me that guy over there, sitting on the right side of someone else, etc., etc. I do not even refer to my friend by his name, let alone saying who he is for me, a friend, an acquaintance or whatever.

On the other hand “what is peculiar, ἴδιον, to something means or signifies what it takes to be the thing that it is. What characterizes something in its peculiarity, what the thing has of its own, its ownness, is a definition: ὅρος. So “An animal that walks on two feet” is the definition, ὁρισμός, of “man”. “A man’s being a walking man on two feet” is what it takes for an animal to be a man, or for something to be someone. 

Text 4

“A 'definition', ὅρος, is a phrase, λόγος, signifying, σημαίνων, a thing's essence, τὸ τί ἦν εἶναι. It is rendered (ἀποδίδοται) in the form either of a phrase in lieu of a term, or of a phrase in lieu of another phrase; for it is sometimes possible to define the meaning of a phrase as well.” Top. 101b37-102a1. 

Text 6

“It is sometimes possible to define what conveys meaning by a phrase as well (τῶν ὑπὸ λόγου τινὰ σημαινομένων ὁρίσασθαι). Those whο give an explanation (τὴν ἀπόδοσιν ποιοῦνται) with only a designation (ὀνόματι) clearly do not render a definition of the thing in question ([ὁ] τοῦ πράγματος ὁρισμός), because a definition is always a phrase of a certain kind (πᾶς ὁρισμὸς λόγος τίς ἐστιν.).”

PhD. Aparato para a sessão de 5 de Novembro

Para além do que ficou pendente, quero analisar a partir de David Charles os Analytica posteriora acerca de definição. Ficam as ocorrências de trovão e eclipse onde se procura aprofundar a operação de definição. 

Bibliografia secundária:

Ackrill, J. L. (1963). Aristotle's categories and de interpretatione. Oxford University Press, USA.

Aristotle, Topics, Books I and VII. (1997). Aristotle, topics, books I and VII. Oxford: Oxford University Press.

Asztalos, M. (1993). Boethius as a transmitter of greek logic to the latin west: The categories. Harvard Studies in Classical Philology, 95, 367-407.

Caston, V. (1998). Aristotle and the problem of intentionality. Philosophical and Phenomenological Research, 249-298.

Charles, David, Meaning and Essence, OUP.

Deslauriers, M., (2007) Aristotle on Definition, Philosophia Antiqua, Brill, Leiden, Boston.

Frank, E. (1940). The fundamental opposition of plato and aristotle. The American Journal of Philology, 61(2), 166-185.

Gillespie, C. M. (1925). The aristotelian categories. The Classical Quarterly, 19(2), 75-84.

Husik, I. (1904). On the categories of aristotle. The Philosophical Review, 13(5), 514-528.

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Results for βροντή and ἔκλειψις in 1. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora.

1. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 93bline 8. 

 ἔστι γὰρ ἡ ἔκλειψις ἀντίφραξις ὑπὸ γῆς. τί

ἐστι βροντή; πυρὸς ἀπόσβεσις ἐν νέφει. διὰ τί βροντᾷ; διὰ

τὸ ἀποσβέννυσθαι τὸ πῦρ ἐν τῷ νέφει. 

2. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 93bline 9. 

ἔστι γὰρ ἡ ἔκλειψις ἀντίφραξις ὑπὸ γῆς. τί

ἐστι βροντή; πυρὸς ἀπόσβεσις ἐν νέφει. διὰ τί βροντᾷ; διὰ

τὸ ἀποσβέννυσθαι τὸ πῦρ ἐν τῷ νέφει. νέφος Γ, βροντὴ Α,

ἀπόσβεσις πυρὸς τὸ Β. 

3. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 94aline 3. 

  Εἷς μὲν δὴ ὅρος ἐστὶν ὅρου ὁ εἰρημένος, ἄλλος δ’ ἐστὶν

ὅρος λόγος ὁ δηλῶν διὰ τί ἔστιν. ὥστε ὁ μὲν πρότερος σημαί-

(94a.) νει μέν, δείκνυσι δ’ οὔ, ὁ δ’ ὕστερος φανερὸν ὅτι ἔσται οἷον

ἀπόδειξις τοῦ τί ἐστι, τῇ θέσει διαφέρων τῆς ἀποδείξεως.

διαφέρει γὰρ εἰπεῖν διὰ τί βροντᾷ καὶ τί ἐστι βροντή· ἐρεῖ

γὰρ οὕτω μὲν “διότι ἀποσβέννυται τὸ πῦρ ἐν τοῖς νέφεσι”·

τί δ’ ἐστὶ βροντή; ψόφος ἀποσβεννυμένου πυρὸς ἐν νέφεσιν. (5)

ὥστε ὁ αὐτὸς λόγος ἄλλον τρόπον λέγεται, καὶ ὡδὶ μὲν ἀπό-

δειξις συνεχής, ὡδὶ δὲ ὁρισμός. (ἔτι ἐστὶν ὅρος βροντῆς ψό-

φος ἐν νέφεσι· τοῦτο δ’ ἐστὶ τῆς τοῦ τί ἐστιν ἀποδείξεως συμ-

4. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 94aline 5. 

(94a.) νει μέν, δείκνυσι δ’ οὔ, ὁ δ’ ὕστερος φανερὸν ὅτι ἔσται οἷον

ἀπόδειξις τοῦ τί ἐστι, τῇ θέσει διαφέρων τῆς ἀποδείξεως.

διαφέρει γὰρ εἰπεῖν διὰ τί βροντᾷ καὶ τί ἐστι βροντή· ἐρεῖ

γὰρ οὕτω μὲν “διότι ἀποσβέννυται τὸ πῦρ ἐν τοῖς νέφεσι”·

τί δ’ ἐστὶ βροντή; ψόφος ἀποσβεννυμένου πυρὸς ἐν νέφεσιν. (5)

ὥστε ὁ αὐτὸς λόγος ἄλλον τρόπον λέγεται, καὶ ὡδὶ μὲν ἀπό-

δειξις συνεχής, ὡδὶ δὲ ὁρισμός. (ἔτι ἐστὶν ὅρος βροντῆς ψό-

φος ἐν νέφεσι· τοῦτο δ’ ἐστὶ τῆς τοῦ τί ἐστιν ἀποδείξεως συμ-

πέρασμα.) ὁ δὲ τῶν ἀμέσων ὁρισμὸς θέσις ἐστὶ τοῦ τί ἐστιν

ἀναπόδεικτος. (10)

5. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 93aline 22. 

δῆλα γίνεται, ἀλλ’ οὔτι πρότερόν γε τὸ διότι δυνατὸν γνωρί-

σαι τοῦ ὅτι, δῆλον ὅτι ὁμοίως καὶ τὸ τί ἦν εἶναι οὐκ ἄνευ τοῦ

ὅτι ἔστιν· ἀδύνατον γὰρ εἰδέναι τί ἐστιν, ἀγνοοῦντας εἰ ἔστιν. (20)

τὸ δ’ εἰ ἔστιν ὁτὲ μὲν κατὰ συμβεβηκὸς ἔχομεν, ὁτὲ δ’

ἔχοντές τι αὐτοῦ τοῦ πράγματος, οἷον βροντήν, ὅτι ψόφος

τις νεφῶν, καὶ ἔκλειψιν, ὅτι στέρησίς τις φωτός, καὶ ἄνθρω-

πον, ὅτι ζῷόν τι, καὶ ψυχήν, ὅτι αὐτὸ αὑτὸ κινοῦν. ὅσα μὲν

οὖν κατὰ συμβεβηκὸς οἴδαμεν ὅτι ἔστιν, ἀναγκαῖον μηδαμῶς (25)

ἔχειν πρὸς τὸ τί ἐστιν· οὐδὲ γὰρ ὅτι ἔστιν ἴσμεν· τὸ δὲ ζητεῖν

τί ἐστι μὴ ἔχοντας ὅτι ἔστι, μηδὲν ζητεῖν ἐστιν. καθ’ ὅσων δ’

6. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 94aline 7. 

διαφέρει γὰρ εἰπεῖν διὰ τί βροντᾷ καὶ τί ἐστι βροντή· ἐρεῖ

γὰρ οὕτω μὲν “διότι ἀποσβέννυται τὸ πῦρ ἐν τοῖς νέφεσι”·

τί δ’ ἐστὶ βροντή; ψόφος ἀποσβεννυμένου πυρὸς ἐν νέφεσιν. (5)

ὥστε ὁ αὐτὸς λόγος ἄλλον τρόπον λέγεται, καὶ ὡδὶ μὲν ἀπό-

δειξις συνεχής, ὡδὶ δὲ ὁρισμός. (ἔτι ἐστὶν ὅρος βροντῆς ψό-

φος ἐν νέφεσι· τοῦτο δ’ ἐστὶ τῆς τοῦ τί ἐστιν ἀποδείξεως συμ-

πέρασμα.) ὁ δὲ τῶν ἀμέσων ὁρισμὸς θέσις ἐστὶ τοῦ τί ἐστιν

ἀναπόδεικτος. (10)

  Ἔστιν ἄρα ὁρισμὸς εἷς μὲν λόγος τοῦ τί ἐστιν ἀναπό-

δεικτος, εἷς δὲ συλλογισμὸς τοῦ τί ἐστι, πτώσει διαφέρων

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Results for εκλειψ

1. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 75b line 34. 

λογίσασθαι καθόλου, ἀλλ’ ὅτι νῦν. ὁμοίως δ’ ἔχει καὶ (30)

περὶ ὁρισμούς, ἐπείπερ ἐστὶν ὁ ὁρισμὸς ἢ ἀρχὴ ἀποδείξεως

ἢ ἀπόδειξις θέσει διαφέρουσα ἢ συμπέρασμά τι ἀποδείξεως.

αἱ δὲ τῶν πολλάκις γινομένων ἀποδείξεις καὶ ἐπιστῆμαι, οἷον

σελήνης ἐκλείψεως, δῆλον ὅτι ᾗ μὲν τοιοῦδ’ εἰσίν, ἀεὶ εἰσίν,

ᾗ δ’ οὐκ ἀεί, κατὰ μέρος εἰσίν. ὥσπερ δ’ ἡ ἔκλειψις, ὡσαύ- (35)

τως τοῖς ἄλλοις.

  Ἐπεὶ δὲ φανερὸν ὅτι ἕκαστον ἀποδεῖξαι οὐκ ἔστιν ἀλλ’

ἢ ἐκ τῶν ἑκάστου ἀρχῶν, ἂν τὸ δεικνύμενον ὑπάρχῃ ᾗ ἐκεῖνο,

οὐκ ἔστι τὸ ἐπίστασθαι τοῦτο, ἂν ἐξ ἀληθῶν καὶ ἀναποδείκτων

2. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 88a line 1. 

ἀπόδειξιν καὶ οὐχ ὥσπερ φασί τινες ἠπιστάμεθα· αἰσθάνε-

σθαι μὲν γὰρ ἀνάγκη καθ’ ἕκαστον, ἡ δ’ ἐπιστήμη τὸ τὸ

καθόλου γνωρίζειν ἐστίν. διὸ καὶ εἰ ἐπὶ τῆς σελήνης ὄντες

ἑωρῶμεν ἀντιφράττουσαν τὴν γῆν, οὐκ ἂν ᾔδειμεν τὴν αἰτίαν (40)

(88a.) τῆς ἐκλείψεως. ᾐσθανόμεθα γὰρ ἂν ὅτι νῦν ἐκλείπει, καὶ

οὐ διότι ὅλως· οὐ γὰρ ἦν τοῦ καθόλου αἴσθησις. οὐ μὴν ἀλλ’

ἐκ τοῦ θεωρεῖν τοῦτο πολλάκις συμβαῖνον τὸ καθόλου ἂν θη-

ρεύσαντες ἀπόδειξιν εἴχομεν· ἐκ γὰρ τῶν καθ’ ἕκαστα πλει-

όνων τὸ καθόλου δῆλον. τὸ δὲ καθόλου τίμιον, ὅτι δηλοῖ τὸ (5)

αἴτιον· ὥστε περὶ τῶν τοιούτων ἡ καθόλου τιμιωτέρα τῶν αἰ-

3. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 90a line 25. 

ἐστὶν ἐν ἀριθμοῖς ὁ λόγος αὐτῶν; λαβόντες δ’ ὅτι ἔστι, τίς

οὖν ἐστιν ὁ λόγος;

  Ὅτι δ’ ἐστὶ τοῦ μέσου ἡ ζήτησις, δηλοῖ ὅσων τὸ μέ-

σον αἰσθητόν. ζητοῦμεν γὰρ μὴ ᾐσθημένοι, οἷον τῆς ἐκλεί-

ψεως, εἰ ἔστιν ἢ μή. εἰ δ’ ἦμεν ἐπὶ τῆς σελήνης, οὐκ ἂν ἐζη- (25)

τοῦμεν οὔτ’ εἰ γίνεται οὔτε διὰ τί, ἀλλ’ ἅμα δῆλον ἂν ἦν.

ἐκ γὰρ τοῦ αἰσθέσθαι καὶ τὸ καθόλου ἐγένετο ἂν ἡμῖν εἰδέ-

ναι. ἡ μὲν γὰρ αἴσθησις ὅτι νῦν ἀντιφράττει (καὶ γὰρ δῆ-

λον ὅτι νῦν ἐκλείπει)· ἐκ δὲ τούτου τὸ καθόλου ἂν ἐγένετο. @1

  Ὥσπερ οὖν λέγομεν, τὸ τί ἐστιν εἰδέναι ταὐτό ἐστι καὶ (30)

4. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 88a line 12. 

τῶν πρώτων ἄλλος λόγος.

  Φανερὸν οὖν ὅτι ἀδύνατον τῷ αἰσθάνεσθαι ἐπίστασθαί τι

τῶν ἀποδεικτῶν, εἰ μή τις τὸ αἰσθάνεσθαι τοῦτο λέγει, τὸ (10)

ἐπιστήμην ἔχειν δι’ ἀποδείξεως. ἔστι μέντοι ἔνια ἀναγόμενα

εἰς αἰσθήσεως ἔκλειψιν ἐν τοῖς προβλήμασιν. ἔνια γὰρ εἰ

ἑωρῶμεν οὐκ ἂν ἐζητοῦμεν, οὐχ ὡς εἰδότες τῷ ὁρᾶν, ἀλλ’ ὡς

ἔχοντες τὸ καθόλου ἐκ τοῦ ὁρᾶν. οἷον εἰ τὴν ὕαλον τετρυπη-

μένην ἑωρῶμεν καὶ τὸ φῶς διιόν, δῆλον ἂν ἦν καὶ διὰ τί (15)

καίει, τῷ ὁρᾶν μὲν χωρὶς ἐφ’ ἑκάστης, νοῆσαι δ’ ἅμα ὅτι

ἐπὶ πασῶν οὕτως. @1

5. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 90a line 13. 

τι, τί οὖν τοῦτ’ ἔστι ζητοῦμεν. τὸ γὰρ αἴτιον τοῦ εἶναι μὴ

τοδὶ ἢ τοδὶ ἀλλ’ ἁπλῶς τὴν οὐσίαν, ἢ τοῦ μὴ ἁπλῶς ἀλ- (10)

λά τι τῶν καθ’ αὑτὸ ἢ κατὰ συμβεβηκός, τὸ μέσον ἐστίν.

λέγω δὲ τὸ μὲν ἁπλῶς τὸ ὑποκείμενον, οἷον σελήνην ἢ γῆν

ἢ ἥλιον ἢ τρίγωνον, τὸ δὲ τὶ ἔκλειψιν, ἰσότητα ἀνισότητα,

εἰ ἐν μέσῳ ἢ μή. ἐν ἅπασι γὰρ τούτοις φανερόν ἐστιν ὅτι

τὸ αὐτό ἐστι τὸ τί ἐστι καὶ διὰ τί ἔστιν. τί ἐστιν ἔκλειψις; (15)

στέρησις φωτὸς ἀπὸ σελήνης ὑπὸ γῆς ἀντιφράξεως. διὰ

τί ἔστιν ἔκλειψις, ἢ διὰ τί ἐκλείπει ἡ σελήνη; διὰ τὸ

ἀπολείπειν τὸ φῶς ἀντιφραττούσης τῆς γῆς. τί ἐστι συμ-

6. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 93a line 23. 

σαι τοῦ ὅτι, δῆλον ὅτι ὁμοίως καὶ τὸ τί ἦν εἶναι οὐκ ἄνευ τοῦ

ὅτι ἔστιν· ἀδύνατον γὰρ εἰδέναι τί ἐστιν, ἀγνοοῦντας εἰ ἔστιν. (20)

τὸ δ’ εἰ ἔστιν ὁτὲ μὲν κατὰ συμβεβηκὸς ἔχομεν, ὁτὲ δ’

ἔχοντές τι αὐτοῦ τοῦ πράγματος, οἷον βροντήν, ὅτι ψόφος

τις νεφῶν, καὶ ἔκλειψιν, ὅτι στέρησίς τις φωτός, καὶ ἄνθρω-

πον, ὅτι ζῷόν τι, καὶ ψυχήν, ὅτι αὐτὸ αὑτὸ κινοῦν. ὅσα μὲν

οὖν κατὰ συμβεβηκὸς οἴδαμεν ὅτι ἔστιν, ἀναγκαῖον μηδαμῶς (25)

ἔχειν πρὸς τὸ τί ἐστιν· οὐδὲ γὰρ ὅτι ἔστιν ἴσμεν· τὸ δὲ ζητεῖν

τί ἐστι μὴ ἔχοντας ὅτι ἔστι, μηδὲν ζητεῖν ἐστιν. καθ’ ὅσων δ’

ἔχομέν τι, ῥᾷον. ὥστε ὡς ἔχομεν ὅτι ἔστιν, οὕτως ἔχομεν καὶ

7. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 75b line 35. 

περὶ ὁρισμούς, ἐπείπερ ἐστὶν ὁ ὁρισμὸς ἢ ἀρχὴ ἀποδείξεως

ἢ ἀπόδειξις θέσει διαφέρουσα ἢ συμπέρασμά τι ἀποδείξεως.

αἱ δὲ τῶν πολλάκις γινομένων ἀποδείξεις καὶ ἐπιστῆμαι, οἷον

σελήνης ἐκλείψεως, δῆλον ὅτι ᾗ μὲν τοιοῦδ’ εἰσίν, ἀεὶ εἰσίν,

ᾗ δ’ οὐκ ἀεί, κατὰ μέρος εἰσίν. ὥσπερ δ’ ἡ ἔκλειψις, ὡσαύ- (35)

τως τοῖς ἄλλοις.

  Ἐπεὶ δὲ φανερὸν ὅτι ἕκαστον ἀποδεῖξαι οὐκ ἔστιν ἀλλ’

ἢ ἐκ τῶν ἑκάστου ἀρχῶν, ἂν τὸ δεικνύμενον ὑπάρχῃ ᾗ ἐκεῖνο,

οὐκ ἔστι τὸ ἐπίστασθαι τοῦτο, ἂν ἐξ ἀληθῶν καὶ ἀναποδείκτων

δειχθῇ καὶ ἀμέσων. ἔστι γὰρ οὕτω δεῖξαι, ὥσπερ Βρύσων (40)

8. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 90a line 15. 

λά τι τῶν καθ’ αὑτὸ ἢ κατὰ συμβεβηκός, τὸ μέσον ἐστίν.

λέγω δὲ τὸ μὲν ἁπλῶς τὸ ὑποκείμενον, οἷον σελήνην ἢ γῆν

ἢ ἥλιον ἢ τρίγωνον, τὸ δὲ τὶ ἔκλειψιν, ἰσότητα ἀνισότητα,

εἰ ἐν μέσῳ ἢ μή. ἐν ἅπασι γὰρ τούτοις φανερόν ἐστιν ὅτι

τὸ αὐτό ἐστι τὸ τί ἐστι καὶ διὰ τί ἔστιν. τί ἐστιν ἔκλειψις; (15)

στέρησις φωτὸς ἀπὸ σελήνης ὑπὸ γῆς ἀντιφράξεως. διὰ

τί ἔστιν ἔκλειψις, ἢ διὰ τί ἐκλείπει ἡ σελήνη; διὰ τὸ

ἀπολείπειν τὸ φῶς ἀντιφραττούσης τῆς γῆς. τί ἐστι συμ-

φωνία; λόγος ἀριθμῶν ἐν ὀξεῖ καὶ βαρεῖ. διὰ τί συμφω-

νεῖ τὸ ὀξὺ τῷ βαρεῖ; διὰ τὸ λόγον ἔχειν ἀριθμῶν τὸ ὀξὺ (20)

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ἢ ἥλιον ἢ τρίγωνον, τὸ δὲ τὶ ἔκλειψιν, ἰσότητα ἀνισότητα,

εἰ ἐν μέσῳ ἢ μή. ἐν ἅπασι γὰρ τούτοις φανερόν ἐστιν ὅτι

τὸ αὐτό ἐστι τὸ τί ἐστι καὶ διὰ τί ἔστιν. τί ἐστιν ἔκλειψις; (15)

στέρησις φωτὸς ἀπὸ σελήνης ὑπὸ γῆς ἀντιφράξεως. διὰ

τί ἔστιν ἔκλειψις, ἢ διὰ τί ἐκλείπει ἡ σελήνη; διὰ τὸ

ἀπολείπειν τὸ φῶς ἀντιφραττούσης τῆς γῆς. τί ἐστι συμ-

φωνία; λόγος ἀριθμῶν ἐν ὀξεῖ καὶ βαρεῖ. διὰ τί συμφω-

νεῖ τὸ ὀξὺ τῷ βαρεῖ; διὰ τὸ λόγον ἔχειν ἀριθμῶν τὸ ὀξὺ (20)

καὶ τὸ βαρύ. ἆρ’ ἔστι συμφωνεῖν τὸ ὀξὺ καὶ τὸ βαρύ; ἆρ’

ἐστὶν ἐν ἀριθμοῖς ὁ λόγος αὐτῶν; λαβόντες δ’ ὅτι ἔστι, τίς

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ἔχειν πρὸς τὸ τί ἐστιν· οὐδὲ γὰρ ὅτι ἔστιν ἴσμεν· τὸ δὲ ζητεῖν

τί ἐστι μὴ ἔχοντας ὅτι ἔστι, μηδὲν ζητεῖν ἐστιν. καθ’ ὅσων δ’

ἔχομέν τι, ῥᾷον. ὥστε ὡς ἔχομεν ὅτι ἔστιν, οὕτως ἔχομεν καὶ

πρὸς τὸ τί ἐστιν. ὧν οὖν ἔχομέν τι τοῦ τί ἐστιν, ἔστω πρῶτον μὲν @1

ὧδε· ἔκλειψις ἐφ’ οὗ τὸ Α, σελήνη ἐφ’ οὗ Γ, ἀντίφραξις (30)

γῆς ἐφ’ οὗ Β. τὸ μὲν οὖν πότερον ἐκλείπει ἢ οὔ, τὸ Β ζη-

τεῖν ἔστιν, ἆρ’ ἔστιν ἢ οὔ. τοῦτο δ’ οὐδὲν διαφέρει ζητεῖν ἢ εἰ

ἔστι λόγος αὐτοῦ· καὶ ἐὰν ᾖ τοῦτο, κἀκεῖνό φαμεν εἶναι. ἢ

ποτέρας τῆς ἀντιφάσεώς ἐστιν ὁ λόγος, πότερον τοῦ ἔχειν δύο

ὀρθὰς ἢ τοῦ μὴ ἔχειν. ὅταν δ’ εὕρωμεν, ἅμα τὸ ὅτι καὶ τὸ (35)

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ἔστι λόγος αὐτοῦ· καὶ ἐὰν ᾖ τοῦτο, κἀκεῖνό φαμεν εἶναι. ἢ

ποτέρας τῆς ἀντιφάσεώς ἐστιν ὁ λόγος, πότερον τοῦ ἔχειν δύο

ὀρθὰς ἢ τοῦ μὴ ἔχειν. ὅταν δ’ εὕρωμεν, ἅμα τὸ ὅτι καὶ τὸ (35)

διότι ἴσμεν, ἂν δι’ ἀμέσων ᾖ· εἰ δὲ μή, τὸ ὅτι, τὸ διότι δ’

οὔ. σελήνη Γ, ἔκλειψις Α, τὸ πανσελήνου σκιὰν μὴ δύ-

νασθαι ποιεῖν μηδενὸς ἡμῶν μεταξὺ ὄντος φανεροῦ, ἐφ’ οὗ

Β. εἰ τοίνυν τῷ Γ ὑπάρχει τὸ Β τὸ μὴ δύνασθαι ποιεῖν

(93b.) σκιὰν μηδενὸς μεταξὺ ἡμῶν ὄντος, τούτῳ δὲ τὸ Α τὸ ἐκλε-

λοιπέναι, ὅτι μὲν ἐκλείπει δῆλον, διότι δ’ οὔπω, καὶ ὅτι

μὲν ἔστιν ἔκλειψις ἴσμεν, τί δ’ ἐστὶν οὐκ ἴσμεν. δήλου δ’ ὄν-

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νασθαι ποιεῖν μηδενὸς ἡμῶν μεταξὺ ὄντος φανεροῦ, ἐφ’ οὗ

Β. εἰ τοίνυν τῷ Γ ὑπάρχει τὸ Β τὸ μὴ δύνασθαι ποιεῖν

(93b.) σκιὰν μηδενὸς μεταξὺ ἡμῶν ὄντος, τούτῳ δὲ τὸ Α τὸ ἐκλε-

λοιπέναι, ὅτι μὲν ἐκλείπει δῆλον, διότι δ’ οὔπω, καὶ ὅτι

μὲν ἔστιν ἔκλειψις ἴσμεν, τί δ’ ἐστὶν οὐκ ἴσμεν. δήλου δ’ ὄν-

τος ὅτι τὸ Α τῷ Γ ὑπάρχει, ἀλλὰ διὰ τί ὑπάρχει, τὸ ζη-

τεῖν τὸ Β τί ἐστι, πότερον ἀντίφραξις ἢ στροφὴ τῆς σελήνης (5)

ἢ ἀπόσβεσις. τοῦτο δ’ ἐστὶν ὁ λόγος τοῦ ἑτέρου ἄκρου, οἷον ἐν

τούτοις τοῦ Α· ἔστι γὰρ ἡ ἔκλειψις ἀντίφραξις ὑπὸ γῆς. τί

ἐστι βροντή; πυρὸς ἀπόσβεσις ἐν νέφει. διὰ τί βροντᾷ; διὰ

13. Aristoteles et Corpus Aristotelicum Phil., Analytica priora et posteriora. {0086.001} Bekker page 93b line 7. 

μὲν ἔστιν ἔκλειψις ἴσμεν, τί δ’ ἐστὶν οὐκ ἴσμεν. δήλου δ’ ὄν-

τος ὅτι τὸ Α τῷ Γ ὑπάρχει, ἀλλὰ διὰ τί ὑπάρχει, τὸ ζη-

τεῖν τὸ Β τί ἐστι, πότερον ἀντίφραξις ἢ στροφὴ τῆς σελήνης (5)

ἢ ἀπόσβεσις. τοῦτο δ’ ἐστὶν ὁ λόγος τοῦ ἑτέρου ἄκρου, οἷον ἐν

τούτοις τοῦ Α· ἔστι γὰρ ἡ ἔκλειψις ἀντίφραξις ὑπὸ γῆς. τί

ἐστι βροντή; πυρὸς ἀπόσβεσις ἐν νέφει. διὰ τί βροντᾷ; διὰ

τὸ ἀποσβέννυσθαι τὸ πῦρ ἐν τῷ νέφει. νέφος Γ, βροντὴ Α,

ἀπόσβεσις πυρὸς τὸ Β. τῷ δὴ Γ τῷ νέφει ὑπάρχει τὸ Β (10)

(ἀποσβέννυται γὰρ ἐν αὐτῷ τὸ πῦρ), τούτῳ δὲ τὸ Α, ψό-

φος· καὶ ἔστι γε λόγος τὸ Β τοῦ Α τοῦ πρώτου ἄκρου. ἂν

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  Τὸ δ’ αὐτὸ αἴτιόν ἐστι τοῖς γινομένοις καὶ τοῖς γεγενη- (10)

μένοις καὶ τοῖς ἐσομένοις ὅπερ καὶ τοῖς οὖσι (τὸ γὰρ μέ-

σον αἴτιον), πλὴν τοῖς μὲν οὖσιν ὄν, τοῖς δὲ γινομένοις γινό-

μενον, τοῖς δὲ γεγενημένοις γεγενημένον καὶ ἐσομένοις ἐσό-

μενον. οἷον διὰ τί γέγονεν ἔκλειψις; διότι ἐν μέσῳ γέγονεν

ἡ γῆ· γίνεται δὲ διότι γίνεται, ἔσται δὲ διότι ἔσται ἐν μέσῳ, (15)

καὶ ἔστι διότι ἔστιν. τί ἐστι κρύσταλλος; εἰλήφθω δὴ ὅτι ὕδωρ

πεπηγός. ὕδωρ ἐφ’ οὗ Γ, πεπηγὸς ἐφ’ οὗ Α, αἴτιον τὸ

μέσον ἐφ’ οὗ Β, ἔκλειψις θερμοῦ παντελής. ὑπάρχει δὴ

τῷ Γ τὸ Β, τούτῳ δὲ τὸ πεπηγέναι τὸ ἐφ’ οὗ Α. γίνεται

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μενον. οἷον διὰ τί γέγονεν ἔκλειψις; διότι ἐν μέσῳ γέγονεν

ἡ γῆ· γίνεται δὲ διότι γίνεται, ἔσται δὲ διότι ἔσται ἐν μέσῳ, (15)

καὶ ἔστι διότι ἔστιν. τί ἐστι κρύσταλλος; εἰλήφθω δὴ ὅτι ὕδωρ

πεπηγός. ὕδωρ ἐφ’ οὗ Γ, πεπηγὸς ἐφ’ οὗ Α, αἴτιον τὸ

μέσον ἐφ’ οὗ Β, ἔκλειψις θερμοῦ παντελής. ὑπάρχει δὴ

τῷ Γ τὸ Β, τούτῳ δὲ τὸ πεπηγέναι τὸ ἐφ’ οὗ Α. γίνεται

δὲ κρύσταλλος γινομένου τοῦ Β, γεγένηται δὲ γεγενημένου, (20)

ἔσται δ’ ἐσομένου.

  Τὸ μὲν οὖν οὕτως αἴτιον καὶ οὗ αἴτιον ἅμα γίνεται,

ὅταν γίνηται, καὶ ἔστιν, ὅταν ᾖ· καὶ ἐπὶ τοῦ γεγονέναι καὶ

ANCIENT PHILOSOPHY. 2nd Session, September the 22nd, 2011. Transcript: on causality. Aristotle, MF, α.

ANCIENT PHILOSOPHY. 2nd Session, September the 22nd, 2011.

Minutes: on causality.

Aristotle, MF, α.

MF 994a1-16:Ἀλλὰ μὴν ὅτι γ’ ἔστιν ἀρχή τις καὶ οὐκ ἄπειρα τὰ/ αἴτια τῶν ὄντων οὔτ’ εἰς εὐθυωρίαν οὔτε κατ’ εἶδος, δῆλον./ οὔτε γὰρ ὡς ἐξ ὕλης τόδ’ ἐκ τοῦδε δυνατὸν ἰέναι εἰς ἄπειρον/ (οἷον σάρκα μὲν ἐκ γῆς, γῆν δ’ ἐξ ἀέρος, ἀέρα δ’ ἐκ πυρός,/ καὶ τοῦτο μὴ ἵστασθαι), οὔτε ὅθεν ἡ ἀρχὴ τῆς κινήσεως (οἷον/ ἡλίου, τὸν δὲ ἥλιον ὑπὸ τοῦ νείκους, καὶ τούτου μηδὲν εἶναι/ πέρας)· ὁμοίως δὲ οὐδὲ τὸ οὗ ἕνεκα εἰς ἄπειρον οἷόν τε ἰέναι,/ βάδισιν μὲν ὑγιείας ἕνεκα, ταύτην δ’ εὐδαιμονίας, τὴν δ’ εὐδαιμο-/ νίαν ἄλλου, καὶ οὕτως ἀεὶ ἄλλο ἄλλου ἕνεκεν εἶναι· καὶ ἐπὶ (10)/ τοῦ τί ἦν εἶναι δ’ ὡσαύτως. τῶν γὰρ μέσων, ὧν ἐστί/ τι ἔσχατον καὶ πρότερον, ἀναγκαῖον εἶναι τὸ πρότερον αἴτιον/ τῶν μετ’ αὐτό. εἰ γὰρ εἰπεῖν ἡμᾶς δέοι τί τῶν τριῶν αἴτιον,/ τὸ πρῶτον ἐροῦμεν· οὐ γὰρ δὴ τό γ’ ἔσχατον, οὐδενὸς γὰρ τὸ/ τελευταῖον· ἀλλὰ μὴν οὐδὲ τὸ μέσον, ἑνὸς γάρ (οὐθὲν δὲ (15)/ διαφέρει ἓν ἢ πλείω εἶναι, οὐδ’ ἄπειρα ἢ πεπερασμένα).

There is a qualitative definition and a finite number of the causes of things. The ΑΙΤΙΑΙ are ARXAI. This is the first meaning of causes being principles. The “wherefrom” things come from and “where of” they get their origin: ΤΑ ΟΝΤΑ are principally “caused”. Intelligibility implies that the causes are provided with a limit: ΟΥΚ ΑΠΕΙΡΑ.

(994a.) Ἀλλὰ μὴν ὅτι γ 'ἔστιν ἀρχή τις καὶ οὐκ ἄπειρα τὰ αἴτια τῶν ὄντων

This theory is tested in two ways on two fronts. I. Aristotle interdicts an infinite progression of the causal/effect series, οὔτ 'εἰς εὐθυωρίαν, 994b2. II. The fundamental forms or essential features of causes are not unlimited:— οὔτε κατ' εἶδος, ibid. This is a condicio sine qua non to getting an explanation.

I. Οὔτ 'εἰς εὐθυωρίαν: Here the progression is thought to proceed indefinitely either descending from cause to effect or ascending from effect to cause. One can also think of time anteriority and posteriority.

The line of causality is thus represented by an ordinate axis.

This line contains a structural relationship between an X and a Y, i. e. different entities involved in causation at different moments in time: one happening earlier, the other later. The way an entity develops or is processed through time: X as a child and X as an adult.

The relationship between the two moments can configure: 

1. Two states of affairs of different things. 
2. Different things happening at the same time. 
3. The same thing happening at different times. 
4. The relationship between X and Y happening at different times, Δ-earlier and Δ-later can happen immediately.
5. Coinciding but not having anything to do with each other. 
6. Or mediately: happening far from each other, but still with an intrinsic connexion between them. 

What precedes can be retrospectively seen up to the very first moment of a thing or all things starting to happen. One can in prospect see the deadline or the last moment of everything in general. After that, nothing happens or is not consciously perceived to happen. 

The first and last moments of a thing can be reduced to two different moments or presentations of that thing, but are as such irreducible. At the first moment a thing starts to happen other things disappear while others also start up. The first moment of a thing also contains its last moment. The last moment of a thing cancels out the first moment of that thing. A fortiori: all other moments between the first and the last are cancelled out.  One thing may end at the precise moment when another begins, and vive versa begin whwn another ends.

One thing is not the first cause of all things and their consequences. Neither can the last moment of all things be reducible to the last moment. The next moment when everything is finished is still in a time dimension that, while not allowing any real determination of what it is, is thought of as having the intrinsic organization of time as such.

II. Οὔτε κατ 'εἶδος

Here the delimitation is horizontally drawn. (See Ross.) Εἶδος means the essential or relevant features of a causal operator. It structures reality in accordance with four fundamental meanings. Traditionally the causes are material, efficient, final or formal. The structuring cause of a thing makes it intelligible. The ΕΙΔΟΣ projects lines of interpretation and explains what and how things are. Usually these lines of interpretation are, if not obscure, merely implicit.

Aristotle’s consideration of the four causes one by one aims to show how none can proceed indefinitely. Each and every one is individually expressed by means of prepositions, thus highlighting the particular “syntactical” structure of reality worked out through causation.

III. Material cause

οὔτε γὰρ ὡς ἐξ ὕλης τόδ 'ἐκ τοῦδε δυνατὸν ἰέναι εἰς ἄπειρον (Οἷον σάρκα μὲν ἐκ γῆς, γῆν δ 'ἐξ ἀέρος, ἀέρα δ' ἐκ πυρός, καὶ τοῦτο μὴ ἵστασθαι)

‘Mater’, ‘Ἡ ὕλη’, ‘the mater X consists in’, ‘ἐξ ὕλης’, ‘this is made of this”,  ‘τόδ 'ἐκ τοῦδε’. The ‘EK’ + genitive expresses the material cause that lets us understand a thing in its ‘make up’, as something made of… or consisting of… Aristotle isolates particular elements: fire, air, water, earth and explains the relationship there is between them. The materials a thing is made of or consists of are its ingredients, component parts or constituent elements. From a culinary point of view this provides an answer to the the question: what does it take? We proceed this way when trying to guess the ingredients a dish is made of, once it is already cooked. But we can think of Aristotle’s usual examples: a marble statue, a copper shield, a house of bricks, wooden furniture, etc.. 

When asking the question about the material ‘make up of’ X, we modify the usual presence of X. If (a…z) are the ingredients of X, X is made of (a…z). The peculiar relationship between a, b, c, …, z and X is expressed prepositionally: X made of (a…z). Matter can be divided into elements, atoms and molecules, but the atom itself can be thought of as composed of subatomic particles: electrons, protons and neutrons, which in turn can be subdivided into quarks. These can be considered as thick, massive and compact or lightweight and thin.

Each quark can be of one of six different types, with different density determinations: up, down, charm, strange, top, bottom. Fundamental relationships are: electromagnetic, gravitational, strong interaction and weak interaction, collision and rotation. Antiquarks are antimatter. They are antagonistic to quark forces. We can see the logic of determining the material cause as a general question about the consistency of something. 

IV. Efficient cause

οὔτε ὅθεν ἡ ἀρχὴ τῆς κινήσεως: where does the principle of change come from?

“Οἷον τὸν μὲν ἄνθρωπον ὑπὸ τοῦ ἀέρος κινηθῆναι, τοῦτον δ 'ὑπὸ τοῦ ἡλίου, τὸν δὲ ἥλιον ὑπὸ τοῦ νείκους, καὶ τούτου μηδὲν εἶναι πέρας (as the man who is carried by the wind, the wind is modified by the sun and the sun is transformed by strife: not true that there is no limit to this principle efficient change)”

X is changed (or moved or altered, or transformed) by Y. The passive voice expresses the relationship between X as the subject undergoing a change produced by the agent Y. A real entity is changed through the agency or action of something different. Reality is the result of an action but described in the passive voice. 

The emphasis is placed on the agent introduced by the particle: ὑπό. It has a variable value. It is a formal structure that allows concrete instantiation. This case is concerned in the violent displacement of a person caused by the wind. 

Why or how is the man carried way? The man is carried by the wind. Wind is the efficient cause that brings to bear its effect on a man: moves X, drags X, pulls X or takes X from one place to another. 

But ΤΙΝΑ Ὑπό τινος κινηθῆναι, can be the wind. Moreover he wind is triggered by the sun. The sun, by strife. Strife is the limit. One cannot ask here what causes the strife itself or hatred between the elements. The point of contention, collision, violent action, is present in each particular case where X is taken by something, dragged, pushed, intervened, acted upon, etc.. Etc. .. The direction of the relationship between a man and wind or wind and heat from the sun, or between the sun and the strife is the same. The efficient cause determines the way the effect is brought about by a passive action and the allocation of a given subject, substrate substance.

Final cause

οὐδὲ τὸ οὗ ἕνεκα εἰς ἄπειρον οἷόν τε ἰέναι: not just about "in view of ...", "because of ...", "thanks to ...", "the for the sake of which."

“βάδισιν μὲν ὑγιείας ἕνεκα, ταύτην δ 'εὐδαιμονίας, τὴν δ' εὐδαιμονίαν ἄλλου, καὶ οὕτως ἀεὶ ἄλλο ἄλλου ἕνεκεν εἶναι” (Walking is for the sake of health and health is for the sake of well-being, but it also happens that well-being is for the sake of happiness) Happiness is the limit: it is the ultimate ‘for the sake of which’.The same happens also with teleologic causation: τέλος, ἀγαθόν, τὸ οὗ ἕνεκα. The telic character of the expression allows us to understand a completely different reading of one thing or state of affairs, circumstance or situation. 

Walking aims at well-being. This is the limit from which several lines are drawn retrospectively to guide our actions. What we do has a purpose. Otherwise, it is in vain and empty.

Formal cause

καὶ ἐπὶ τοῦ τί ἦν εἶναι δ 'ὡσαύτως.

Τῶν γὰρ μέσων, ὧν ἐστί τι ἔσχατον καὶ πρότερον, ἀναγκαῖον εἶναι τὸ πρότερον αἴτιον τῶν μετ 'αὐτό. εἰ γὰρ εἰπεῖν ἡμᾶς δέοι τί τῶν τριῶν αἴτιον, τὸ πρῶτον ἐροῦμεν · οὐ γὰρ δὴ τό γ 'ἔσχατον, οὐδενὸς γὰρ τὸ τελευταῖον · ἀλλὰ μὴν οὐδὲ τὸ μέσον, ἑνὸς γάρ

The formal cause is expressed in many ways by Aristotle. This is one of the most puzzling: ‘What is it to be an X?’. Being what it is happens to this thing that exists here in the way it is. The essential aspect of something features in the several things that exist in that particular way. This thing here is not a feature, or an essential aspect. I do not sit down on a idea or on an essential feature of a chair. I sit down on the chair. This chair here is the sort of thing that has what it takes for it to be what it is. The form lets this exact thing take what it needs to be of that form. We could better understand what is at stake here if we said “to chair”, verb, is the way a ‘chair’, noun, happens. Or the chair is expressed by the adverb: the way the thing chair is. 

ANTIGA. PROTOCOLO de 27 de Outubro de 2011

PROTOCOLO de 27 de Outubro de 2011.

A questão passa naturalmente por saber como é que uma acção é completa ou se completa. “Completa é aquela acção pela qual a completude existe intrinsecamente ao mesmo tempo que o seu decurso (ἐκείνη <ᾗ> ἐνυπάρχει τὸ τέλος καὶ [ἡ] πρᾶξις.)” MF, 1048b22-23. Em causa está pensar no modo como uma possibilidade se concretiza, se torna realidade. Ou seja, como é que o que existe em potência, δυνάμει, passa a entrar em actividade de forma completa, ἐνέργειᾳ, ou, como diz Ross, passa a existir em actualização, ἐντελέχειᾳ. Embora, o sentido de “actualizar-se” não signifique tornar-se acto, activar-se, nem accionar, sem mais, mas diz em português qualquer coisa como aperfeiçoar-se, renovar-se, etc.. 

Aristóteles emprega o advérbio: “ᾗ” que é o dativo do feminino no singular do pronome relativo: ὅς, ἥ, ὅ, com sentido adverbial. Como advérbio de lugar enuncia o complemento circunstancial de lugar por onde, ou seja: o percurso por onde se percorre o de onde… aonde. Como advérbio de modo: é a maneira como.

 Ora uma possibilidade não é pensada como estando num sítio. Não se desloca de um lugar de onde para ir por um caminho até chegar ao lugar onde chega. Nem se pode pensar que por essa deslocação como quer que seja pensada, se transforma em actualidade, entra em actividade, passa a estar em acção, se actualiza e fica plenamente desenvolvida. E se se pensar que de algum modo a possibilidade como condição do possível e a concretização do possível como a sua entrada em acção, esse modo é indeterminado. 

A transformação do possível em realidade acabada dá-se numa dimensão temporal. O por onde é determinado pelo tempo em que se processa a transformação. Aquilo por que tem de passar algo para deixar de ser algo possível e passar a ser esse algo mas concretizado, numa realidade plena. Assim, pode perceber-se que o emagrecimento, a aprendizagem, a cura, o amadurecimento, o crescimento, o envelhecimento, são processos que se desenvolvem no tempo. Tratam-se de processos que se encontram em vias de ser nos seus encaminhamentos específicos, mas dependem do tempo para se “aperfeiçoarem”, “para chegarem ao fim”. Por outro lado, ver, pensar, intuir, viver, ser feliz, são processos que quando ocorrem estão já “aperfeiçoados”, “são já totais e completos”. 

O que para já importa acentuar é o carácter específico de cada processo. O emagrecimento altera o corpo. Torna-o magro. A aprendizagem torna quem passa por ela dotado de uma habilitação que não tinha. Torna esse alguém entendido numa matéria. A cura dá saúde a quem foi tratado. O amadurecimento transforma o verde e imaturo. O crescimento aumenta o que é menor. O envelhecimento envelhece o jovem. Ou seja, o emagrecimento emagrece, a aprendizagem ensina, o crescimento faz crescer, o amadurecimento amadurece, o envelhecimento envelhece. Nos sufixos: -ecer, está pensado o processo incoativo: -sc-, -σκ-. Mas cada processo tem concreta e especificamente o seu modo de ser accionado, o seu particular desenvolvimento, o seu resultado ou terminus ad quem específicos. O emagrecimento emagrece, mas, enquanto tal, não ensina, não faz aumentar de volume ou maça, não amadurece, não envelhece. O mesmo se passando com cada um dos processos. Há um modo específico como se concretizam, há operadores determinados que actuam diferentemente consoante os processos em causa. A realização é pensada abstractamente como o que acontece no tempo e requer tempo para acontecer. O que não era passa a ser. Mas na verdade todos os processos são vias específicas, com ritmos e tempos próprios, formas de actuação e transformação dos materiais específicos que transformam. Mesmo que se trate sempre do humano, do corpo humano ou da alma humana, as transformações que operam não têm que ver, isoladamente, com nenhuma das outras. Pode-se pensar que é a mesma pessoa que emagrece, aprende, fica crescida, amadurece e envelhece. Mas o que lhe acontece por força dessas acções e dos processos que elaboram é completamente diferente nos seus resultados. Dão-se em tempos diferentes, em campos diferentes. O modo como se emagrece não é o modo como se aprende. O modo como se aprende não é como se envelhece, etc. 

O que desencadeia uma acção, mesmo que incompleta, o que leva à mudança tem o seu campo específico de aplicação. O terminal das operações é diferente e depende especificamente dos agentes da transformação. O possível e inerte pode permanecer apenas possível e inerte, ou seja, impassível, insusceptível de accionamento, actividade, ser actualizado. Para emagrecer, podemos pensar no corte parcial, gradual ou total e de uma só vez de açucares, álcool, hidratos de carbono, etc., etc.. Mas não basta pensar. Importa efectivamente suspender a ingestão de alimentos que contenham esses elementos. Importa a suspensão sistemática e o actuação do tempo. A composição do corpo humano permite a compreensão dessa possibilidade. Ao ser posto em prática um regime dietético, percebe-se a sua acção. O mesmo se passa no processo de aprendizagem. A alguém pode ocorrer ir estudar uma determinada matéria. Às dez horas da manhã de um dia de um mês. Por essa ideia, pode alterar a vida. Ao decidir-se por estudar uma matéria, implica: inscrever-se num local, mudar de vida, organizar-se em função dessa realidade, aplicar-se, estudar, etc., etc.. Os campos de aplicação são diferentes, os resultados diferentes. Mas para cada caso há um por onde o possível deixa de ser possível, inerte e ineficaz e passa a ser posto em prática. Passamos a estar lá, por assim dizer, a fazer por isso como colaboradores numa decisão que tem os instrumentos próprios para a sua aplicação.

Os operadores são: τὸ κινοῦν, o motor ou mutante, o agente da mutação, o que tem a possibilidade de ser mutável, de sofrer a acção do agente da mudança, τὸ δυνάμει ὂν κινητόν. O κινητόν é enquanto passível de mudança mas não ainda mudado, aquilo relativamente ao qual a imutabilidade é o repouso ou a inércia: οὗ ἡ ἀκινησία ἠρεμία ἐστίν.

Ou seja a mudança é aquilo relativamente ao qual a ausência dela é repouso (ᾧ γὰρ ἡ κίνησις ὑπάρχει, τούτου ἡ ἀκινησία ἠρεμία).

A mudança é pensada como possibilidade. O agente pode não actuar e assim não surtir efeito. Nesse sentido a mudança possível fica inerte, não é activada, accionada ou actualizada. Nesse sentido não muda. É o que se diz de algo que não mudou. Não é desprovido da possibilidade de mudança, mas não mudou efectivamente. Ou seja, encontra-se onde estava, em sossego e inerte. Mas o que sucede quando o mutável é arrancado ao sossego, à inércia, à letargia em que se encontra? Isto é: o que transforma a ἀκινησία do κινητόν, a sua ἀδυναμία específica em κίνησις? Por onde? Qual é o buraco da agulha que encontra para se concretizar, activar, accionar, actualizar? Como é que o que não é ainda passa a estar em actividade. O que faz a actualidade de um possível?

Aristóteles diz que tem de haver em acréscimo a estas condições de possibilidade, necessárias mas não suficientes, algo que execute a mudança. É o ἐνεργεῖν: o operar intrínseco da actividade que transforma o possível: põe-no a trabalhar, em funcionamento, em exercício, conecta-o, liga-o, etc., etc.. O que faz entrar em actividade algo, arrancando-o à inércia e pondo-o em movimento, a mexer é o próprio mudar. τὸ γὰρ πρὸς τοῦτο ἐνεργεῖν, ᾗ τοιοῦτον, αὐτὸ τὸ κινεῖν ἐστι, Phys. 202a5-6. 

Uma vez mais surge o enigmático advérbio ᾗ. A κίνησις é pensada como o ‘por onde’ a δύναμις passa a ἐνέργεια. Ou seja, por onde o possível é transformado em actividade. Não está dito que é completo. Mas está dito que há uma inércia vencida. Há uma não impossibilidade que resulta no início que se dá ao accionamento do possível. Como é que se inicia um processo de realização? Como é que o mutável em potência passa a ser feito entrar em acção? Como é que o mutável passa a encontrar-se em mudança activa? Como é que o susceptível de mudança é mudado?

Aristóteles descreve a mudança do mutável em mudado como um acontecimento, um contacto entre o agente da mudança e o mutável. O agente da mudança, o mutante, intervém no mutável. Essa intervenção é pensada como um toque, uma intervenção “cinérgica”, se assim se pode dizer, à semelhança de uma intervenção cirúrgica. Há uma θίξις, um contacto, bidimensional. Por um lado, pelo toque do agente interveniente dá-se uma operação, produz-se um efeito. Por outro lado, simultaneamente o mutável sofre esse toque, é “intervencionado”: τοῦτο δὲ ποιεῖ θίξει, ὥστε ἅμα καὶ πάσχει. O toque existe entre o interveniente e o intervencionado. A acção cinérgica actua cinergicamente no que é susceptível de mudança, no modo específico como actua a acção específica de que é agente e transforma o objecto específico da sua intervenção ao modo como intervém. 

Tínhamos visto numa das sessões passadas de que forma é possível restabelecer a saúde no corpo humano por aquecimento através de uma fricção, τρίψις, (1132b26). O corpo humano é δυνάμει κινητόν, é susceptível de uma mutação, neste caso de temperatura. O quadro geral diz que a temperatura tem de ser homogeneizada, τὸ ὁμαλυνθῆναι (1032b19). Tal é obtido se o corpo humano vier a ser aquecido, εἰ θερμανθήσεται, (b20). O agente do aquecimento do corpo não é a percussão nem o aumento da temperatura ambiente (entrar num sauna, ligar o aquecimento), mas altamente específico: é uma fricção. No momento em que se compreende o corpo como susceptível de aquecer através de uma fricção, descobre-se uma possibilidade de alteração do seu estado de um determinado modo: ὑπάρχει δὲ τοδὶ δυνάμει· τοῦτο δὲ ἤδη ἐπ’ αὐτῷ (b20-21). A τρίψις realiza essa possibilidade. É o princípio da mudança que altera a doença em saúde: τὸ δὴ ποιοῦν καὶ ὅθεν ἄρχεται ἡ κίνησις τοῦ ὑγιαίνειν (b21-22). Ou seja, a τρίψις, fricção, é uma forma de θίξις, tal como o emagrecimento, a aprendizagem, o amadurecimento, o crescimento, o envelhecimento, etc., etc.: mutatis mutandis. 

É por essa razão que a mudança não apenas acciona o mutável mas actualiza-o, fá-lo ser  na acção específica que nele é accionada:  διὸ ἡ κίνησις ἐντελέχεια τοῦ κινητοῦ, ᾗ κινητόν, συμβαίνει δὲ τοῦτο θίξει τοῦ κινητικοῦ, ὥσθ’ ἅμα καὶ πάσχει. O agente da mudança transfere continuamente a forma específica para o que pode mudar: εἶδος δὲ ἀεὶ οἴσεταί τι τὸ κινοῦν. Isto é, “põe-no em forma” quando não a tinha adquirido ou a penas a tinha na possibilidade. O agente transforma o mutável em qualquer coisa aqui mesmo que passa a ser deste modo e desta maneira a ter este tamanho: ἤτοι τό εἶδος ἢ τοιόνδε ἢ τοσόνδε, é o princípio e a causa da mudança no momento em que muda, actua como o agente da mudança: ὃ ἔσται ἀρχὴ καὶ αἴτιον τῆς κινήσεως, ὅταν κινῇ. É assim que o homem que existe completamente acabado faz um homem concreto a partir do homem na possibilidade (Phys. 202a5-12).

Themistius, in Aristotelis Physica Paraphrasis: 

ἐπὶ τὸν ὁρισμὸν

τῆς κινήσεως. ὅταν δή τι ἄλλο ὂν ἐνεργείᾳ δυνάμει ἄλλο ᾖ, ἡ ἐνέργεια @1

(71.) αὐτοῦ, ἣ καθὸ δυνάμει ἐστί, κίνησίς ἐστιν· οὐδὲν γὰρ ἁπλῶς δυνάμει ὂν

μόνον, ἐνεργείᾳ δὲ οὐδὲν ἂν κινηθείη ποτ’ ἄν. διὰ τοῦτο οὐδὲ ἡ ὕλη

κινεῖται καθ’ ἑαυτήν, ὅτι μηδὲ ἔστι καθ’ ἑαυτὴν ἐνεργείᾳ. δεῖ οὖν ἐνερ-

γείᾳ τι εἶναι καὶ ἐνεργεῖν οὐ καθό τί ἐστιν, ἀλλὰ καθὸ δύναται εἶναι ἄλλο

τι, λέγω δὲ τὸ ‘καθὸ δύναται’· τοῦτον τὸν τρόπον· ἔστι γὰρ ὁ χαλκὸς (5)

δυνάμει ἀνδριάς, ἀλλ’ ὅμως οὐχ ἡ τοῦ χαλκοῦ ἐντελέχεια, ᾗ χαλκός,

κίνησίς ἐστιν (ἠρεμεῖ γὰρ καθὸ χαλκός), ἀλλ’ ἡ τοῦ δυνάμει αὐτῷ προ-

σόντος, ὑπάρχει δὲ αὐτῷ δυνάμει τὸ ἀνδριάντι γενέσθαι, ἡ δὴ τούτου

ἐνέργεια κίνησίς ἐστιν. οὐδὲν δὲ κωλύει καθὸ μὲν χαλκός ἐστιν, ἠρεμεῖν,

καθὸ δὲ δυνάμει ἀνδριάς, κατὰ τοῦτο κινεῖσθαι· οὐ γὰρ ταὐτὸν ἁπλῶς (10)

χαλκῷ τε εἶναι καὶ δυνάμει ἀνδριάντι· ἦν γὰρ ἂν καὶ τῷ λόγῳ ταὐτόν,

νῦν δὲ ἕτερα ταῦτα κατὰ τὸν λόγον, εἰ καὶ κατὰ τὸ ὑποκείμενον ἕν. καὶ

τοῦτο δέδεικται μέν, οὐδὲν δὲ κωλύει καὶ νῦν ἔτι σαφέστερον ἐπιδεῖξαι.

οὐκ ἔστι ταὐτὸν τῷ λόγῳ σώματί τε εἶναι καὶ δύνασθαι ὑγιαίνειν ἢ καὶ

δύνασθαι νοσεῖν· τὸ μὲν γὰρ σῶμα ἓν καὶ ταὐτὸν ἑαυτῷ, τὸ δὲ δύνασθαι (15)

ὑγιαίνειν καὶ δύνασθαι νοσεῖν οὐ μόνον ἕτερα ἀλλήλων, ἀλλὰ καὶ ἐναντία·

καὶ γὰρ αἱ ἐνέργειαι αὐτῶν ἐναντίαι. εἰ δὲ ταὐτὸν ἦν τὸ σῶμα ταῖς δυνά-

μεσιν, ἦσαν ἂν αἱ αὐταὶ καὶ αἱ δυνάμεις ἀλλήλαις. πάλιν οὐκ ἔστι ταὐτὸν

τῷ λόγῳ χρώματί τε εἶναι καὶ ὁρατῷ εἶναι (χρῶμα μὲν γάρ ἐστι τὸ

κινητικὸν τοῦ κατ’ ἐνέργειαν διαφανοῦς, ὁρατὸν δὲ τὸ συμβεβηκὸς τῷ (20)

χρώματι ἢ ὃ οἷόν τε ὁραθῆναι † καὶ τὸ ὁρατόν) οὐδὲ μὴν ψόφῳ καὶ

ἀκουστῷ οὐδὲ δὴ θερμῷ καὶ ἁπτῷ· οὐδὲ ἁπλῶς τῷ κατ’ ἐνέργειαν ὄντι

τὰ δυνάμει αὐτῷ προσόντα.