Authors/Aristotle/posteriora/L/L2

Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10

Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19

Book 2

Latin	English
c1	Chapter 1
Τὰ ζητούμενά ἐστιν ἴσα τὸν ἀριθμὸν ὅσαπερ ἐπιστάμεθα. ζητοῦμεν δὲ τέτταρα, τὸ ὅτι, τὸ διότι, εἰ ἔστι, τί ↵ἐστιν.	Aristotle Posterior Analytics Book II 1 89b21 THE kinds of question we ask are as many as the kinds of things which we know. They are in fact four:-(1) whether the connexion of an attribute with a thing is a fact, (2) what is the reason of the connexion, (3) whether a thing exists, (4) What is the nature of the thing.
ὅταν μὲν γὰρ πότερον τόδε ἢ τόδε ζητῶμεν, εἰς ἀριθμὸν θέντες, οἷον πότερον ἐκλείπει ὁ ἥλιος ἢ οὔ, τὸ ὅτι ζητοῦμεν. σημεῖον δὲ τούτου• εὑρόντες γὰρ ὅτι ἐκλείπει πεπαύμεθα• καὶ ἐὰν ἐξ ἀρχῆς εἰδῶμεν ὅτι ἐκλείπει, οὐ ζητοῦμεν πότερον.	89b26 Thus, when our question concerns a complex of thing and attribute and we ask whether the thing is thus or otherwise qualified-whether, e.g. the sun suffers eclipse or not-then we are asking as to the fact of a connexion. That our inquiry ceases with the discovery that the sun does suffer eclipse is an indication of this; and if we know from the start that the sun suffers eclipse, we do not inquire whether it does so or not.
ὅταν δὲ εἰδῶμεν τὸ ὅτι, τὸ διότι ζητοῦμεν, οἷον ↵εἰδότες ὅτι ἐκλείπει καὶ ὅτι κινεῖται ἡ γῆ, τὸ διότι ἐκλείπει ἢ διότι κινεῖται ζητοῦμεν. ταῦτα μὲν οὖν οὕτως,	89b28 On the other hand, when we know the fact we ask the reason; as, for example, when we know that the sun is being eclipsed and that an earthquake is in progress, it is the reason of eclipse or earthquake into which we inquire. Where a complex is concerned, then, those are the two questions we ask;
ἔνια δ᾽ ἄλλον τρόπον ζητοῦμεν, οἷον εἰ ἔστιν ἢ μὴ ἔστι κένταυρος ἢ θεός• τὸ δ᾽ εἰ ἔστιν ἢ μὴ ἁπλῶς λέγω, ἀλλ᾽ οὐκ εἰ λευκὸς ἢ μή. γνόντες δὲ ὅτι ἔστι, τί ἐστι ζητοῦμεν, οἷον τί οὖν ἐστι θεός, ἢ ↵τί ἐστιν ἄνθρωπος;	89b32 but for some objects of inquiry we have a different kind of question to ask, such as whether there is or is not a centaur or a God. (By ‘is or is not’ I mean ‘is or is not, without further qualification’; as opposed to ‘is or is not [e.g.] white’.) On the other hand, when we have ascertained the thing’s existence, we inquire as to its nature, asking, for instance, ‘what, then, is God?’ or ‘what is man?’.
c2	Chapter 2
Ἃ μὲν οὖν ζητοῦμεν καὶ ἃ εὑρόντες ἴσμεν, ταῦτα καὶ τοσαῦτά ἐστιν.	2 These, then, are the four kinds of question we ask, and it is in the answers to these questions that our knowledge consists.
ζητοῦμεν δέ, ὅταν μὲν ζητῶμεν τὸ ὅτι ἢ τὸ εἰ ἔστιν ἁπλῶς, ἆρ᾽ ἔστι μέσον αὐτοῦ ἢ οὐκ ἔστιν• ὅταν δὲ γνόντες ἢ τὸ ὅτι ἢ εἰ ἔστιν, ἢ τὸ ἐπὶ μέρους ἢ τὸ ἁπλῶς, πάλιν [90a]τὸ διὰ τί ζητῶμεν ἢ τὸ τί ἐστι, τότε ζητοῦμεν τί τὸ μέσον.	89b38 Now when we ask whether a connexion is a fact, or whether a thing without qualification is, we are really asking whether the connexion or the thing has a ‘middle’; and when we have ascertained either that the connexion is a fact or that the thing is-i.e. ascertained either the partial or the unqualified being of the thing-and are proceeding to ask the reason of the connexion or the nature of the thing, then we are asking what the ‘middle’ is.
λέγω δὲ τὸ ὅτι ἔστιν ἐπὶ μέρους καὶ ἁπλῶς, ἐπὶ μέρους μέν, ἆρ᾽ ἐκλείπει ἡ σελήνη ἢ αὔξεται; εἰ γάρ ἐστι τὶ ἢ μὴ ἔστι τί, ἐν τοῖς τοιούτοις ζητοῦμεν• ἁπλῶς δ᾽, εἰ ἔστιν ↵ἢ μὴ σελήνη ἢ νύξ.	90a2 (By distinguishing the fact of the connexion and the existence of the thing as respectively the partial and the unqualified being of the thing, I mean that if we ask ‘does the moon suffer eclipse?’, or ‘does the moon wax?’, the question concerns a part of the thing’s being; for what we are asking in such questions is whether a thing is this or that, i.e. has or has not this or that attribute: whereas, if we ask whether the moon or night exists, the question concerns the unqualified being of a thing.)
συμβαίνει ἄρα ἐν ἁπάσαις ταῖς ζητήσεσι ζητεῖν ἢ εἰ ἔστι μέσον ἢ τί ἐστι τὸ μέσον. τὸ μὲν γὰρ αἴτιον τὸ μέσον, ἐν ἅπασι δὲ τοῦτο ζητεῖται. ἆρ᾽ ἐκλείπει; ἆρ᾽ ἔστι τι αἴτιον ἢ οὔ; μετὰ ταῦτα γνόντες ὅτι ἔστι τι, τί οὖν τοῦτ᾽ ἔστι ζητοῦμεν. τὸ γὰρ αἴτιον τοῦ εἶναι μὴ ↵τοδὶ ἢ τοδὶ ἀλλ᾽ ἁπλῶς τὴν οὐσίαν, ἢ τοῦ μὴ ἁπλῶς ἀλλά 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; 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 συμφωνία; λόγος ἀριθμῶν ἐν ὀξεῖ καὶ βαρεῖ. διὰ τί συμφω↵νεῖ τὸ ὀξὺ τῶι βαρεῖ; διὰ τὸ λόγον ἔχειν ἀριθμῶν τὸ ὀξὺ καὶ τὸ βαρύ. ἆρ᾽ ἔστι συμφωνεῖν τὸ ὀξὺ καὶ τὸ βαρύ; ἆρ᾽ ἐστὶν ἐν ἀριθμοῖς ὁ λόγος αὐτῶν; λαβόντες δ᾽ ὅτι ἔστι, τίς οὖν ἐστιν ὁ λόγος;	90a5 We conclude that in all our inquiries we are asking either whether there is a ‘middle’ or what the ‘middle’ is: for the ‘middle’ here is precisely the cause, and it is the cause that we seek in all our inquiries. Thus, ‘Does the moon suffer eclipse?’ means ‘Is there or is there not a cause producing eclipse of the moon?’, and when we have learnt that there is, our next question is, ‘What, then, is this cause? for the cause through which a thing is-not is this or that, i.e. has this or that attribute, but without qualification is-and the cause through which it is-not is without qualification, but is this or that as having some essential attribute or some accident-are both alike the middle’. By that which is without qualification I mean the subject, e.g. moon or earth or sun or triangle; by that which a subject is (in the partial sense) I mean a property, e.g. eclipse, equality or inequality, interposition or non-interposition. For in all these examples it is clear that the nature of the thing and the reason of the fact are identical: the question 'What is eclipse?' and its answer 'The privation of the moon's light by the interposition of the earth' are identical with the question 'What is the reason of eclipse?' or 'Why does the moon suffer eclipse?' and the reply 'Because of the failure of light through the earth's shutting it out'. Again, for 'What is a concord? A commensurate numerical ratio of a high and a low note', we may substitute 'What ratio makes a high and a low note concordant? Their relation according to a commensurate numerical ratio.' 'Are the high and the low note concordant?' is equivalent to 'Is their ratio commensurate?'; and when we find that it is commensurate, we ask 'What, then, is their ratio?'. Cases in which the 'middle' is sensible show that the object of our inquiry is always the 'middle': we inquire, because we have not perceived it, whether there is or is not a 'middle' causing, e.g. an eclipse. On the other hand, if we were on the moon we should not be inquiring either as to the fact or the reason, but both fact and reason would be obvious simultaneously. For the act of perception would have enabled us to know the universal too; since, the present fact of an eclipse being evident, perception would then at the same time give us the present fact of the earth's screening the sun's light, and from this would arise the universal.
Ὅτι δ᾽ ἐστὶ τοῦ μέσου ἡ ζήτησις, δηλοῖ ὅσων τὸ μέ↵σον αἰσθητόν. ζητοῦμεν γὰρ μὴ ἠισθημένοι, οἷον τῆς ἐκλείψεως, εἰ ἔστιν ἢ μή. εἰ δ᾽ ἦμεν ἐπὶ τῆς σελήνης, οὐκ ἂν ἐζητοῦμεν οὔτ᾽ εἰ γίνεται οὔτε διὰ τί, ἀλλ᾽ ἅμα δῆλον ἂν ἦν. ἐκ γὰρ τοῦ αἰσθέσθαι καὶ τὸ καθόλου ἐγένετο ἂν ἡμῖν εἰδέναι. ἡ μὲν γὰρ αἴσθησις ὅτι νῦν ἀντιφράττει (καὶ γὰρ δῆ↵λον ὅτι νῦν ἐκλείπει)• ἐκ δὲ τούτου τὸ καθόλου ἂν ἐγένετο. Ὥσπερ οὖν λέγομεν, τὸ τί ἐστιν εἰδέναι ταὐτό ἐστι καὶ διὰ τί ἔστιν, τοῦτο δ᾽ ἢ ἁπλῶς καὶ μὴ τῶν ὑπαρχόντων τι, ἢ τῶν ὑπαρχόντων, οἷον ὅτι δύο ὀρθαί, ἢ ὅτι μεῖζον ἢ ἔλαττον.	90a24 Cases in which the ‘middle’ is sensible show that the object of our inquiry is always the ‘middle’: we inquire, because we have not perceived it, whether there is or is not a ‘middle’ causing, e.g. an eclipse. On the other hand, if we were on the moon we should not be inquiring either as to the fact or the reason, but both fact and reason would be obvious simultaneously. For the act of perception would have enabled us to know the universal too; since, the present fact of an eclipse being evident, perception would then at the same time give us the present fact of the earth’s screening the sun’s light, and from this would arise the universal. Thus, as we maintain, to know a thing’s nature is to know the reason why it is; and this is equally true of things in so far as they are said without qualification to he as opposed to being possessed of some attribute, and in so far as they are said to be possessed of some attribute such as equal to right angles, or greater or less.
c3	Chapter 3
Ὅτι μὲν οὖν πάντα τὰ ζητούμενα μέσου ζήτησίς ἐστι, δῆλον•	3 It is clear, then, that all questions are a search for a 'middle'.
πῶς δὲ τὸ τί ἐστι δείκνυται, καὶ τίς ὁ τρόπος τῆς ἀναγωγῆς, καὶ τί ἐστιν ὁρισμὸς καὶ τίνων, εἴπωμεν, διαπορήσαντες πρῶτον περὶ αὐτῶν. ἀρχὴ δ᾽ ἔστω τῶν μελλόντων	90a36 Let us now state how essential nature is revealed and in what way it can be reduced to demonstration; what definition is, and what things are definable. And let us first discuss certain difficulties which these questions raise,
[90b]ἥπερ ἐστὶν οἰκειοτάτη τῶν ἐχομένων λόγων. ἀπορήσειε γὰρ ἄν τις, ἆρ᾽ ἔστι τὸ αὐτὸ καὶ κατὰ τὸ αὐτὸ ὁρισμῶι εἰδέναι καὶ ἀποδείξει, ἢ ἀδύνατον;	90b1 beginning what we have to say with a point most intimately connected with our immediately preceding remarks, namely the doubt that might be felt as to whether or not it is possible to know the same thing in the same relation, both by definition and by demonstration.
ὁ μὲν γὰρ ὁρισμὸς τοῦ τί ἐστιν εἶναι δοκεῖ, τὸ δὲ τί ἐστιν ἅπαν καθόλου καὶ κατηγορικόν• ↵συλλογισμοὶ δ᾽ εἰσὶν οἱ μὲν στερητικοί, οἱ δ᾽ οὐ καθόλου, οἷον οἱ μὲν ἐν τῶι δευτέρωι σχήματι στερητικοὶ πάντες, οἱ δ᾽ ἐν τῶι τρίτωι οὐ καθόλου.	90b3 It might, I mean, be urged that definition is held to concern essential nature and is in every case universal and affirmative; whereas, on the other hand, some conclusions are negative and some are not universal; e.g. all in the second figure are negative, none in the third are universal.
εἶτα οὐδὲ τῶν ἐν τῶι πρώτωι σχήματι κατηγορικῶν ἁπάντων ἔστιν ὁρισμός, οἷον ὅτι πᾶν τρίγωνον δυσὶν ὀρθαῖς ἴσας ἔχει. τούτου δὲ λόγος, ὅτι τὸ ἐπί↵στασθαί ἐστι τὸ ἀποδεικτὸν τὸ ἀπόδειξιν ἔχειν, ὥστ᾽ ἐπεὶ τῶν τοιούτων ἀπόδειξις ἔστι, δῆλον ὅτι οὐκ ἂν εἴη αὐτῶν καὶ ὁρισμός• ἐπίσταιτο γὰρ ἄν τις καὶ κατὰ τὸν ὁρισμόν, οὐκ ἔχων τὴν ἀπόδειξιν• οὐδὲν γὰρ κωλύει μὴ ἅμα ἔχειν.	90b7 And again, not even all affirmative conclusions in the first figure are definable, e.g. ‘every triangle has its angles equal to two right angles’. An argument proving this difference between demonstration and definition is that to have scientific knowledge of the demonstrable is identical with possessing a demonstration of it: hence if demonstration of such conclusions as these is possible, there clearly cannot also be definition of them. If there could, one might know such a conclusion also in virtue of its definition without possessing the demonstration of it; for there is nothing to stop our having the one without the other.
ἱκανὴ δὲ πίστις καὶ ἐκ τῆς ἐπαγωγῆς• οὐδὲν γὰρ πώποτε ὁρισά↵μενοι ἔγνωμεν, οὔτε τῶν καθ᾽ αὑτὸ ὑπαρχόντων οὔτε τῶν συμβεβηκότων.	90b14 Induction too will sufficiently convince us of this difference; for never yet by defining anything-essential attribute or accident-did we get knowledge of it.
ἔτι εἰ ὁ ὁρισμὸς οὐσίας τινὸς γνωρισμός, τά γε τοιαῦτα φανερὸν ὅτι οὐκ οὐσίαι.	90b16 Again, if to define is to acquire knowledge of a substance, at any rate such attributes are not substances. It is evident, then, that not everything demonstrable can be defined.
Ὅτι μὲν οὖν οὐκ ἔστιν ὁρισμὸς ἅπαντος οὗπερ καὶ ἀπόδειξις, δῆλον. τί δαί, οὗ ὁρισμός, ἆρα παντὸς ἀπόδειξις ἔστιν ↵ἢ οὔ; εἷς μὲν δὴ λόγος καὶ περὶ τούτου ὁ αὐτός. τοῦ γὰρ ἑνός, ἧι ἕν, μία ἐπιστήμη. ὥστ᾽ εἴπερ τὸ ἐπίστασθαι τὸ ἀποδεικτόν ἐστι τὸ τὴν ἀπόδειξιν ἔχειν, συμβήσεταί τι ἀδύνατον• ὁ γὰρ τὸν ὁρισμὸν ἔχων ἄνευ τῆς ἀποδείξεως ἐπιστήσε↵ται.	90b19 What then? Can everything definable be demonstrated, or not? There is one of our previous arguments which covers this too. Of a single thing qua single there is a single scientific knowledge. Hence, since to know the demonstrable scientifically is to possess the demonstration of it, an impossible consequence will follow:-possession of its definition without its demonstration will give knowledge of the demonstrable.
ἔτι αἱ ἀρχαὶ τῶν ἀποδείξεων ὁρισμοί, ὧν ὅτι οὐκ ἔσονται ἀποδείξεις δέδεικται πρότερον – ἢ ἔσονται αἱ ἀρχαὶ ἀπο- δεικταὶ καὶ τῶν ἀρχῶν ἀρχαί, καὶ τοῦτ᾽ εἰς ἄπειρον βαδιεῖται, ἢ τὰ πρῶτα ὁρισμοὶ ἔσονται ἀναπόδεικτοι.	90b23 Moreover, the basic premisses of demonstrations are definitions, and it has already been shown that these will be found indemonstrable; either the basic premisses will be demonstrable and will depend on prior premisses, and the regress will be endless; or the primary truths will be indemonstrable definitions.
Ἀλλ᾽ ἆρα, εἰ μὴ παντὸς τοῦ αὐτοῦ, ἀλλὰ τινὸς τοῦ αὐτοῦ ἔστιν ὁρισμὸς καὶ ἀπόδειξις; ἢ ἀδύνατον; οὐ γὰρ ἔστιν ↵ἀπόδειξις οὗ ὁρισμός. ὁρισμὸς μὲν γὰρ τοῦ τί ἐστι καὶ οὐσίας• αἱ δ᾽ ἀποδείξεις φαίνονται πᾶσαι ὑποτιθέμεναι καὶ λαμβάνουσαι τὸ τί ἐστιν, οἷον αἱ μαθηματικαὶ τί μονὰς καὶ τί τὸ περιττόν, καὶ αἱ ἄλλαι ὁμοίως.	90b28 But if the definable and the demonstrable are not wholly the same, may they yet be partially the same? Or is that impossible, because there can be no demonstration of the definable? There can be none, because definition is of the essential nature or being of something, and all demonstrations evidently posit and assume the essential nature-mathematical demonstrations, for example, the nature of unity and the odd, and all the other sciences likewise.
ἔτι πᾶσα ἀπόδειξις τὶ κατὰ τινὸς δείκνυσιν, οἷον ὅτι ἔστιν ἢ οὐκ ἔστιν• ἐν δὲ τῶι ↵ὁρισμῶι οὐδὲν ἕτερον ἑτέρου κατηγορεῖται, οἷον οὔτε τὸ ζῶιον κατὰ τοῦ δίποδος οὔτε τοῦτο κατὰ τοῦ ζώιου, οὐδὲ δὴ κατὰ τοῦ ἐπιπέδου τὸ σχῆμα• οὐ γάρ ἐστι τὸ ἐπίπεδον σχῆμα, οὐδὲ τὸ σχῆμα ἐπίπεδον.	90b33 Moreover, every demonstration proves a predicate of a subject as attaching or as not attaching to it, but in definition one thing is not predicated of another; we do not, e.g. predicate animal of biped nor biped of animal, nor yet figure of plane-plane not being figure nor figure plane.
ἔτι ἕτερον τὸ τί ἐστι καὶ ὅτι ἔστι δεῖξαι. [91a]ὁ μὲν οὖν ὁρισμὸς τί ἐστι δηλοῖ, ἡ δὲ ἀπόδειξις ὅτι ἔστι τόδε κατὰ τοῦδε ἢ οὐκ ἔστιν. ἑτέρου δὲ ἑτέρα ἀπόδειξις, ἐὰν μὴ ὡς μέρος ἦι τι τῆς ὅλης. τοῦτο δὲ λέγω, ὅτι δέδεικται τὸ ἰσοσκελὲς δύο ὀρθαί, εἰ πᾶν τρίγωνον δέδεικται• μέρος ↵γάρ, τὸ δ᾽ ὅλον. ταῦτα δὲ πρὸς ἄλληλα οὐκ ἔχει οὕτως, τὸ ὅτι ἔστι καὶ τί ἐστιν• οὐ γάρ ἐστι θατέρου θάτερον μέρος. Φανερὸν ἄρα ὅτι οὔτε οὗ ὁρισμός, τούτου παντὸς ἀπόδειξις, οὔτε οὗ ἀπόδειξις, τούτου παντὸς ὁρισμός, οὔτε ὅλως τοῦ αὐτοῦ οὐδενὸς ἐνδέχεται ἄμφω ἔχειν. ὥστε δῆλον ὡς οὐδὲ ↵ὁρισμὸς καὶ ἀπόδειξις οὔτε τὸ αὐτὸ ἂν εἴη οὔτε θάτερον ἐν θατέρωι• καὶ γὰρ ἂν τὰ ὑποκείμενα ὁμοίως εἶχεν.	90b38 Again, to prove essential nature is not the same as to prove the fact of a connexion. Now definition reveals essential nature, demonstration reveals that a given attribute attaches or does not attach to a given subject; but different things require different demonstrations-unless the one demonstration is related to the other as part to whole. I add this because if all triangles have been proved to possess angles equal to two right angles, then this attribute has been proved to attach to isosceles; for isosceles is a part of which all triangles constitute the whole. But in the case before us the fact and the essential nature are not so related to one another, since the one is not a part of the other. So it emerges that not all the definable is demonstrable nor all the demonstrable definable; and we may draw the general conclusion that there is no identical object of which it is possible to possess both a definition and a demonstration. It follows obviously that definition and demonstration are neither identical nor contained either within the other: if they were, their objects would be related either as identical or as whole and part.
c4	Chapter 4
Ταῦτα μὲν οὖν μέχρι τούτου διηπορήσθω• τοῦ δὲ τί ἐστι πότερον ἔστι συλλογισμὸς καὶ ἀπόδειξις ἢ οὐκ ἔστι, καθάπερ νῦν ὁ λόγος ὑπέθετο;	4 91a12 So much, then, for the first stage of our problem. The next step is to raise the question whether syllogism-i.e. demonstration-of the definable nature is possible or, as our recent argument assumed, impossible.
ὁ μὲν γὰρ συλλογισμὸς τὶ κατὰ ↵τινὸς δείκνυσι διὰ τοῦ μέσου• τὸ δὲ τί ἐστιν ἴδιόν τε, καὶ ἐν τῶι τί ἐστι κατηγορεῖται. ταῦτα δ᾽ ἀνάγκη ἀντιστρέφειν.	91a14 We might argue it impossible on the following grounds:-(a) syllogism proves an attribute of a subject through the middle term; on the other hand (b) its definable nature is both ‘peculiar’ to a subject and predicated of it as belonging to its essence. But in that case (1) the subject, its definition, and the middle term connecting them must be reciprocally predicable of one another;
εἰ γὰρ τὸ Α τοῦ Γ ἴδιον, δῆλον ὅτι καὶ τοῦ Β καὶ τοῦτο τοῦ Γ, ὥστε πάντα ἀλλήλων.	91a18 for if A is to C, obviously A is ‘peculiar’ to B and B to C-in fact all three terms are ‘peculiar’ to one another:
ἀλλὰ μὴν καὶ εἰ τὸ Α ἐν τῶι τί ἐστιν ὑπάρχει παντὶ τῶι Β, καὶ καθόλου τὸ Β παντὸς τοῦ Γ ἐν ↵τῶι τί ἐστι λέγεται, ἀνάγκη καὶ τὸ Α ἐν τῶι τί ἐστι τοῦ Γ λέγεσθαι.	91a19 and further (2) if A inheres in the essence of all B and B is predicated universally of all C as belonging to C’s essence, A also must be predicated of C as belonging to its essence.
εἰ δὲ μὴ οὕτω τις λήψεται διπλώσας, οὐκ ἀνάγκη ἔσται τὸ Α τοῦ Γ κατηγορεῖσθαι ἐν τῶι τί ἐστιν, εἰ τὸ μὲν Α τοῦ Β ἐν τῶι τί ἐστι, μὴ καθ᾽ ὅσων δὲ τὸ Β, ἐν τῶι τί ἐστιν. τὸ δὲ τί ἐστιν ἄμφω ταῦτα ἕξει• ἔσται ἄρα καὶ τὸ Β κατὰ ↵τοῦ Γ τὸ τί ἐστιν.	91a22 If one does not take this relation as thus duplicated-if, that is, A is predicated as being of the essence of B, but B is not of the essence of the subjects of which it is predicated-A will not necessarily be predicated of C as belonging to its essence. So both premisses will predicate essence, and consequently B also will be predicated of C as its essence.
εἰ δὴ τὸ τί ἐστι καὶ τὸ τί ἦν εἶναι ἄμφω ἔχει, ἐπὶ τοῦ μέσου ἔσται πρότερον τὸ τί ἦν εἶναι.	91a25 Since, therefore, both premisses do predicate essence-i.e. definable form-C’s definable form will appear in the middle term before the conclusion is drawn.
ὅλως τε, εἰ ἔστι δεῖξαι τί ἐστιν ἄνθρωπος, ἔστω τὸ Γ ἄνθρωπος, τὸ δὲ Α τὸ τί ἐστιν, εἴτε ζῶιον δίπουν εἴτ᾽ ἄλλο τι. εἰ τοίνυν συλλογιεῖται, ἀνάγκη κατὰ τοῦ Β τὸ Α παντὸς κατηγορεῖσθαι. ↵τοῦτο δ᾽ ἔσται ἄλλος λόγος μέσος, ὥστε καὶ τοῦτο ἔσται τί ἐστιν ἄνθρωπος. λαμβάνει οὖν ὁ δεῖ δεῖξαι• καὶ γὰρ τὸ Β ἔσται τί ἐστιν ἄνθρωπος.	91a28 We may generalize by supposing that it is possible to prove the essential nature of man. Let C be man, A man’s essential nature — two-footed animal, or aught else it may be. Then, if we are to syllogize, A must be predicated of all B. But this premiss will be mediated by a fresh definition, which consequently will also be the essential nature of man. Therefore the argument assumes what it has to prove, since B too is the essential nature of man.
Δεῖ δ᾽ ἐν ταῖς δυσὶ προτάσεσι καὶ τοῖς πρώτοις καὶ ἀμέσοις σκοπεῖν• μάλιστα γὰρ φανερὸν τὸ λεγόμενον γίνε↵ται.	91a32 It is, however, the case in which there are only the two premisses-i.e. in which the premisses are primary and immediate-which we ought to investigate, because it best illustrates the point under discussion.
οἱ μὲν οὖν διὰ τοῦ ἀντιστρέφειν δεικνύντες τί ἐστι ψυχή, ἢ τί ἐστιν ἄνθρωπος ἢ ἄλλο ὁτιοῦν τῶν ὄντων, τὸ ἐξ ἀρχῆς αἰτοῦνται, οἷον εἴ τις ἀξιώσειε ψυχὴν εἶναι τὸ αὐτὸ αὑτῶι αἴτιον τοῦ ζῆν, τοῦτο δ᾽ ἀριθμὸν αὐτὸν αὑτὸν κινοῦντα• ἀνάγκη γὰρ αἰτῆσαι τὴν ψυχὴν ὅπερ ἀριθμὸν εἶναι αὐτὸν αὑτὸν κι[91b]νοῦντα, οὕτως ὡς τὸ αὐτὸ ὄν.	91a35 Thus they who prove the essential nature of soul or man or anything else through reciprocating terms beg the question. It would be begging the question, for example, to contend that the soul is that which causes its own life, and that what causes its own life is a self-moving number; for one would have to postulate that the soul is a self-moving number in the sense of being identical with it.
οὐ γὰρ εἰ ἀκολουθεῖ τὸ Α τῶι Β καὶ τοῦτο τῶι Γ, ἔσται τῶι Γ τὸ Α τὸ τί ἦν εἶναι, ἀλλ᾽ ἀληθὲς εἰπεῖν ἔσται μόνον• οὐδ᾽ εἰ ἔστι τὸ Α ὅπερ τι καὶ κατὰ τοῦ Β κατηγορεῖται παντός. καὶ γὰρ τὸ ζώιωι εἶ↵ναι κατηγορεῖται κατὰ τοῦ ἀνθρώπωι εἶναι (ἀληθὲς γὰρ πᾶν τὸ ἀνθρώπωι εἶναι ζώιωι εἶναι, ὥσπερ καὶ πάντα ἄνθρωπον ζῶιον), ἀλλ᾽ οὐχ οὕτως ὥστε ἓν εἶναι. ἐὰν μὲν οὖν μὴ οὕτω λάβηι, οὐ συλλογιεῖται ὅτι τὸ Α ἐστὶ τῶι Γ τὸ τί ἦν εἶναι καὶ ἡ οὐσία• ἐὰν δὲ οὕτω λάβηι, πρότερον ἔσται εἰληφὼς τῶι ↵Γ τί ἐστι τὸ τί ἦν εἶναι [τὸ Β]. ὥστ᾽ οὐκ ἀποδέδεικται• τὸ γὰρ ἐν ἀρχῆι εἴληφεν.	91b1 For if A is predicable as a mere consequent of B and B of C, A will not on that account be the definable form of C: A will merely be what it was true to say of C. Even if A is predicated of all B inasmuch as B is identical with a species of A, still it will not follow: being an animal is predicated of being a man-since it is true that in all instances to be human is to be animal, just as it is also true that every man is an animal-but not as identical with being man. We conclude, then, that unless one takes both the premisses as predicating essence, one cannot infer that A is the definable form and essence of C: but if one does so take them, in assuming B one will have assumed, before drawing the conclusion, what the definable form of C is; so that there has been no inference, for one has begged the question.
c5	Chapter 5
Ἀλλὰ μὴν οὐδ᾽ ἡ διὰ τῶν διαιρέσεων ὁδὸς συλλογίζεται, καθάπερ ἐν τῆι ἀναλύσει τῆι περὶ τὰ σχήματα εἴρηται. οὐδαμοῦ γὰρ ἀνάγκη γίνεται τὸ πρᾶγμα ἐκεῖνο εἶναι ↵τωνδὶ ὄντων, ἀλλ᾽ ὥσπερ οὐδ᾽ ὁ ἐπάγων ἀποδείκνυσιν. οὐ γὰρ δεῖ τὸ συμπέρασμα ἐρωτᾶν, οὐδὲ τῶι δοῦναι εἶναι, ἀλλ᾽ ἀνάγκη εἶναι ἐκείνων ὄντων, κἂν μὴ φῆι ὁ ἀποκρινόμενος. ἆρ᾽ ὁ ἄνθρωπος ζῶιον ἢ ἄψυχον; εἶτ᾽ ἔλαβε ζῶιον, οὐ συλλελόγισται. πάλιν ἅπαν ζῶιον ἢ πεζὸν ἢ ἔνυδρον• ἔλαβε ↵πεζόν. καὶ τὸ εἶναι τὸν ἄνθρωπον τὸ ὅλον, ζῶιον πεζόν, οὐκ ἀνάγκη ἐκ τῶν εἰρημένων, ἀλλὰ λαμβάνει καὶ τοῦτο. διαφέρει δ᾽ οὐδὲν ἐπὶ πολλῶν ἢ ὀλίγων οὕτω ποιεῖν• τὸ αὐτὸ γάρ ἐστιν. (ἀσυλλόγιστος μὲν οὖν καὶ ἡ χρῆσις γίνεται τοῖς οὕτω μετιοῦσι καὶ τῶν ἐνδεχομένων συλλογισθῆναι.)	5 91b12 Nor, as was said in my formal logic, is the method of division a process of inference at all, since at no point does the characterization of the subject follow necessarily from the premising of certain other facts: division demonstrates as little as does induction. For in a genuine demonstration the conclusion must not be put as a question nor depend on a concession, but must follow necessarily from its premisses, even if the respondent deny it. The definer asks ‘Is man animal or inanimate?’ and then assumes-he has not inferred-that man is animal. Next, when presented with an exhaustive division of animal into terrestrial and aquatic, he assumes that man is terrestrial. Moreover, that man is the complete formula, terrestrial-animal, does not follow necessarily from the premisses: this too is an assumption, and equally an assumption whether the division comprises many differentiae or few. (Indeed as this method of division is used by those who proceed by it, even truths that can be inferred actually fail to appear as such.)
τί γὰρ ↵κωλύει τοῦτο ἀληθὲς μὲν τὸ πᾶν εἶναι κατὰ τοῦ ἀνθρώπου, μὴ μέντοι τὸ τί ἐστι μηδὲ τὸ τί ἦν εἶναι δηλοῦν;	91b25 For why should not the whole of this formula be true of man, and yet not exhibit his essential nature or definable form?
ἔτι τί κωλύει ἢ προσθεῖναί τι ἢ ἀφελεῖν ἢ ὑπερβεβηκέναι τῆς οὐσίας;	91b26 Again, what guarantee is there against an unessential addition, or against the omission of the final or of an intermediate determinant of the substantial being?
Ταῦτα μὲν οὖν παρίεται μέν, ἐνδέχεται δὲ λῦσαι τῶι λαμβάνειν ἐν τῶι τί ἐστι πάντα, καὶ τὸ ἐφεξῆς τῆι διαιρέσει ↵ποιεῖν, αἰτούμενον τὸ πρῶτον, καὶ μηδὲν παραλείπειν. τοῦτο δ᾽ ἀναγκαῖον, εἰ ἅπαν εἰς τὴν διαίρεσιν ἐμπίπτει καὶ μηδὲν ἐλλείπει• [τοῦτο δ᾽ ἀναγκαῖον,] ἄτομον γὰρ ἤδη δεῖ εἶναι. ἀλλὰ συλλογισμὸς ὅμως οὐκ ἔστι, ἀλλ᾽ εἴπερ, ἄλλον τρόπον γνωρίζειν ποιεῖ.	91b28 The champion of division might here urge that though these lapses do occur, yet we can solve that difficulty if all the attributes we assume are constituents of the definable form, and if, postulating the genus, we produce by division the requisite uninterrupted sequence of terms, and omit nothing; and that indeed we cannot fail to fulfil these conditions if what is to be divided falls whole into the division at each stage, and none of it is omitted; and that this-the dividendum-must without further question be (ultimately) incapable of fresh specific division.
καὶ τοῦτο μὲν οὐδὲν ἄτοπον• οὐδὲ γὰρ ὁ ἐπάγων ἴσως ἀποδείκνυσιν, ἀλλ᾽ ὅμως δηλοῖ τι. συλλογι↵σμὸν δ᾽ οὐ λέγει ὁ ἐκ τῆς διαιρέσεως λέγων τὸν ὁρισμόν. ὥσπερ γὰρ ἐν τοῖς συμπεράσμασι τοῖς ἄνευ τῶν μέσων, ἐάν τις εἴπηι ὅτι τούτων ὄντων ἀνάγκη τοδὶ εἶναι, ἐνδέχεται ἐρωτῆσαι διὰ τί, οὕτως καὶ ἐν τοῖς διαιρετικοῖς ὅροις. τί ἐστιν [92a]ἄνθρωπος; ζῶιον θνητόν, ὑπόπουν, δίπουν, ἄπτερον. διὰ τί, παρ᾽ ἑκάστην πρόσθεσιν; ἐρεῖ γάρ, καὶ δείξει τῆι διαιρέσει, ὡς οἴεται, ὅτι πᾶν ἢ θνητὸν ἢ ἀθάνατον. ὁ δὲ τοιοῦτος λόγος ἅπας οὐκ ἔστιν ὁρισμός, ὥστ᾽ εἰ καὶ ἀπεδείκνυτο τῆι διαι↵ρέσει, ἀλλ᾽ ὅ γ᾽ ὁρισμὸς οὐ συλλογισμὸς γίνεται.	91b33 Nevertheless, we reply, division does not involve inference; if it gives knowledge, it gives it in another way. Nor is there any absurdity in this: induction, perhaps, is not demonstration any more than is division, et it does make evident some truth. Yet to state a definition reached by division is not to state a conclusion: as, when conclusions are drawn without their appropriate middles, the alleged necessity by which the inference follows from the premisses is open to a question as to the reason for it, so definitions reached by division invite the same question. Thus to the question ‘What is the essential nature of man?’ the divider replies ‘Animal, mortal, footed, biped, wingless’; and when at each step he is asked ‘Why?’, he will say, and, as he thinks, proves by division, that all animal is mortal or immortal: but such a formula taken in its entirety is not definition; so that even if division does demonstrate its formula, definition at any rate does not turn out to be a conclusion of inference.
c6	Chapter 6
Ἀλλ᾽ ἆρα ἔστι καὶ ἀποδεῖξαι τὸ τί ἐστι κατ᾽ οὐσίαν, ἐξ ὑποθέσεως δέ, λαβόντα τὸ μὲν τί ἦν εἶναι τὸ ἐκ τῶν ἐν τῶι τί ἐστιν ἴδιον, ταδὶ δὲ ἐν τῶι τί ἐστι μόνα, καὶ ἴδιον τὸ πᾶν; τοῦτο γάρ ἐστι τὸ εἶναι ἐκείνωι.	6 92a6 Can we nevertheless actually demonstrate what a thing essentially and substantially is, but hypothetically, i.e. by premising (1) that its definable form is constituted by the ‘peculiar’ attributes of its essential nature; (2) that such and such are the only attributes of its essential nature, and that the complete synthesis of them is peculiar to the thing; and thus-since in this synthesis consists the being of the thing-obtaining our conclusion?
ἢ πάλιν εἴληφε τὸ τί ↵ἦν εἶναι καὶ ἐν τούτωι; ἀνάγκη γὰρ διὰ τοῦ μέσου δεῖξαι.	92a9 Or is the truth that, since proof must be through the middle term, the definable form is once more assumed in this minor premiss too?
ἔτι ὥσπερ οὐδ᾽ ἐν συλλογισμῶι λαμβάνεται τί ἐστι τὸ συλλελογίσθαι (ἀεὶ γὰρ ὅλη ἢ μέρος ἡ πρότασις, ἐξ ὧν ὁ συλλογισμόσ), οὕτως οὐδὲ τὸ τί ἦν εἶναι δεῖ ἐνεῖναι ἐν τῶι συλλογισμῶι, ἀλλὰ χωρὶς τοῦτο τῶν κειμένων εἶναι, καὶ πρὸς ↵τὸν ἀμφισβητοῦντα εἰ συλλελόγισται ἢ μή, τοῦτο ἀπαντᾶν ὅτι "τοῦτο γὰρ ἦν συλλογισμόσ", καὶ πρὸς τὸν ὅτι οὐ τὸ τί ἦν εἶναι συλλελόγισται, ὅτι "ναί• τοῦτο γὰρ ἔκειτο ἡμῖν τὸ τί ἦν εἶναι". ὥστε ἀνάγκη καὶ ἄνευ τοῦ τί συλλογισμὸς ἢ τὸ τί ἦν εἶναι συλλελογίσθαι τι.	92a12 Further, just as in syllogizing we do not premise what syllogistic inference is (since the premisses from which we conclude must be related as whole and part), so the definable form must not fall within the syllogism but remain outside the premisses posited. It is only against a doubt as to its having been a syllogistic inference at all that we have to defend our argument as conforming to the definition of syllogism. It is only when some one doubts whether the conclusion proved is the definable form that we have to defend it as conforming to the definition of definable form which we assumed. Hence syllogistic inference must be possible even without the express statement of what syllogism is or what definable form is.
↵Κἂν ἐξ ὑποθέσεως δὲ δεικνύηι, οἷον εἰ τὸ κακῶι ἐστὶ τὸ διαιρετῶι εἶναι, τὸ δ᾽ ἐναντίωι τὸ τῶι ἐναντίωι ‹ἐναντίωι› εἶναι, ὅσοις ἔστι τι ἐναντίον• τὸ δ᾽ ἀγαθὸν τῶι κακῶι ἐναντίον καὶ τὸ ἀδιαίρετον τῶι διαιρετῶι• ἔστιν ἄρα τὸ ἀγαθῶι εἶναι τὸ ἀδιαιρέτωι εἶναι.	92a20 The following type of hypothetical proof also begs the question. If evil is definable as the divisible, and the definition of a thing’s contrary-if it has one the contrary of the thing’s definition; then, if good is the contrary of evil and the indivisible of the divisible, we conclude that to be good is essentially to be indivisible.
καὶ γὰρ ἐνταῦθα λαβὼν τὸ τί ἦν εἶναι δείκνυσι• [?]	92a23 The question is begged because definable form is assumed as a premiss,
λαμ↵βάνει δ᾽ εἰς τὸ δεῖξαι τὸ τί ἦν εἶναι. "ἕτερον μέντοι". ἔστω• καὶ γὰρ ἐν ταῖς ἀποδείξεσιν, ὅτι ἐστὶ τόδε κατὰ τοῦδε• ἀλλὰ μὴ αὐτό, μηδὲ οὗ ὁ αὐτὸς λόγος, καὶ ἀντιστρέφει.	92a24 and as a premiss which is to prove definable form. ‘But not the same definable form’, you may object. That I admit, for in demonstrations also we premise that ‘this’ is predicable of ‘that’; but in this premiss the term we assert of the minor is neither the major itself nor a term identical in definition, or convertible, with the major.
πρὸς ἀμφοτέρους δέ, τόν τε κατὰ διαίρεσιν δεικνύντα καὶ πρὸς τὸν οὕτω συλλογισμόν, τὸ αὐτὸ ἀπόρημα• διὰ τί ἔσται ὁ ἄνθρω↵πος ζῶιον πεζὸν δίπουν, ἀλλ᾽ οὐ ζῶιον καὶ πεζόν ‹καὶ δίπουν›; ἐκ γὰρ τῶν λαμβανομένων οὐδεμία ἀνάγκη ἐστὶν ἓν γίνεσθαι τὸ κατηγορούμενον, ἀλλ᾽ ὥσπερ ἂν ἄνθρωπος ὁ αὐτὸς εἴη μουσικὸς καὶ γραμματικός.	92a28 Again, both proof by division and the syllogism just described are open to the question why man should be animal-biped-terrestrial and not merely animal and terrestrial, since what they premise does not ensure that the predicates shall constitute a genuine unity and not merely belong to a single subject as do musical and grammatical when predicated of the same man.
c7	Chapter 7
Πῶς οὖν δὴ ὁ ὁριζόμενος δείξει τὴν οὐσίαν ἢ τὸ τί ↵ἐστιν; οὔτε γὰρ ὡς ἀποδεικνὺς ἐξ ὁμολογουμένων εἶναι δῆλον ποιήσει ὅτι ἀνάγκη ἐκείνων ὄντων ἕτερόν τι εἶναι (ἀπόδειξις γὰρ τοῦτο), οὔθ᾽ ὡς ὁ ἐπάγων διὰ τῶν καθ᾽ ἕκαστα δήλων ὄντων, ὅτι πᾶν οὕτως τῶι μηδὲν ἄλλως• οὐ γὰρ τί [92b]ἐστι δείκνυσιν, ἀλλ᾽ ὅτι ἢ ἔστιν ἢ οὐκ ἔστιν. τίς οὖν ἄλλος τρό- πος λοιπός; οὐ γὰρ δὴ δείξει γε τῆι αἰσθήσει ἢ τῶι δακτύλωι.	7 92a34 How then by definition shall we prove substance or essential nature? We cannot show it as a fresh fact necessarily following from the assumption of premisses admitted to be facts-the method of demonstration: we may not proceed as by induction to establish a universal on the evidence of groups of particulars which offer no exception, because induction proves not what the essential nature of a thing is but that it has or has not some attribute. Therefore, since presumably one cannot prove essential nature by an appeal to sense perception or by pointing with the finger, what other method remains?
Ἔτι πῶς δείξει τὸ τί ἐστιν; ἀνάγκη γὰρ τὸν εἰδότα τὸ ↵τί ἐστιν ἄνθρωπος ἢ ἄλλο ὁτιοῦν, εἰδέναι καὶ ὅτι ἔστιν (τὸ γὰρ μὴ ὂν οὐδεὶς οἶδεν ὅ τι ἐστίν, ἀλλὰ τί μὲν σημαίνει ὁ λόγος ἢ τὸ ὄνομα, ὅταν εἴπω τραγέλαφος, τί δ᾽ ἐστὶ τραγέλαφος ἀδύνατον εἰδέναι).	92b3 To put it another way: how shall we by definition prove essential nature? He who knows what human-or any other-nature is, must know also that man exists; for no one knows the nature of what does not exist-one can know the meaning of the phrase or name ‘goat-stag’ but not what the essential nature of a goat-stag is.
ἀλλὰ μὴν εἰ δείξει τί ἐστι καὶ ὅτι ἔστι, πῶς τῶι αὐτῶι λόγωι δείξει; ὅ τε γὰρ ὁρισμὸς ἕν τι ↵δηλοῖ καὶ ἡ ἀπόδειξις• τὸ δὲ τί ἐστιν ἄνθρωπος καὶ τὸ εἶναι ἄνθρωπον ἄλλο.	92b7 But further, if definition can prove what is the essential nature of a thing, can it also prove that it exists? And how will it prove them both by the same process, since definition exhibits one single thing and demonstration another single thing, and what human nature is and the fact that man exists are not the same thing?
Εἶτα καὶ δι᾽ ἀποδείξεώς φαμεν ἀναγκαῖον εἶναι δείκνυσθαι ἅπαν ὅ τι ἐστίν, εἰ μὴ οὐσία εἴη. τὸ δ᾽ εἶναι οὐκ οὐσία οὐδενί• οὐ γὰρ γένος τὸ ὄν. ἀπόδειξις ἄρ᾽ ἔσται ὅτι ↵ἔστιν. ὅπερ καὶ νῦν ποιοῦσιν αἱ ἐπιστῆμαι. τί μὲν γὰρ σημαίνει τὸ τρίγωνον, ἔλαβεν ὁ γεωμέτρης, ὅτι δ᾽ ἔστι, δείκνυσιν. τί οὖν δείξει ὁ ὁριζόμενος ἢ τί ἐστι τὸ τρίγωνον; εἰδὼς ἄρα τις ὁρισμῶι τί ἐστιν, εἰ ἔστιν οὐκ εἴσεται. ἀλλ᾽ ἀδύνατον.	92b11 Then too we hold that it is by demonstration that the being of everything must be proved-unless indeed to be were its essence; and, since being is not a genus, it is not the essence of anything. Hence the being of anything as fact is matter for demonstration; and this is the actual procedure of the sciences, for the geometer assumes the meaning of the word triangle, but that it is possessed of some attribute he proves. What is it, then, that we shall prove in defining essential nature? Triangle? In that case a man will know by definition what a thing’s nature is without knowing whether it exists. But that is impossible.
Φανερὸν δὲ καὶ κατὰ τοὺς νῦν τρόπους τῶν ὅρων ὡς οὐ ↵δεικνύουσιν οἱ ὁριζόμενοι ὅτι ἔστιν. εἰ γὰρ καὶ ἔστιν ἐκ τοῦ μέσου τι ἴσον, ἀλλὰ διὰ τί ἔστι τὸ ὁρισθέν; καὶ διὰ τί τοῦτ᾽ ἔστι κύκλος; εἴη γὰρ ἂν καὶ ὀρειχάλκου φάναι εἶναι αὐτόν. οὔτε γὰρ ὅτι δυνατὸν εἶναι τὸ λεγόμενον προσδηλοῦσιν οἱ ὅροι, οὔτε ὅτι ἐκεῖνο οὗ φασὶν εἶναι ὁρισμοί, ἀλλ᾽ ἀεὶ ἔξεστι ↵λέγειν τὸ διὰ τί.	92b18 Moreover it is clear, if we consider the methods of defining actually in use, that definition does not prove that the thing defined exists: since even if there does actually exist something which is equidistant from a centre, yet why should the thing named in the definition exist? Why, in other words, should this be the formula defining circle? One might equally well call it the definition of mountain copper. For definitions do not carry a further guarantee that the thing defined can exist or that it is what they claim to define: one can always ask why.
Εἰ ἄρα ὁ ὁριζόμενος δείκνυσιν ἢ τί ἐστιν ἢ τί σημαίνει τοὔνομα, εἰ μὴ ἔστι μηδαμῶς τοῦ τί ἐστιν, εἴη ἂν ὁ ὁρισμὸς λόγος ὀνόματι τὸ αὐτὸ σημαίνων.	92b26 Since, therefore, to define is to prove either a thing’s essential nature or the meaning of its name, we may conclude that definition, if it in no sense proves essential nature, is a set of words signifying precisely what a name signifies.
ἀλλ᾽ ἄτοπον. πρῶτον μὲν γὰρ καὶ μὴ οὐσιῶν ἂν εἴη καὶ τῶν μὴ ὄντων• σημαίνειν ↵γὰρ ἔστι καὶ τὰ μὴ ὄντα.	92b28 But that were a strange consequence; for (1) both what is not substance and what does not exist at all would be definable, since even non-existents can be signified by a name:
ἔτι πάντες οἱ λόγοι ὁρισμοὶ ἂν εἶεν• εἴη γὰρ ἂν ὄνομα θέσθαι ὁποιωιοῦν λόγωι, ὥστε ὅρους ἂν διαλεγοίμεθα πάντες καὶ ἡ Ἰλιὰς ὁρισμὸς ἂν εἴη.	92b30 (2) all sets of words or sentences would be definitions, since any kind of sentence could be given a name; so that we should all be talking in definitions, and even the Iliad would be a definition:
ἔτι οὐδεμία ἀπόδειξις ἀποδείξειεν ἂν ὅτι τοῦτο τοὔνομα τουτὶ δηλοῖ• οὐδ᾽ οἱ ὁρισμοὶ τοίνυν τοῦτο προσδηλοῦσιν.	92b32 (3) no demonstration can prove that any particular name means any particular thing: neither, therefore, do definitions, in addition to revealing the meaning of a name, also reveal that the name has this meaning.
↵Ἐκ μὲν τοίνυν τούτων οὔτε ὁρισμὸς καὶ συλλογισμὸς φαίνεται ταὐτὸν ὄν, οὔτε ταὐτοῦ συλλογισμὸς καὶ ὁρισμός• πρὸς δὲ τούτοις, ὅτι οὔτε ὁ ὁρισμὸς οὐδὲν οὔτε ἀποδείκνυσιν οὔτε δείκνυσιν, οὔτε τὸ τί ἐστιν οὔθ᾽ ὁρισμῶι οὔτ᾽ ἀποδείξει ἔστι γνῶναι.	92b35 It appears then from these considerations that neither definition and syllogism nor their objects are identical, and further that definition neither demonstrates nor proves anything, and that knowledge of essential nature is not to be obtained either by definition or by demonstration.
c8	Chapter 8
[93a]Πάλιν δὲ σκεπτέον τί τούτων λέγεται καλῶς καὶ τί οὐ καλῶς, καὶ τί ἐστιν ὁ ὁρισμός, καὶ τοῦ τί ἐστιν ἆρά πως ἔστιν ἀπόδειξις καὶ ὁρισμὸς ἢ οὐδαμῶς.	8 93a1 We must now start afresh and consider which of these conclusions are sound and which are not, and what is the nature of definition, and whether essential nature is in any sense demonstrable and definable or in none.
ἐπεὶ δ᾽ ἐστίν, ὡς ἔφαμεν, ταὐτὸν τὸ εἰδέναι τί ἐστι καὶ τὸ εἰδέναι τὸ αἴτιον τοῦ εἰ ἔστι ↵(λόγος δὲ τούτου, ὅτι ἔστι τι τὸ αἴτιον, καὶ τοῦτο ἢ τὸ αὐτὸ ἢ ἄλλο, κἂν ἦι ἄλλο, ἢ ἀποδεικτὸν ἢ ἀναπόδεικτον) – εἰ τοίνυν ἐστὶν ἄλλο καὶ ἐνδέχεται ἀποδεῖξαι, ἀνάγκη μέσον εἶναι τὸ αἴτιον καὶ ἐν τῶι σχήματι τῶι πρώτωι δείκνυσθαι• καθόλου τε γὰρ καὶ κατηγορικὸν τὸ δεικνύμενον. εἷς μὲν δὴ ↵τρόπος ἂν εἴη ὁ νῦν ἐξητασμένος, τὸ δι᾽ ἄλλου του τί ἐστι δείκνυσθαι. τῶν τε γὰρ τί ἐστιν ἀνάγκη τὸ μέσον εἶναι τί ἐστι, καὶ τῶν ἰδίων ἴδιον. ὥστε τὸ μὲν δείξει, τὸ δ᾽ οὐ δείξει τῶν τί ἦν εἶναι τῶι αὐτῶι πράγματι. Οὗτος μὲν οὖν ὁ τρόπος ὅτι οὐκ ἂν εἴη ἀπόδειξις, εἴρηται ↵πρότερον• ἀλλ᾽ ἔστι λογικὸς συλλογισμὸς τοῦ τί ἐστιν.	93a4 Now to know its essential nature is, as we said, the same as to know the cause of a thing’s existence, and the proof of this depends on the fact that a thing must have a cause. Moreover, this cause is either identical with the essential nature of the thing or distinct from it; and if its cause is distinct from it, the essential nature of the thing is either demonstrable or indemonstrable. Consequently, if the cause is distinct from the thing’s essential nature and demonstration is possible, the cause must be the middle term, and, the conclusion proved being universal and affirmative, the proof is in the first figure. So the method just examined of proving it through another essential nature would be one way of proving essential nature, because a conclusion containing essential nature must be inferred through a middle which is an essential nature just as a ‘peculiar’ property must be inferred through a middle which is a ‘peculiar’ property; so that of the two definable natures of a single thing this method will prove one and not the other. Now it was said before that this method could not amount to demonstration of essential nature-it is actually a dialectical proof of it-
ὃν δὲ τρόπον ἐνδέχεται, λέγωμεν, εἰπόντες πάλιν ἐξ ἀρχῆς. ὥσπερ γὰρ τὸ διότι ζητοῦμεν ἔχοντες τὸ ὅτι, ἐνίοτε δὲ καὶ ἅμα δῆλα γίνεται, ἀλλ᾽ οὔτι πρότερόν γε τὸ διότι δυνατὸν γνωρίσαι τοῦ ὅτι, δῆλον ὅτι ὁμοίως καὶ τὸ τί ἦν εἶναι οὐκ ἄνευ τοῦ ↵ὅτι ἔστιν• ἀδύνατον γὰρ εἰδέναι τί ἐστιν, ἀγνοοῦντας εἰ ἔστιν.	93a16 so let us begin again and explain by what method it can be demonstrated. When we are aware of a fact we seek its reason, and though sometimes the fact and the reason dawn on us simultaneously, yet we cannot apprehend the reason a moment sooner than the fact; and clearly in just the same way we cannot apprehend a thing’s definable form without apprehending that it exists, since while we are ignorant whether it exists we cannot know its essential nature.
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 ἄνθρωπον, ὅτι ζῶιόν τι, καὶ ψυχήν, ὅτι αὐτὸ αὑτὸ κινοῦν.	93a21 Moreover we are aware whether a thing exists or not sometimes through apprehending an element in its character, and sometimes accidentally, as, for example, when we are aware of thunder as a noise in the clouds, of eclipse as a privation of light, or of man as some species of animal, or of the soul as a self-moving thing.
ὅσα μὲν ↵οὖν κατὰ συμβεβηκὸς οἴδαμεν ὅτι ἔστιν, ἀναγκαῖον μηδαμῶς 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.	93a24 As often as we have accidental knowledge that the thing exists, we must be in a wholly negative state as regards awareness of its essential nature; for we have not got genuine knowledge even of its existence, and to search for a thing’s essential nature when we are unaware that it exists is to search for nothing. On the other hand, whenever we apprehend an element in the thing’s character there is less difficulty. Thus it follows that the degree of our knowledge of a thing’s essential nature is determined by the sense in which we are aware that it exists.
ὧν οὖν ἔχομέν τι τοῦ τί ἐστιν, ἔστω πρῶτον μὲν ↵ὧδε• ἔκλειψις ἐφ᾽ οὗ τὸ Α, σελήνη ἐφ᾽ οὗ Γ, ἀντίφραξις γῆς ἐφ᾽ οὗ Β. τὸ μὲν οὖν πότερον ἐκλείπει ἢ οὔ, τὸ Β ζητεῖν 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 διότι ἴσμεν, ἂν δι᾽ ἀμέσων ἦι• εἰ δὲ μή, τὸ ὅτι, τὸ διότι δ᾽ οὔ. σελήνη Γ, ἔκλειψις Α, τὸ πανσελήνου σκιὰν μὴ δύνασθαι 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 ἐκλελοιπέναι, ὅτι μὲν ἐκλείπει δῆλον, διότι δ᾽ οὔπω, καὶ ὅτι μὲν ἔστιν ἔκλειψις ἴσμεν, τί δ᾽ ἐστὶν οὐκ ἴσμεν. δήλου δ᾽ ὄντος ὅτι τὸ Α τῶι Γ ὑπάρχει, ἀλλὰ διὰ τί ὑπάρχει, τὸ ζη↵τεῖν τὸ Β τί ἐστι, πότερον ἀντίφραξις ἢ στροφὴ τῆς σελήνης 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 βροντᾶ; διὰ τὸ ἀποσβέννυσθαι τὸ πῦρ ἐν τῶι νέφει. νέφος Γ, βροντὴ Α, ↵ἀπόσβεσις πυρὸς τὸ Β. τῶι δὴ Γ τῶι νέφει ὑπάρχει τὸ Β (ἀποσβέννυται γὰρ ἐν αὐτῶι τὸ πῦρ), τούτωι δὲ τὸ Α, ψόφος• καὶ ἔστι γε λόγος τὸ Β τοῦ Α τοῦ πρώτου ἄκρου. ἂν δὲ πάλιν τούτου ἄλλο μέσον ἦι, ἐκ τῶν παραλοίπων ἔσται λόγων.	93a28 Let us then take the following as our first instance of being aware of an element in the essential nature. Let A be eclipse, C the moon, B the earth’s acting as a screen. Now to ask whether the moon is eclipsed or not is to ask whether or not B has occurred. But that is precisely the same as asking whether A has a defining condition; and if this condition actually exists, we assert that A also actually exists. Or again we may ask which side of a contradiction the defining condition necessitates: does it make the angles of a triangle equal or not equal to two right angles? When we have found the answer, if the premisses are immediate, we know fact and reason together; if they are not immediate, we know the fact without the reason, as in the following example: let C be the moon, A eclipse, B the fact that the moon fails to produce shadows though she is full and though no visible body intervenes between us and her. Then if B, failure to produce shadows in spite of the absence of an intervening body, is attributable A to C, and eclipse, is attributable to B, it is clear that the moon is eclipsed, but the reason why is not yet clear, and we know that eclipse exists, but we do not know what its essential nature is. But when it is clear that A is attributable to C and we proceed to ask the reason of this fact, we are inquiring what is the nature of B: is it the earth's acting as a screen, or the moon's rotation or her extinction? But B is the definition of the other term, viz. in these examples, of the major term A; for eclipse is constituted by the earth acting as a screen. Thus, (1) 'What is thunder?' 'The quenching of fire in cloud', and (2) 'Why does it thunder?' 'Because fire is quenched in the cloud', are equivalent. Let C be cloud, A thunder, B the quenching of fire. Then B is attributable to C, cloud, since fire is quenched in it; and A, noise, is attributable to B; and B is assuredly the definition of the major term A. If there be a further mediating cause of B, it will be one of the remaining partial definitions of A.
↵Ὡς μὲν τοίνυν λαμβάνεται τὸ τί ἐστι καὶ γίνεται γνώριμον, εἴρηται, ὥστε συλλογισμὸς μὲν τοῦ τί ἐστιν οὐ γίνεται οὐδ᾽ ἀπόδειξις, δῆλον μέντοι διὰ συλλογισμοῦ καὶ δι᾽ ἀποδείξεως• ὥστ᾽ οὔτ᾽ ἄνευ ἀποδείξεως ἔστι γνῶναι τὸ τί ἐστιν, οὗ ἔστιν αἴτιον ἄλλο, οὔτ᾽ ἔστιν ἀπόδειξις αὐτοῦ, ὥσπερ καὶ ↵ἐν τοῖς διαπορήμασιν εἴπομεν.	93b15 We have stated then how essential nature is discovered and becomes known, and we see that, while there is no syllogism-i.e. no demonstrative syllogism-of essential nature, yet it is through syllogism, viz. demonstrative syllogism, that essential nature is exhibited. So we conclude that neither can the essential nature of anything which has a cause distinct from itself be known without demonstration, nor can it be demonstrated; and this is what we contended in our preliminary discussions.
c9	Chapter 9
Ἔστι δὲ τῶν μὲν ἕτερόν τι αἴτιον, τῶν δ᾽ οὐκ ἔστιν. ὥστε δῆλον ὅτι καὶ τῶν τί ἐστι τὰ μὲν ἄμεσα καὶ ἀρχαί εἰσιν, ἃ καὶ εἶναι καὶ τί ἐστιν ὑποθέσθαι δεῖ ἢ ἄλλον τρόπον φανερὰ ποιῆσαι (ὅπερ ὁ ἀριθμητικὸς ποιεῖ• καὶ γὰρ τί ↵ἐστι τὴν μονάδα ὑποτίθεται, καὶ ὅτι ἔστιν)• τῶν δ᾽ ἐχόντων μέσον, καὶ ὧν ἔστι τι ἕτερον αἴτιον τῆς οὐσίας, ἔστι δι᾽ ἀποδείξεως, ὥσπερ εἴπομεν, δηλῶσαι, μὴ τὸ τί ἐστιν ἀποδεικνύντας.	9 93b22 Now while some things have a cause distinct from themselves, others have not. Hence it is evident that there are essential natures which are immediate, that is are basic premisses; and of these not only that they are but also what they are must be assumed or revealed in some other way. This too is the actual procedure of the arithmetician, who assumes both the nature and the existence of unit. On the other hand, it is possible (in the manner explained) to exhibit through demonstration the essential nature of things which have a ‘middle’, i.e. a cause of their substantial being other than that being itself; but we do not thereby demonstrate it.
c10	Chapter 10
Ὁρισμὸς δ᾽ ἐπειδὴ λέγεται εἶναι λόγος τοῦ τί ἐστι, φα↵νερὸν ὅτι ὁ μέν τις ἔσται λόγος τοῦ τί σημαίνει τὸ ὄνομα ἢ λόγος ἕτερος ὀνοματώδης, οἷον τί σημαίνει [τί ἐστι] τρίγωνον. ὅπερ ἔχοντες ὅτι ἔστι, ζητοῦμεν διὰ τί ἔστιν• χαλεπὸν δ᾽ οὕτως ἐστὶ λαβεῖν ἃ μὴ ἴσμεν ὅτι ἔστιν. ἡ δ᾽ αἰτία εἴρηται πρότερον τῆς χαλεπότητος, ὅτι οὐδ᾽ εἰ ἔστιν ἢ μὴ ↵ἴσμεν, ἀλλ᾽ ἢ κατὰ συμβεβηκός. (λόγος δ᾽ εἷς ἐστὶ διχῶς, ὁ μὲν συνδέσμωι, ὥσπερ ἡ Ἰλιάς, ὁ δὲ τῶι ἓν καθ᾽ ἑνὸς δηλοῦν μὴ κατὰ συμβεβηκός.) Εἷς μὲν δὴ ὅρος ἐστὶν ὅρου ὁ εἰρημένος,	10 93b28 Since definition is said to be the statement of a thing’s nature, obviously one kind of definition will be a statement of the meaning of the name, or of an equivalent nominal formula. A definition in this sense tells you, e.g. the meaning of the phrase ‘triangular character’. When we are aware that triangle exists, we inquire the reason why it exists. But it is difficult thus to learn the definition of things the existence of which we do not genuinely know-the cause of this difficulty being, as we said before, that we only know accidentally whether or not the thing exists. Moreover, a statement may be a unity in either of two ways, by conjunction, like the Iliad, or because it exhibits a single predicate as inhering not accidentally in a single subject. That then is one way of defining definition.
ἄλλος δ᾽ ἐστὶν ὅρος λόγος ὁ δηλῶν διὰ τί ἔστιν.	93b38 Another kind of definition is a formula exhibiting the cause of a thing’s existence.
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.	93b39 Thus the former signifies without proving, but the latter will clearly be a quasi-demonstration of essential nature, differing from demonstration in the arrangement of its terms.
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. ὥστε ὁ αὐτὸς λόγος ἄλλον τρόπον λέγεται, καὶ ὡδὶ μὲν ἀπόδειξις συνεχής, ὡδὶ δὲ ὁρισμός. (ἔτι ἐστὶν ὅρος βροντῆς ψόφος ἐν νέφεσι• τοῦτο δ᾽ ἐστὶ τῆς τοῦ τί ἐστιν ἀποδείξεως συμπέρασμα.)	94a2 For there is a difference between stating why it thunders, and stating what is the essential nature of thunder; since the first statement will be ‘Because fire is quenched in the clouds’, while the statement of what the nature of thunder is will be ‘The noise of fire being quenched in the clouds’. Thus the same statement takes a different form: in one form it is continuous demonstration, in the other definition. Again, thunder can be defined as noise in the clouds, which is the conclusion of the demonstration embodying essential nature.
ὁ δὲ τῶν ἀμέσων ὁρισμὸς θέσις ἐστὶ τοῦ τί ἐστιν ↵ἀναπόδεικτος. Ἔστιν ἄρα ὁρισμὸς εἷς μὲν λόγος τοῦ τί ἐστιν ἀναπόδεικτος, εἷς δὲ συλλογισμὸς τοῦ τί ἐστι, πτώσει διαφέρων τῆς ἀποδείξεως, τρίτος δὲ τῆς τοῦ τί ἐστιν ἀποδείξεως συμπέρασμα.	94a9 On the other hand the definition of immediates is an indemonstrable positing of essential nature. We conclude then that definition is (a) an indemonstrable statement of essential nature, or (b) a syllogism of essential nature differing from demonstration in grammatical form, or (c) the conclusion of a demonstration giving essential nature.
φανερὸν οὖν ἐκ τῶν εἰρημένων καὶ πῶς ἔστι τοῦ τί ↵ἐστιν ἀπόδειξις καὶ πῶς οὐκ ἔστι, καὶ τίνων ἔστι καὶ τίνων οὐκ ἔστιν, ἔτι δ᾽ ὁρισμὸς ποσαχῶς τε λέγεται καὶ πῶς τὸ τί ἐστι δείκνυσι καὶ πῶς οὔ, καὶ τίνων ἔστι καὶ τίνων οὔ, ἔτι δὲ πρὸς ἀπόδειξιν πῶς ἔχει, καὶ πῶς ἐνδέχεται τοῦ αὐτοῦ εἶναι καὶ πῶς οὐκ ἐνδέχεται.	94a13 Our discussion has therefore made plain (1) in what sense and of what things the essential nature is demonstrable, and in what sense and of what things it is not; (2) what are the various meanings of the term definition, and in what sense and of what things it proves the essential nature, and in what sense and of what things it does not; (3) what is the relation of definition to demonstration, and how far the same thing is both definable and demonstrable and how far it is not.
c11	Chapter 11
Ἐπεὶ δὲ ἐπίστασθαι οἰόμεθα ὅταν εἰδῶμεν τὴν αἰτίαν, αἰτίαι δὲ τέτταρες, μία μὲν τὸ τί ἦν εἶναι, μία δὲ τὸ τίνων ὄντων ἀνάγκη τοῦτ᾽ εἶναι, ἑτέρα δὲ ἡ τί πρῶτον ἐκίνησε, τετάρτη δὲ τὸ τίνος ἕνεκα,	11 94a20 We think we have scientific knowledge when we know the cause, and there are four causes: (1) the definable form, (2) an antecedent which necessitates a consequent, (3) the efficient cause, (4) the final cause. Hence each of these can be the middle term of a proof,
πᾶσαι αὗται διὰ τοῦ μέσου δείκνυνται. τό τε γὰρ οὗ ὄντος τοδὶ ἀνάγκη εἶναι μιᾶς μὲν ↵προτάσεως ληφθείσης οὐκ ἔστι, δυοῖν δὲ τοὐλάχιστον• τοῦτο δ᾽ ἐστίν, ὅταν ἓν μέσον ἔχωσιν.	94a24 for (a) though the inference from antecedent to necessary consequent does not hold if only one premiss is assumed-two is the minimum-still when there are two it holds on condition that they have a single common middle term. So it is from the assumption of this single middle term that the conclusion follows necessarily.
τούτου οὖν ἑνὸς ληφθέντος τὸ συμπέρασμα ἀνάγκη εἶναι. δῆλον δὲ καὶ ὧδε. διὰ τί ὀρθὴ ἡ ἐν ἡμικυκλίωι; τίνος ὄντος ὀρθή; ἔστω δὴ ὀρθὴ ἐφ᾽ ἧς Α, ἡμίσεια δυοῖν ὀρθαῖν ἐφ᾽ ἧς Β, ἡ ἐν ἡμικυ↵κλίωι ἐφ᾽ ἧς Γ. τοῦ δὴ τὸ Α τὴν ὀρθὴν ὑπάρχειν τῶι Γ τῆι ἐν τῶι ἡμικυκλίωι αἴτιον τὸ Β. αὕτη μὲν γὰρ τῆι Α ἴση, ἡ δὲ τὸ Γ τῆι Β• δύο γὰρ ὀρθῶν ἡμίσεια. τοῦ Β οὖν ὄντος ἡμίσεος δύο ὀρθῶν τὸ Α τῶι Γ ὑπάρχει (τοῦτο δ᾽ ἦν τὸ ἐν ἡμικυκλίωι ὀρθὴν εἶναι). τοῦτο δὲ ταὐτόν ἐστι τῶι τί ἦν εἶναι, ↵τῶι τοῦτο σημαίνειν τὸν λόγον.	94a28 The following example will also show this. Why is the angle in a semicircle a right angle?-or from what assumption does it follow that it is a right angle? Thus, let A be right angle, B the half of two right angles, C the angle in a semicircle. Then B is the cause in virtue of which A, right angle, is attributable to C, the angle in a semicircle, since B=A and the other, viz. C,=B, for C is half of two right angles. Therefore it is the assumption of B, the half of two right angles, from which it follows that A is attributable to C, i.e. that the angle in a semicircle is a right angle. Moreover, B is identical with (b) the defining form of A, since it is what A’s definition signifies.
ἀλλὰ μὴν καὶ τὸ τί ἦν εἶναι αἴτιον δέδεικται τὸ μέσον ‹ὄν›.	94a35 Moreover, the formal cause has already been shown to be the middle.
Τὸ δὲ διὰ τί ὁ Μηδικὸς πόλεμος ἐγένετο Ἀθηναίοις; τίς αἰτία τοῦ πολεμεῖσθαι Ἀθηναίους; ὅτι [94b]εἰς Σάρδεις μετ᾽ Ἐρετριέων ἐνέβαλον• τοῦτο γὰρ ἐκίνησε πρῶτον. πόλεμος ἐφ᾽ οὗ Α, προτέρους εἰσβαλεῖν Β, Ἀθηναῖοι τὸ Γ. ὑπάρχει δὴ τὸ Β τῶι Γ, τὸ προτέροις ἐμβαλεῖν τοῖς Ἀθηναίοις, τὸ δὲ Α τῶι Β• πολεμοῦσι γὰρ τοῖς πρό↵τερον ἀδικήσασιν. ὑπάρχει ἄρα τῶι μὲν Β τὸ Α, τὸ πολεμεῖσθαι τοῖς προτέροις ἄρξασι• τοῦτο δὲ τὸ Β τοῖς Ἀθηναίοις• πρότεροι γὰρ ἦρξαν. μέσον ἄρα καὶ ἐνταῦθα τὸ αἴτιον, τὸ πρῶτον κινῆσαν.	94a36 (c) ‘Why did the Athenians become involved in the Persian war?’ means ‘What cause originated the waging of war against the Athenians?’ and the answer is, ‘Because they raided Sardis with the Eretrians’, since this originated the war. Let A be war, B unprovoked raiding, C the Athenians. Then B, unprovoked raiding, is true of C, the Athenians, and A is true of B, since men make war on the unjust aggressor. So A, having war waged upon them, is true of B, the initial aggressors, and B is true of C, the Athenians, who were the aggressors. Hence here too the cause-in this case the efficient cause-is the middle term.
Ὅσων δ᾽ αἴτιον τὸ ἕνεκα τίνος – οἷον διὰ τί περιπατεῖ; ὅπως ὑγιαίνηι• διὰ τί οἰκία ἔστιν; ↵ὅπως σώιζηται τὰ σκεύη – τὸ μὲν ἕνεκα τοῦ ὑγιαίνειν, τὸ δ᾽ ἕνεκα τοῦ σώιζεσθαι. διὰ τί δὲ ἀπὸ δείπνου δεῖ περιπατεῖν, καὶ ἕνεκα τίνος δεῖ, οὐδὲν διαφέρει. περίπατος ἀπὸ δείπνου Γ, τὸ μὴ ἐπιπολάζειν τὰ σιτία ἐφ᾽ οὗ Β, τὸ ὑγιαίνειν ἐφ᾽ οὗ Α. ἔστω δὴ τῶι ἀπὸ δείπνου περιπατεῖν ὑπάρχον τὸ ποι↵εῖν μὴ ἐπιπολάζειν τὰ σιτία πρὸς τῶι στόματι τῆς κοιλίας, καὶ τοῦτο ὑγιεινόν. δοκεῖ γὰρ ὑπάρχειν τῶι περιπατεῖν τῶι Γ τὸ Β τὸ μὴ ἐπιπολάζειν τὰ σιτία, τούτωι δὲ τὸ Α τὸ ὑγιεινόν. τί οὖν αἴτιον τῶι Γ τοῦ τὸ Α ὑπάρχειν τὸ οὗ ἕνεκα; τὸ Β τὸ μὴ ἐπιπολάζειν. τοῦτο δ᾽ ἐστὶν ὥσπερ ἐκείνου λό↵γος• τὸ γὰρ Α οὕτως ἀποδοθήσεται. διὰ τί δὲ τὸ Β τῶι Γ ἔστιν; ὅτι τοῦτ᾽ ἔστι τὸ ὑγιαίνειν, τὸ οὕτως ἔχειν.	94b8 (d) This is no less true where the cause is the final cause. E.g. why does one take a walk after supper? For the sake of one’s health. Why does a house exist? For the preservation of one’s goods. The end in view is in the one case health, in the other preservation. To ask the reason why one must walk after supper is precisely to ask to what end one must do it. Let C be walking after supper, B the non-regurgitation of food, A health. Then let walking after supper possess the property of preventing food from rising to the orifice of the stomach, and let this condition be healthy; since it seems that B, the non-regurgitation of food, is attributable to C, taking a walk, and that A, health, is attributable to B. What, then, is the cause through which A, the final cause, inheres in C? It is B, the non-regurgitation of food; but B is a kind of definition of A, for A will be explained by it. Why is B the cause of A’s belonging to C? Because to be in a condition such as B is to be in health.
δεῖ δὲ μεταλαμβάνειν τοὺς λόγους, καὶ οὕτως μᾶλλον ἕκαστα φανεῖται. αἱ δὲ γενέσεις ἀνάπαλιν ἐνταῦθα καὶ ἐπὶ τῶν κατὰ κίνησιν αἰτίων• ἐκεῖ μὲν γὰρ τὸ μέσον δεῖ γενέσθαι ↵πρῶτον, ἐνταῦθα δὲ τὸ Γ, τὸ ἔσχατον, τελευταῖον δὲ τὸ οὗ ἕνεκα.	94b23 Incidentally, here the order of coming to be is the reverse of what it is in proof through the efficient cause: in the efficient order the middle term must come to be first, whereas in the teleological order the minor, C, must first take place, and the end in view comes last in time.
Ἐνδέχεται δὲ τὸ αὐτὸ καὶ ἕνεκά τινος εἶναι καὶ ἐξ ἀνάγκης, οἷον διὰ τοῦ λαμπτῆρος τὸ φῶς• καὶ γὰρ ἐξ ἀνάγκης διέρχεται τὸ μικρομερέστερον διὰ τῶν μειζόνων πόρων, ↵εἴπερ φῶς γίνεται τῶι διιέναι, καὶ ἕνεκά τινος, ὅπως μὴ πταίωμεν. ἆρ᾽ οὖν εἰ εἶναι ἐνδέχεται, καὶ γίνεσθαι ἐνδέχεται• ὥσπερ εἰ βροντᾶι ‹ὅτι› ἀποσβεννυμένου τε τοῦ πυρὸς ἀνάγκη σίζειν καὶ ψοφεῖν καί, εἰ ὡς οἱ Πυθαγόρειοί φασιν, ἀπειλῆς ἕνεκα τοῖς ἐν τῶι ταρτάρωι, ὅπως φοβῶνται;	94b27 The same thing may exist for an end and be necessitated as well. For example, light shines through a lantern (1) because that which consists of relatively small particles necessarily passes through pores larger than those particles-assuming that light does issue by penetrationand (2) for an end, namely to save us from stumbling. If then, a thing can exist through two causes, can it come to be through two causes-as for instance if thunder be a hiss and a roar necessarily produced by the quenching of fire, and also designed, as the Pythagoreans say, for a threat to terrify those that lie in Tartarus?
πλεῖστα ↵δὲ τοιαῦτ᾽ ἔστι, καὶ μάλιστα ἐν τοῖς κατὰ φύσιν συνισταμένοις καὶ συνεστῶσιν• ἡ μὲν γὰρ ἕνεκά του ποιεῖ φύσις, ἡ δ᾽ ἐξ ἀνάγκης. ἡ δ᾽ ἀνάγκη διττή• ἡ μὲν γὰρ κατὰ φύ[95a]σιν καὶ τὴν ὁρμήν, ἡ δὲ βίαι ἡ παρὰ τὴν ὁρμήν, ὥσπερ λίθος ἐξ ἀνάγκης καὶ ἄνω καὶ κάτω φέρεται, ἀλλ᾽ οὐ διὰ τὴν αὐτὴν ἀνάγκην.	94b35 Indeed, there are very many such cases, mostly among the processes and products of the natural world; for nature, in different senses of the term ‘nature’, produces now for an end, now by necessity. Necessity too is of two kinds. It may work in accordance with a thing’s natural tendency, or by constraint and in opposition to it; as, for instance, by necessity a stone is borne both upwards and downwards, but not by the same necessity.
ἐν δὲ τοῖς ἀπὸ διανοίας τὰ μὲν οὐδέποτε ἀπὸ τοῦ αὐτομάτου ὑπάρχει, οἷον οἰκία ἢ ἀνδριάς, οὐδ᾽ ἐξ ↵ἀνάγκης, ἀλλ᾽ ἕνεκά του, τὰ δὲ καὶ ἀπὸ τύχης, οἷον ὑγίεια καὶ σωτηρία. μάλιστα δὲ ἐν ὅσοις ἐνδέχεται καὶ ὧδε καὶ ἄλλως, ὅταν, μὴ ἀπὸ τύχης, ἡ γένεσις ἦι ὥστε τὸ τέλος ἀγαθόν,	95a3 Of the products of man’s intelligence some are never due to chance or necessity but always to an end, as for example a house or a statue; others, such as health or safety, may result from chance as well. It is mostly in cases where the issue is indeterminate (though only where the production does not originate in chance,
ἕνεκά του γίνεται, καὶ ἢ φύσει ἢ τέχνηι. ἀπὸ τύχης δ᾽ οὐδὲν ἕνεκά του γίνεται.	95a7 and the end is consequently good), that a result is due to an end, and this is true alike in nature or in art. By chance, on the other hand, nothing comes to be for an end.
c12	Chapter 12
Τὸ δ᾽ αὐτὸ αἴτιόν ἐστι τοῖς γινομένοις καὶ τοῖς γεγενημένοις καὶ τοῖς ἐσομένοις ὅπερ καὶ τοῖς οὖσι (τὸ γὰρ μέσον αἴτιον), πλὴν τοῖς μὲν οὖσιν ὄν, τοῖς δὲ γινομένοις γινόμενον, τοῖς δὲ γεγενημένοις γεγενημένον καὶ ἐσομένοις ἐσόμενον.	12 95a10 The effect may be still coming to be, or its occurrence may be past or future, yet the cause will be the same as when it is actually existent-for it is the middle which is the cause-except that if the effect actually exists the cause is actually existent, if it is coming to be so is the cause, if its occurrence is past the cause is past, if future the cause is future.
οἷον διὰ τί γέγονεν ἔκλειψις; διότι ἐν μέσωι γέγονεν ↵ἡ γῆ• γίνεται δὲ διότι γίνεται, ἔσται δὲ διότι ἔσται ἐν μέσωι, 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, ἔσται δ᾽ ἐσομένου.	95a13 For example, the moon was eclipsed because the earth intervened, is becoming eclipsed because the earth is in process of intervening, will be eclipsed because the earth will intervene, is eclipsed because the earth intervenes. To take a second example: assuming that the definition of ice is solidified water, let C be water, A solidified, B the middle, which is the cause, namely total failure of heat. Then B is attributed to C, and A, solidification, to B: ice when B is occurring, has formed when B has occurred, and will form when B shall occur. This sort of cause, then, and its effect come to be simultaneously when they are in process of becoming, and exist simultaneously when they actually exist; and the same holds good when they are past and when they are future.
Τὸ μὲν οὖν οὕτως αἴτιον καὶ οὗ αἴτιον ἅμα γίνεται, ὅταν γίνηται, καὶ ἔστιν,	95a23 But what of cases where they are not simultaneous? Can causes and effects different from one another form,
ὅταν ἦι• καὶ ἐπὶ τοῦ γεγονέναι καὶ ἔσεσθαι ὡσαύτως. ἐπὶ δὲ τῶν μὴ ἅμα ἆρ᾽ ἔστιν ἐν τῶι συ↵νεχεῖ χρόνωι, ὥσπερ δοκεῖ ἡμῖν, ἄλλα ἄλλων αἴτια εἶναι,	95a24 as they seem to us to form, a continuous succession, a past effect resulting from a past cause different from itself, a future effect from a future cause different from it, and an effect which is coming-to-be from a cause different from and prior to it?
τοῦ τόδε γενέσθαι ἕτερον γενόμενον, καὶ τοῦ ἔσεσθαι ἕτερον ἐσόμενον, καὶ τοῦ γίνεσθαι δέ, εἴ τι ἔμπροσθεν ἐγένετο; ἔστι δὴ ἀπὸ τοῦ ὕστερον γεγονότος ὁ συλλογισμός (ἀρχὴ δὲ καὶ τούτων τὰ γεγονότα)• διὸ καὶ ἐπὶ τῶν γινομένων ὡσαύτως. ↵ἀπὸ δὲ τοῦ προτέρου οὐκ ἔστιν, οἷον ἐπεὶ τόδε γέγονεν, ὅτι τόδ᾽ ὕστερον γέγονεν• καὶ ἐπὶ τοῦ ἔσεσθαι ὡσαύτως.	95a27 Now on this theory it is from the posterior event that we reason (and this though these later events actually have their source of origin in previous events — a fact which shows that also when the effect is coming-to-be we still reason from the posterior event), and from the event we cannot reason (we cannot argue that because an event A has occurred, therefore an event B has occurred subsequently to A but still in the past-and the same holds good if the occurrence is future)-cannot reason because,
οὔτε γὰρ ἀορίστου οὔθ᾽ ὁρισθέντος ἔσται τοῦ χρόνου ὥστ᾽ ἐπεὶ τοῦτ᾽ ἀληθὲς εἰπεῖν γεγονέναι, τόδ᾽ ἀληθὲς εἰπεῖν γεγονέναι τὸ ὕστερον. ἐν γὰρ τῶι μεταξὺ ψεῦδος ἔσται τὸ εἰπεῖν τοῦτο, ↵ἤδη θατέρου γεγονότος.	95a32 be the time interval definite or indefinite, it will never be possible to infer that because it is true to say that A occurred, therefore it is true to say that B, the subsequent event, occurred; for in the interval between the events, though A has already occurred, the latter statement will be false.
ὁ δ᾽ αὐτὸς λόγος καὶ ἐπὶ τοῦ ἐσομένου, οὐδ᾽ ἐπεὶ τόδε γέγονε, τόδ᾽ ἔσται. τὸ γὰρ μέσον ὁμόγονον δεῖ εἶναι, τῶν γενομένων γενόμενον, τῶν ἐσομένων ἐσόμενον, τῶν γινομένων γινόμενον, τῶν ὄντων ὄν• τοῦ δὲ γέ- γονε καὶ τοῦ ἔσται οὐκ ἐνδέχεται εἶναι ὁμόγονον.	95a35 And the same argument applies also to future events; i.e. one cannot infer from an event which occurred in the past that a future event will occur. The reason of this is that the middle must be homogeneous, past when the extremes are past, future when they are future, coming to be when they are coming-to-be, actually existent when they are actually existent; and there cannot be a middle term homogeneous with extremes respectively past and future.
ἔτι οὔτε ἀόριστον ἐνδέχεται εἶναι τὸν χρόνον τὸν μεταξὺ οὔθ᾽ ὡρι[95b]σμένον•	95a39 And it is a further difficulty in this theory that the time interval can be neither indefinite nor definite, since during it the inference will be false.
ψεῦδος γὰρ ἔσται τὸ εἰπεῖν ἐν τῶι μεταξύ. ἐπισκεπτέον δὲ τί τὸ συνέχον ὥστε μετὰ τὸ γεγονέναι τὸ γίνεσθαι ὑπάρχειν ἐν τοῖς πράγμασιν. ἢ δῆλον ὅτι οὐκ ἔστιν ἐχόμενον γεγονότος γινόμενον; οὐδὲ γὰρ γενόμενον γενομένου• πέ↵ρατα γὰρ καὶ ἄτομα• ὥσπερ οὖν οὐδὲ στιγμαί εἰσιν ἀλλήλων ἐχόμεναι, οὐδὲ γενόμενα• ἄμφω γὰρ ἀδιαίρετα. οὐδὲ δὴ γινόμενον γεγενημένου διὰ τὸ αὐτό• τὸ μὲν γὰρ γινόμενον διαιρετόν, τὸ δὲ γεγονὸς ἀδιαίρετον. ὥσπερ οὖν γραμμὴ πρὸς στιγμὴν ἔχει, οὕτω τὸ γινόμενον πρὸς τὸ γεγονός• ἐν↵υπάρχει γὰρ ἄπειρα γεγονότα ἐν τῶι γινομένωι. μᾶλλον δὲ φανερῶς ἐν τοῖς καθόλου περὶ κινήσεως δεῖ λεχθῆναι περὶ τούτων.	95b1 We have also to inquire what it is that holds events together so that the coming-to-be now occurring in actual things follows upon a past event. It is evident, we may suggest, that a past event and a present process cannot be ‘contiguous’, for not even two past events can be ‘contiguous’. For past events are limits and atomic; so just as points are not ‘contiguous’ neither are past events, since both are indivisible. For the same reason a past event and a present process cannot be ‘contiguous’, for the process is divisible, the event indivisible. Thus the relation of present process to past event is analogous to that of line to point, since a process contains an infinity of past events. These questions, however, must receive a more explicit treatment in our general theory of change.
Περὶ μὲν οὖν τοῦ πῶς ἂν ἐφεξῆς γινομένης τῆς γενέσεως ἔχοι τὸ μέσον τὸ αἴτιον ἐπὶ τοσοῦτον εἰλήφθω. ἀνάγκη ↵γὰρ καὶ ἐν τούτοις τὸ μέσον καὶ τὸ πρῶτον ἄμεσα εἶναι. οἷον τὸ Α γέγονεν, ἐπεὶ τὸ Γ γέγονεν (ὕστερον δὲ τὸ Γ γέγονεν, ἔμπροσθεν δὲ τὸ Α• ἀρχὴ δὲ τὸ Γ διὰ τὸ ἐγγύτερον τοῦ νῦν εἶναι, ὅ ἐστιν ἀρχὴ τοῦ χρόνου). τὸ δὲ Γ γέγονεν, εἰ τὸ Δ γέγονεν. τοῦ δὴ Δ γενομένου ἀνάγκη τὸ Α γεγονέναι. ↵αἴτιον δὲ τὸ Γ• τοῦ γὰρ Δ γενομένου τὸ Γ ἀνάγκη γεγονέναι, τοῦ δὲ Γ γεγονότος ἀνάγκη πρότερον τὸ Α γεγονέναι. οὕτω δὲ λαμβάνοντι τὸ μέσον στήσεταί που εἰς ἄμεσον, ἢ ἀεὶ παρεμπεσεῖται διὰ τὸ ἄπειρον;	95b12 The following must suffice as an account of the manner in which the middle would be identical with the cause on the supposition that coming-to-be is a series of consecutive events: for in the terms of such a series too the middle and major terms must form an immediate premiss; e.g. we argue that, since C has occurred, therefore A occurred: and C’s occurrence was posterior, A’s prior; but C is the source of the inference because it is nearer to the present moment, and the starting-point of time is the present. We next argue that, since D has occurred, therefore C occurred. Then we conclude that, since D has occurred, therefore A must have occurred; and the cause is C, for since D has occurred C must have occurred, and since C has occurred A must previously have occurred. If we get our middle term in this way, will the series terminate in an immediate premiss,
οὐ γάρ ἐστιν ἐχόμενον γεγονὸς γεγονότος, ὥσπερ ἐλέχθη. ἀλλ᾽ ἄρξασθαί γε ὅμως ↵ἀνάγκη ἀπ᾽ ἀμέσου καὶ ἀπὸ τοῦ νῦν πρώτου.	95b23 or since, as we said, no two events are ‘contiguous’, will a fresh middle term always intervene because there is an infinity of middles? No: though no two events are ‘contiguous’, yet we must start from a premiss consisting of a middle and the present event as major.
ὁμοίως δὲ καὶ ἐπὶ τοῦ ἔσται. εἰ γὰρ ἀληθὲς εἰπεῖν ὅτι ἔσται τὸ Δ, ἀνάγκη πρότερον ἀληθὲς εἰπεῖν ὅτι τὸ Α ἔσται. τούτου δ᾽ αἴτιον τὸ Γ• εἰ μὲν γὰρ τὸ Δ ἔσται, πρότερον τὸ Γ ἔσται• εἰ δὲ τὸ Γ ἔσται, πρότερον τὸ Α ἔσται. ὁμοίως δ᾽ ἄπειρος ↵ἡ τομὴ καὶ ἐν τούτοις• οὐ γὰρ ἔστιν ἐσόμενα ἐχόμενα ἀλλήλων.	95b25 The like is true of future events too, since if it is true to say that D will exist, it must be a prior truth to say that A will exist, and the cause of this conclusion is C; for if D will exist, C will exist prior to D, and if C will exist, A will exist prior to it. And here too the same infinite divisibility might be urged, since future events are not ‘contiguous’. But here too an immediate basic premiss must be assumed.
ἀρχὴ δὲ καὶ ἐν τούτοις ἄμεσος ληπτέα. ἔχει δὲ οὕτως ἐπὶ τῶν ἔργων• εἰ γέγονεν οἰκία, ἀνάγκη τετμῆσθαι λίθους καὶ γεγονέναι. τοῦτο διὰ τί; ὅτι ἀνάγκη θεμέλιον γεγονέναι, εἴπερ καὶ οἰκία γέγονεν• εἰ δὲ θεμέλιον, πρό↵τερον λίθους γεγονέναι ἀνάγκη. πάλιν εἰ ἔσται οἰκία, ὡσαύτως πρότερον ἔσονται λίθοι. δείκνυται δὲ διὰ τοῦ μέσου ὁμοίως• ἔσται γὰρ θεμέλιος πρότερον.	95b31 And in the world of fact this is so: if a house has been built, then blocks must have been quarried and shaped. The reason is that a house having been built necessitates a foundation having been laid, and if a foundation has been laid blocks must have been shaped beforehand. Again, if a house will be built, blocks will similarly be shaped beforehand; and proof is through the middle in the same way, for the foundation will exist before the house.
Ἐπεὶ δ᾽ ὁρῶμεν ἐν τοῖς γινομένοις κύκλωι τινὰ γένεσιν οὖσαν, ἐνδέχεται τοῦτο εἶναι, εἴπερ ἕποιντο ἀλλήλοις τὸ μέσον καὶ οἱ ἄκροι• ἐν γὰρ τούτοις τὸ ἀντιστρέφειν ἐστίν. δέ[96a]δεικται δὲ τοῦτο ἐν τοῖς πρώτοις, ὅτι ἀντιστρέφει τὰ συμπεράσματα• τὸ δὲ κύκλωι τοῦτό ἐστιν.	95b38 Now we observe in Nature a certain kind of circular process of coming-to-be; and this is possible only if the middle and extreme terms are reciprocal, since conversion is conditioned by reciprocity in the terms of the proof. This-the convertibility of conclusions and premisses-has been proved in our early chapters, and the circular process is an instance of this.
ἐπὶ δὲ τῶν ἔργων φαίνεται ὧδε• βεβρεγμένης τῆς γῆς ἀνάγκη ἀτμίδα γενέσθαι, τούτου δὲ γενομένου νέφος, τούτου δὲ γενομένου ὕδωρ• ↵τούτου δὲ γενομένου ἀνάγκη βεβρέχθαι τὴν γῆν• τοῦτο δ᾽ ἦν τὸ ἐξ ἀρχῆς, ὥστε κύκλωι περιελήλυθεν• ἑνὸς γὰρ αὐτῶν ὁτουοῦν ὄντος ἕτερον ἔστι, κἀκείνου ἄλλο, καὶ τούτου τὸ πρῶτον.	96a2 In actual fact it is exemplified thus: when the earth had been moistened an exhalation was bound to rise, and when an exhalation had risen cloud was bound to form, and from the formation of cloud rain necessarily resulted and by the fall of rain the earth was necessarily moistened: but this was the starting-point, so that a circle is completed; for posit any one of the terms and another follows from it, and from that another, and from that again the first.
Ἔστι δ᾽ ἔνια μὲν γινόμενα καθόλου (ἀεί τε γὰρ καὶ ἐπὶ παντὸς οὕτως ἢ ἔχει ἢ γίνεται), τὰ δὲ ἀεὶ μὲν οὔ, ὡς ↵ἐπὶ τὸ πολὺ δέ, οἷον οὐ πᾶς ἄνθρωπος ἄρρην τὸ γένειον τριχοῦται, ἀλλ᾽ ὡς ἐπὶ τὸ πολύ.	96a8 Some occurrences are universal (for they are, or come-to-be what they are, always and in ever case); others again are not always what they are but only as a general rule: for instance, not every man can grow a beard, but it is the general rule. In the case of such connexions the middle term too must be a general rule.
τῶν δὴ τοιούτων ἀνάγκη καὶ τὸ μέσον ὡς ἐπὶ τὸ πολὺ εἶναι. εἰ γὰρ τὸ Α κατὰ τοῦ Β καθόλου κατηγορεῖται, καὶ τοῦτο κατὰ τοῦ Γ καθόλου, ἀνάγκη καὶ τὸ Α κατὰ τοῦ Γ ἀεὶ καὶ ἐπὶ παντὸς κατηγορεῖσθαι• ↵τοῦτο γάρ ἐστι τὸ καθόλου, τὸ ἐπὶ παντὶ καὶ ἀεί. ἀλλ᾽ ὑπέκειτο ὡς ἐπὶ τὸ πολύ• ἀνάγκη ἄρα καὶ τὸ μέσον ὡς ἐπὶ τὸ πολὺ εἶναι τὸ ἐφ᾽ οὗ τὸ Β. ἔσονται τοίνυν καὶ τῶν ὡς ἐπὶ τὸ πολὺ ἀρχαὶ ἄμεσοι, ὅσα ὡς ἐπὶ τὸ πολὺ οὕτως ἔστιν ἢ γίνεται.	96a12 For if A is predicated universally of B and B of C, A too must be predicated always and in every instance of C, since to hold in every instance and always is of the nature of the universal. But we have assumed a connexion which is a general rule; consequently the middle term B must also be a general rule. So connexions which embody a general rule-i.e. which exist or come to be as a general rule-will also derive from immediate basic premisses.
c13	Chapter 13
Πῶς μὲν οὖν τὸ τί ἐστιν εἰς τοὺς ὅρους ἀποδίδοται, καὶ τίνα τρόπον ἀπόδειξις ἢ ὁρισμὸς ἔστιν αὐτοῦ ἢ οὐκ ἔστιν,	13 96a20 We have already explained how essential nature is set out in the terms of a demonstration, and the sense in which it is or is not demonstrable or definable;
εἴρη γορούμενα, νῦν λέγωμεν. ται πρότερον• πῶς δὲ δεῖ θηρεύειν τὰ ἐν τῶι τί ἐστι κατη- [?]	96a22 so let us now discuss the method to be adopted in tracing the elements predicated as constituting the definable form.
Τῶν δὴ ὑπαρχόντων ἀεὶ ἑκάστωι ἔνια ἐπεκτείνει ἐπὶ ↵πλέον, οὐ μέντοι ἔξω τοῦ γένους. λέγω δὲ ἐπὶ πλέον ὑπάρχειν ὅσα ὑπάρχει μὲν ἑκάστωι καθόλου, οὐ μὴν ἀλλὰ καὶ ἄλλωι. οἷον ἔστι τι ὁ πάσηι τριάδι ὑπάρχει, ἀλλὰ καὶ μὴ τριάδι, ὥσπερ τὸ ὂν ὑπάρχει τῆι τριάδι, ἀλλὰ καὶ μὴ ἀριθμῶι, ἀλλὰ καὶ τὸ περιττὸν ὑπάρχει τε πάσηι τριάδι ↵καὶ ἐπὶ πλέον ὑπάρχει (καὶ γὰρ τῆι πεντάδι ὑπάρχει), ἀλλ᾽ οὐκ ἔξω τοῦ γένους• ἡ μὲν γὰρ πεντὰς ἀριθμός, οὐδὲν δὲ ἔξω ἀριθμοῦ περιττόν.	96a24 Now of the attributes which inhere always in each several thing there are some which are wider in extent than it but not wider than its genus (by attributes of wider extent mean all such as are universal attributes of each several subject, but in their application are not confined to that subject). while an attribute may inhere in every triad, yet also in a subject not a triad-as being inheres in triad but also in subjects not numbers at all-odd on the other hand is an attribute inhering in every triad and of wider application (inhering as it does also in pentad), but which does not extend beyond the genus of triad; for pentad is a number, but nothing outside number is odd.
τὰ δὴ τοιαῦτα ληπτέον μέχρι τούτου, ἕως τοσαῦτα ληφθῆι πρῶτον ὧν ἕκαστον μὲν ἐπὶ πλέον ὑπάρξει, ἅπαντα δὲ μὴ ἐπὶ πλέον• ταύτην γὰρ ἀνάγκη οὐσίαν εἶναι ↵τοῦ πράγματος.	96a32 It is such attributes which we have to select, up to the exact point at which they are severally of wider extent than the subject but collectively coextensive with it; for this synthesis must be the substance of the thing.
οἷον τριάδι ὑπάρχει πάσηι ἀριθμός, τὸ περιττόν, τὸ πρῶτον ἀμφοτέρως, καὶ ὡς μὴ μετρεῖσθαι ἀριθμῶι καὶ ὡς μὴ συγκεῖσθαι ἐξ ἀριθμῶν. τοῦτο τοίνυν ἤδη ἐστὶν ἡ τριάς, ἀριθμὸς περιττὸς πρῶτος καὶ ὡδὶ πρῶτος. τούτων γὰρ ἕκαστον, τὰ μὲν καὶ τοῖς περιττοῖς πᾶσιν ὑπάρχει,	96a34 For example every triad possesses the attributes number, odd, and prime in both senses, i.e. not only as possessing no divisors, but also as not being a sum of numbers. This, then, is precisely what triad is, viz. a number, odd, and prime in the former and also the latter sense of the term: for these attributes taken severally apply, the first two to all odd numbers, the last to the dyad also as well as to the triad, but, taken collectively, to no other subject.
[96b]τὸ δὲ τελευταῖον καὶ τῆι δυάδι, πάντα δὲ οὐδενί. ἐπεὶ δὲ δεδήλωται ἡμῖν ἐν τοῖς ἄνω ὅτι καθόλου μέν ἐστι τὰ ἐν τῶι τί ἐστι κατηγορούμενα (τὰ καθόλου δὲ ἀναγκαῖα), τῆι δὲ τριάδι, καὶ ἐφ᾽ οὗ ἄλλου οὕτω λαμβάνεται, ἐν τῶι τί ἐστι τὰ ↵λαμβανόμενα, οὕτως ἐξ ἀνάγκης μὲν ἂν εἴη τριὰς ταῦτα.	96b2 Now since we have shown above’ that attributes predicated as belonging to the essential nature are necessary and that universals are necessary, and since the attributes which we select as inhering in triad, or in any other subject whose attributes we select in this way, are predicated as belonging to its essential nature, triad will thus possess these attributes necessarily.
ὅτι δ᾽ οὐσία, ἐκ τῶνδε δῆλον. ἀνάγκη γάρ, εἰ μὴ τοῦτο ἦν τριάδι εἶναι, οἷον γένος τι εἶναι τοῦτο, ἢ ὠνομασμένον ἢ ἀνώνυμον. ἔσται τοίνυν ἐπὶ πλέον ἢ τῆι τριάδι ὑπάρχον. ὑποκείσθω γὰρ τοιοῦτον εἶναι τὸ γένος ὥστε ὑπάρχειν κατὰ δύ↵ναμιν ἐπὶ πλέον. εἰ τοίνυν μηδενὶ ὑπάρχει ἄλλωι ἢ ταῖς ἀτόμοις τριάσι, τοῦτ᾽ ἂν εἴη τὸ τριάδι εἶναι (ὑποκείσθω γὰρ καὶ τοῦτο, ἡ οὐσία ἡ ἑκάστου εἶναι ἡ ἐπὶ τοῖς ἀτόμοις ἔσχατος τοιαύτη κατηγορία)• ὥστε ὁμοίως καὶ ἄλλωι ὁτωιοῦν τῶν οὕτω δειχθέντων τὸ αὐτῶι εἶναι ἔσται.	96b6 Further, that the synthesis of them constitutes the substance of triad is shown by the following argument. If it is not identical with the being of triad, it must be related to triad as a genus named or nameless. It will then be of wider extent than triad-assuming that wider potential extent is the character of a genus. If on the other hand this synthesis is applicable to no subject other than the individual triads, it will be identical with the being of triad, because we make the further assumption that the substance of each subject is the predication of elements in its essential nature down to the last differentia characterizing the individuals. It follows that any other synthesis thus exhibited will likewise be identical with the being of the subject.
↵Χρὴ δέ, ὅταν ὅλον τι πραγματεύηταί τις, διελεῖν τὸ γένος εἰς τὰ ἄτομα τῶι εἴδει τὰ πρῶτα, οἷον ἀριθμὸν εἰς τριάδα καὶ δυάδα, εἶθ᾽ οὕτως ἐκείνων ὁρισμοὺς πειρᾶσθαι λαμβάνειν, οἷον εὐθείας γραμμῆς καὶ κύκλου, καὶ ὀρθῆς γωνίας,	96b15 The author of a hand-book on a subject that is a generic whole should divide the genus into its first infimae species-number e.g. into triad and dyad-and then endeavour to seize their definitions by the method we have described-the definition, for example, of straight line or circle or right angle.
μετὰ δὲ τοῦτο λαβόντα τί τὸ γένος, οἷον πότερον τῶν ↵ποσῶν ἢ τῶν ποιῶν, τὰ ἴδια πάθη θεωρεῖν διὰ τῶν κοινῶν πρώτων. τοῖς γὰρ συντιθεμένοις ἐκ τῶν ἀτόμων τὰ συμβαίνοντα ἐκ τῶν ὁρισμῶν ἔσται δῆλα, διὰ τὸ ἀρχὴν εἶναι πάντων τὸν ὁρισμὸν καὶ τὸ ἁπλοῦν καὶ τοῖς ἁπλοῖς καθ᾽ αὑτὰ ὑπάρχειν τὰ συμβαίνοντα μόνοις, τοῖς δ᾽ ἄλλοις κατ᾽ ↵ἐκεῖνα.	96b18 After that, having established what the category is to which the subaltern genus belongs-quantity or quality, for instance-he should examine the properties ‘peculiar’ to the species, working through the proximate common differentiae. He should proceed thus because the attributes of the genera compounded of the infimae species will be clearly given by the definitions of the species; since the basic element of them all is the definition, i.e. the simple infirma species, and the attributes inhere essentially in the simple infimae species, in the genera only in virtue of these.
αἱ δὲ διαιρέσεις αἱ κατὰ τὰς διαφορὰς χρήσιμοί εἰσιν εἰς τὸ οὕτω μετιέναι• ὡς μέντοι δεικνύουσιν, εἴρηται ἐν τοῖς πρότερον. χρήσιμοι δ᾽ ἂν εἶεν ὧδε μόνον πρὸς τὸ συλλογίζεσθαι τὸ τί ἐστιν. καίτοι δόξειέν γ᾽ ἂν οὐδέν, ἀλλ᾽ εὐθὺς λαμβάνειν ἅπαντα, ὥσπερ ἂν εἰ ἐξ ἀρχῆς ἐλάμβανέ ↵τις ἄνευ τῆς διαιρέσεως.	96b25 Divisions according to differentiae are a useful accessory to this method. What force they have as proofs we did, indeed, explain above, but that merely towards collecting the essential nature they may be of use we will proceed to show. They might, indeed, seem to be of no use at all, but rather to assume everything at the start and to be no better than an initial assumption made without division.
διαφέρει δέ τι τὸ πρῶτον καὶ ὕστερον τῶν κατηγορουμένων κατηγορεῖσθαι, οἷον εἰπεῖν ζῶιον ἥμερον δίπουν ἢ δίπουν ζῶιον ἥμερον. εἰ γὰρ ἅπαν ἐκ δύο ἐστί, καὶ ἕν τι τὸ ζῶιον ἥμερον, καὶ πάλιν ἐκ τούτου καὶ τῆς διαφορᾶς ὁ ἄνθρωπος ἢ ὅ τι δήποτ᾽ ἐστὶ τὸ ἓν γινόμενον, ἀναγ↵καῖον διελόμενον αἰτεῖσθαι.	96b30 But, in fact, the order in which the attributes are predicated does make a difference — it matters whether we say animal-tame-biped, or biped-animal-tame. For if every definable thing consists of two elements and ‘animal-tame’ forms a unity, and again out of this and the further differentia man (or whatever else is the unity under construction) is constituted, then the elements we assume have necessarily been reached by division.
Ἔτι πρὸς τὸ μηδὲν παραλιπεῖν ἐν τῶι τί ἐστιν οὕτω μόνως ἐνδέχεται. ὅταν γὰρ τὸ πρῶτον ληφθῆι γένος, ἂν μὲν τῶν κάτωθέν τινα διαιρέσεων λαμβάνηι, οὐκ ἐμπεσεῖται ἅπαν εἰς τοῦτο, οἷον οὐ πᾶν ζῶιον ἢ ὁλόπτερον ἢ σχιζόπτερον, ἀλλὰ πτηνὸν ζῶιον ἅπαν• τούτου [97a]γὰρ διαφορὰ αὕτη. πρώτη δὲ διαφορά ἐστι ζώιου εἰς ἣν ἅπαν ζῶιον ἐμπίπτει. ὁμοίως δὲ καὶ τῶν ἄλλων ἑκάστου, καὶ τῶν ἔξω γενῶν καὶ τῶν ὑπ᾽ αὐτό, οἷον ὄρνιθος, εἰς ἣν ἅπας ὄρνις, καὶ ἰχθύος, εἰς ἣν ἅπας ἰχθύς. οὕτω μὲν οὖν ↵βαδίζοντι ἔστιν εἰδέναι ὅτι οὐδὲν παραλέλειπται• ἄλλως δὲ καὶ παραλιπεῖν ἀναγκαῖον καὶ μὴ εἰδέναι.	96b35 Again, division is the only possible method of avoiding the omission of any element of the essential nature. Thus, if the primary genus is assumed and we then take one of the lower divisions, the dividendum will not fall whole into this division: e.g. it is not all animal which is either whole-winged or split-winged but all winged animal, for it is winged animal to which this differentiation belongs. The primary differentiation of animal is that within which all animal falls. The like is true of every other genus, whether outside animal or a subaltern genus of animal; e.g. the primary differentiation of bird is that within which falls every bird, of fish that within which falls every fish. So, if we proceed in this way, we can be sure that nothing has been omitted: by any other method one is bound to omit something without knowing it.
οὐδὲν δὲ δεῖ τὸν ὁριζόμενον καὶ διαιρούμενον ἅπαντα εἰδέναι τὰ ὄντα.	97a6 To define and divide one need not know the whole of existence.
καίτοι ἀδύνατόν φασί τινες εἶναι τὰς διαφορὰς εἰδέναι τὰς πρὸς ἕκαστον μὴ εἰδότα ἕκαστον• ἄνευ δὲ τῶν διαφορῶν οὐκ εἶναι ↵ἕκαστον εἰδέναι• οὗ γὰρ μὴ διαφέρει, ταὐτὸν εἶναι τούτωι, οὗ δὲ διαφέρει, ἕτερον τούτου.	97a7 Yet some hold it impossible to know the differentiae distinguishing each thing from every single other thing without knowing every single other thing; and one cannot, they say, know each thing without knowing its differentiae, since everything is identical with that from which it does not differ, and other than that from which it differs.
πρῶτον μὲν οὖν τοῦτο ψεῦδος• οὐ γὰρ κατὰ πᾶσαν διαφορὰν ἕτερον• πολλαὶ γὰρ διαφοραὶ ὑπάρχουσι τοῖς αὐτοῖς τῶι εἴδει, ἀλλ᾽ οὐ κατ᾽ οὐσίαν οὐδὲ καθ᾽ αὑτά.	97a11 Now first of all this is a fallacy: not every differentia precludes identity, since many differentiae inhere in things specifically identical, though not in the substance of these nor essentially.
εἶτα ὅταν λάβηι τἀντικείμενα καὶ τὴν διαφορὰν καὶ ↵ὅτι πᾶν ἐμπίπτει ἐνταῦθα ἢ ἐνταῦθα, καὶ λάβηι ἐν θατέρωι τὸ ζητούμενον εἶναι, καὶ τοῦτο γινώσκηι, οὐδὲν διαφέρει εἰδέναι ἢ μὴ εἰδέναι ἐφ᾽ ὅσων κατηγοροῦνται ἄλλων αἱ διαφοραί. φανερὸν γὰρ ὅτι ἂν οὕτω βαδίζων ἔλθηι εἰς ταῦτα ὧν μηκέτι ἔστι διαφορά, ἕξει τὸν λόγον τῆς οὐσίας.	97a13 Secondly, when one has taken one’s differing pair of opposites and assumed that the two sides exhaust the genus, and that the subject one seeks to define is present in one or other of them, and one has further verified its presence in one of them; then it does not matter whether or not one knows all the other subjects of which the differentiae are also predicated. For it is obvious that when by this process one reaches subjects incapable of further differentiation one will possess the formula defining the substance.
τὸ δ᾽ ↵ἅπαν ἐμπίπτειν εἰς τὴν διαίρεσιν, ἂν ἦι ἀντικείμενα ὧν μὴ ἔστι μεταξύ, οὐκ αἴτημα• ἀνάγκη γὰρ ἅπαν ἐν θατέρωι αὐτῶν εἶναι, εἴπερ ἐκείνου διαφορά ἐστι.	97a19 Moreover, to postulate that the division exhausts the genus is not illegitimate if the opposites exclude a middle; since if it is the differentia of that genus, anything contained in the genus must lie on one of the two sides.
Εἰς δὲ τὸ κατασκευάζειν ὅρον διὰ τῶν διαιρέσεων τριῶν δεῖ στοχάζεσθαι, τοῦ λαβεῖν τὰ κατηγορούμενα ἐν τῶι τί ↵ἐστι, καὶ ταῦτα τάξαι τί πρῶτον ἢ δεύτερον, καὶ ὅτι ταῦτα πάντα.	97a23 In establishing a definition by division one should keep three objects in view: (1) the admission only of elements in the definable form, (2) the arrangement of these in the right order, (3) the omission of no such elements.
ἔστι δὲ τούτων ἓν πρῶτον διὰ τοῦ δύνασθαι, ὥσπερ πρὸς συμβεβηκὸς συλλογίσασθαι ὅτι ὑπάρχει, καὶ διὰ τοῦ γένους κατασκευάσαι.	97a25 The first is feasible because one can establish genus and differentia through the topic of the genus, just as one can conclude the inherence of an accident through the topic of the accident.
τὸ δὲ τάξαι ὡς δεῖ ἔσται, ἐὰν τὸ πρῶτον λάβηι. τοῦτο δ᾽ ἔσται, ἐὰν ληφθῆι ὁ πᾶσιν ἀκολου↵θεῖ, ἐκείνωι δὲ μὴ πάντα• ἀνάγκη γὰρ εἶναί τι τοιοῦτον. ληφθέντος δὲ τούτου ἤδη ἐπὶ τῶν κάτω ὁ αὐτὸς τρόπος• δεύτερον γὰρ τὸ τῶν ἄλλων πρῶτον ἔσται, καὶ τρίτον τὸ τῶν ἐχομένων• ἀφαιρεθέντος γὰρ τοῦ ἄνωθεν τὸ ἐχόμενον τῶν ἄλλων πρῶτον ἔσται. ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.	97a28 The right order will be achieved if the right term is assumed as primary, and this will be ensured if the term selected is predicable of all the others but not all they of it; since there must be one such term. Having assumed this we at once proceed in the same way with the lower terms; for our second term will be the first of the remainder, our third the first of those which follow the second in a ‘contiguous’ series, since when the higher term is excluded, that term of the remainder which is ‘contiguous’ to it will be primary, and so on.
↵ὅτι δ᾽ ἅπαντα ταῦτα, φανερὸν ἐκ τοῦ λαβεῖν τό τε πρῶτον κατὰ διαίρεσιν, ὅτι ἅπαν ἢ τόδε ἢ τόδε ζῶιον, ὑπάρχει δὲ τόδε, καὶ πάλιν τούτου ὅλου τὴν διαφοράν, τοῦ δὲ τελευταίου μηκέτι εἶναι διαφοράν, ἢ καὶ εὐθὺς μετὰ τῆς τελευταίας διαφορᾶς τοῦ συνόλου μὴ διαφέρειν εἴδει ἔτι τοῦτο.	97a34 Our procedure makes it clear that no elements in the definable form have been omitted: we have taken the differentia that comes first in the order of division, pointing out that animal, e.g. is divisible exhaustively into A and B, and that the subject accepts one of the two as its predicate. Next we have taken the differentia of the whole thus reached, and shown that the whole we finally reach is not further divisible-i.e. that as soon as we have taken the last differentia to form the concrete totality, this totality admits of no division into species.
[97b]δῆλον γὰρ ὅτι οὔτε πλεῖον πρόσκειται (πάντα γὰρ ἐν τῶι τί ἐστιν εἴληπται τούτων) οὔτε ἀπολείπει οὐδέν• ἢ γὰρ γένος ἢ διαφορὰ ἂν εἴη. γένος μὲν οὖν τό τε πρῶτον, καὶ μετὰ τῶν διαφορῶν τοῦτο προσλαμβανόμενον• αἱ διαφοραὶ δὲ πᾶ↵σαι ἔχονται• οὐ γὰρ ἔτι ἔστιν ὑστέρα• εἴδει γὰρ ἂν διέφερε τὸ τελευταῖον, τοῦτο δ᾽ εἴρηται μὴ διαφέρειν.	97b1 For it is clear that there is no superfluous addition, since all these terms we have selected are elements in the definable form; and nothing lacking, since any omission would have to be a genus or a differentia. Now the primary term is a genus, and this term taken in conjunction with its differentiae is a genus: moreover the differentiae are all included, because there is now no further differentia; if there were, the final concrete would admit of division into species, which, we said, is not the case.
Ζητεῖν δὲ δεῖ ἐπιβλέποντα ἐπὶ τὰ ὅμοια καὶ ἀδιά- φορα, πρῶτον τί ἅπαντα ταὐτὸν ἔχουσιν, εἶτα πάλιν ἐφ᾽ ἑτέροις, ἃ ἐν ταὐτῶι μὲν γένει ἐκείνοις, εἰσὶ δὲ αὑτοῖς μὲν ↵ταὐτὰ τῶι εἴδει, ἐκείνων δ᾽ ἕτερα. ὅταν δ᾽ ἐπὶ τούτων ληφθῆι τί πάντα ταὐτόν, καὶ ἐπὶ τῶν ἄλλων ὁμοίως, ἐπὶ τῶν εἰλημμένων πάλιν σκοπεῖν εἰ ταὐτόν, ἕως ἂν εἰς ἕνα ἔλθηι λόγον• οὗτος γὰρ ἔσται τοῦ πράγματος ὁρισμός. ἐὰν δὲ μὴ βαδίζηι εἰς ἕνα ἀλλ᾽ εἰς δύο ἢ πλείους, δῆλον ὅτι οὐκ ἂν εἴη ↵ἕν τι εἶναι τὸ ζητούμενον, ἀλλὰ πλείω.	97b7 To resume our account of the right method of investigation: We must start by observing a set of similar-i.e. specifically identical-individuals, and consider what element they have in common. We must then apply the same process to another set of individuals which belong to one species and are generically but not specifically identical with the former set. When we have established what the common element is in all members of this second species, and likewise in members of further species, we should again consider whether the results established possess any identity, and persevere until we reach a single formula, since this will be the definition of the thing. But if we reach not one formula but two or more, evidently the definiendum cannot be one thing but must be more than one.
οἷον λέγω, εἰ τί ἐστι μεγαλοψυχία ζητοῖμεν, σκεπτέον ἐπί τινων μεγαλοψύχων, οὓς ἴσμεν, τί ἔχουσιν ἓν πάντες ἧι τοιοῦτοι. οἷον εἰ Ἀλκιβιάδης μεγαλόψυχος ἢ ὁ Ἀχιλλεὺς καὶ ὁ Αἴας, τί ἓν ἅπαντες; τὸ μὴ ἀνέχεσθαι ὑβριζόμενοι• ὁ μὲν γὰρ ἐπο↵λέμησεν, ὁ δ᾽ ἐμήνισεν, ὁ δ᾽ ἀπέκτεινεν ἑαυτόν. πάλιν ἐφ᾽ ἑτέρων, οἷον Λυσάνδρου ἢ Σωκράτους. εἰ δὴ τὸ ἀδιάφοροι εἶναι εὐτυχοῦντες καὶ ἀτυχοῦντες, ταῦτα δύο λαβὼν σκοπῶ τί τὸ αὐτὸ ἔχουσιν ἥ τε ἀπάθεια ἡ περὶ τὰς τύχας καὶ ἡ μὴ ὑπομονὴ ἀτιμαζομένων. εἰ δὲ μηδέν, δύο εἴδη ἂν εἴη ↵τῆς μεγαλοψυχίας.	97b15 I may illustrate my meaning as follows. If we were inquiring what the essential nature of pride is, we should examine instances of proud men we know of to see what, as such, they have in common; e.g. if Alcibiades was proud, or Achilles and Ajax were proud, we should find on inquiring what they all had in common, that it was intolerance of insult; it was this which drove Alcibiades to war, Achilles wrath, and Ajax to suicide. We should next examine other cases, Lysander, for example, or Socrates, and then if these have in common indifference alike to good and ill fortune, I take these two results and inquire what common element have equanimity amid the vicissitudes of life and impatience of dishonour. If they have none, there will be two genera of pride.
αἰεὶ δ᾽ ἐστὶ πᾶς ὅρος καθόλου• οὐ γάρ τινι ὀφθαλμῶι λέγει τὸ ὑγιεινὸν ὁ ἰατρός, ἀλλ᾽ ἢ παντὶ ἢ εἴδει ἀφορίσας.	97b26 Besides, every definition is always universal and commensurate: the physician does not prescribe what is healthy for a single eye, but for all eyes or for a determinate species of eye.
ῥᾶιόν τε τὸ καθ᾽ ἕκαστον ὁρίσασθαι ἢ τὸ καθόλου, διὸ δεῖ ἀπὸ τῶν καθ᾽ ἕκαστα ἐπὶ τὰ καθόλου μεταβαίνειν• καὶ ↵γὰρ αἱ ὁμωνυμίαι λανθάνουσι μᾶλλον ἐν τοῖς καθόλου ἢ ἐν τοῖς ἀδιαφόροις.	97b28 It is also easier by this method to define the single species than the universal, and that is why our procedure should be from the several species to the universal genera-this for the further reason too that equivocation is less readily detected in genera than in infimae species.
ὥσπερ δὲ ἐν ταῖς ἀποδείξεσι δεῖ τό γε συλλελογίσθαι ὑπάρχειν, οὕτω καὶ ἐν τοῖς ὅροις τὸ σαφές. τοῦτο δ᾽ ἔσται, ἐὰν διὰ τῶν καθ᾽ ἕκαστον εἰλημμένων ἦι τὸ ἐν ἑκάστωι γένει ὁρίζεσθαι χωρίς, οἷον τὸ ὅμοιον μὴ πᾶν ἀλλὰ ↵τὸ ἐν χρώμασι καὶ σχήμασι, καὶ ὀξὺ τὸ ἐν φωνῆι, καὶ οὕτως ἐπὶ τὸ κοινὸν βαδίζειν, εὐλαβούμενον μὴ ὁμωνυμίαι ἐντύχηι.	97b31 Indeed, perspicuity is essential in definitions, just as inferential movement is the minimum required in demonstrations; and we shall attain perspicuity if we can collect separately the definition of each species through the group of singulars which we have established e.g. the definition of similarity not unqualified but restricted to colours and to figures; the definition of acuteness, but only of sound-and so proceed to the common universal with a careful avoidance of equivocation.
εἰ δὲ μὴ διαλέγεσθαι δεῖ μεταφοραῖς, δῆλον ὅτι οὐδ᾽ ὁρίζεσθαι οὔτε μεταφοραῖς οὔτε ὅσα λέγεται μεταφοραῖς• διαλέγεσθαι γὰρ ἀνάγκη ἔσται μεταφοραῖς.	97b38 We may add that if dialectical disputation must not employ metaphors, clearly metaphors and metaphorical expressions are precluded in definition: otherwise dialectic would involve metaphors.
c14	Chapter 14
[98a]Πρὸς δὲ τὸ ἔχειν τὰ προβλήματα ἐκλέγειν δεῖ τάς τε ἀνατομὰς καὶ τὰς διαιρέσεις, οὕτω δὲ ἐκλέγειν, ὑποθέμενον τὸ γένος τὸ κοινὸν ἁπάντων, οἷον εἰ ζῶια εἴη τὰ τεθεωρημένα, ποῖα παντὶ ζώιωι ὑπάρχει, ληφθέντων δὲ τούτων, ↵πάλιν τῶν λοιπῶν τῶι πρώτωι ποῖα παντὶ ἕπεται, οἷον εἰ τοῦτο ὄρνις, ποῖα παντὶ ἕπεται ὄρνιθι, καὶ οὕτως αἰεὶ τῶι ἐγγύτατα• δῆλον γὰρ ὅτι ἕξομεν ἤδη λέγειν τὸ διὰ τί ὑπάρχει τὰ ἑπόμενα τοῖς ὑπὸ τὸ κοινόν, οἷον διὰ τί ἀνθρώπωι ἢ ἵππωι ὑπάρχει. ἔστω δὲ ζῶιον ἐφ᾽ οὗ Α, τὸ δὲ Β τὰ ↵ἑπόμενα παντὶ ζώιωι, ἐφ᾽ ὧν δὲ Γ Δ Ε τὰ τινὰ ζῶια. δῆλον δὴ διὰ τί τὸ Β ὑπάρχει τῶι Δ• διὰ γὰρ τὸ Α. ὁμοίως δὲ καὶ τοῖς ἄλλοις• καὶ ἀεὶ ἐπὶ τῶν κάτω ὁ αὐτὸς λόγος.	14 98a1In order to formulate the connexions we wish to prove we have to select our analyses and divisions. The method of selection consists in laying down the common genus of all our subjects of investigation-if e.g. they are animals, we lay down what the properties are which inhere in every animal. These established, we next lay down the properties essentially connected with the first of the remaining classes-e.g. if this first subgenus is bird, the essential properties of every bird-and so on, always characterizing the proximate subgenus. This will clearly at once enable us to say in virtue of what character the subgenera-man, e.g. or horse-possess their properties. Let A be animal, B the properties of every animal, C D E various species of animal. Then it is clear in virtue of what character B inheres in D-namely A-and that it inheres in C and E for the same reason: and throughout the remaining subgenera always the same rule applies.
Νῦν μὲν οὖν κατὰ τὰ παραδεδομένα κοινὰ ὀνόματα λέγομεν, δεῖ δὲ μὴ μόνον ἐπὶ τούτων σκοπεῖν, ἀλλὰ καὶ ↵ἂν ἄλλο τι ὀφθῆι ὑπάρχον κοινόν, ἐκλαμβάνοντα, εἶτα τίσι τοῦτ᾽ ἀκολουθεῖ καὶ ποῖα τούτωι ἕπεται, οἷον τοῖς κέρατα ἔχουσι τὸ ἔχειν ἐχῖνον, τὸ μὴ ἀμφώδοντ᾽ εἶναι• πάλιν τὸ κέρατ᾽ ἔχειν τίσιν ἕπεται. δῆλον γὰρ διὰ τί ἐκείνοις ὑπάρξει τὸ εἰρημένον• διὰ γὰρ τὸ κέρατ᾽ ἔχειν ὑπάρξει.	98a13 We are now taking our examples from the traditional class-names, but we must not confine ourselves to considering these. We must collect any other common character which we observe, and then consider with what species it is connected and what.properties belong to it. For example, as the common properties of horned animals we collect the possession of a third stomach and only one row of teeth. Then since it is clear in virtue of what character they possess these attributes-namely their horned character-the next question is, to what species does the possession of horns attach?
↵Ἔτι δ᾽ ἄλλος τρόπος ἐστὶ κατὰ τὸ ἀνάλογον ἐκλέγειν. ἓν γὰρ λαβεῖν οὐκ ἔστι τὸ αὐτό, ὁ δεῖ καλέσαι σήπιον καὶ ἄκανθαν καὶ ὀστοῦν• ἔσται δ᾽ ἑπόμενα καὶ τούτοις ὥσπερ μιᾶς τινος φύσεως τῆς τοιαύτης οὔσης.	98a20 Yet a further method of selection is by analogy: for we cannot find a single identical name to give to a squid’s pounce, a fish’s spine, and an animal’s bone, although these too possess common properties as if there were a single osseous nature.
c15	Chapter 15
Τὰ δ᾽ αὐτὰ προβλήματά ἐστι τὰ μὲν τῶι τὸ αὐτὸ ↵μέσον ἔχειν, οἷον ὅτι πάντα ἀντιπερίστασις. τούτων δ᾽ ἔνια τῶι γένει ταὐτά, ὅσα ἔχει διαφορὰς τῶι ἄλλων ἢ ἄλλως εἶναι, οἷον διὰ τί ἠχεῖ, ἢ διὰ τί ἐμφαίνεται, καὶ διὰ τί ἶρις• ἅπαντα γὰρ ταῦτα τὸ αὐτὸ πρόβλημά ἐστι γένει (πάντα γὰρ ἀνάκλασισ), ἀλλ᾽ εἴδει ἕτερα.	15 98a23 Some connexions that require proof are identical in that they possess an identical ‘middle’ e.g. a whole group might be proved through ‘reciprocal replacement’-and of these one class are identical in genus, namely all those whose difference consists in their concerning different subjects or in their mode of manifestation. This latter class may be exemplified by the questions as to the causes respectively of echo, of reflection, and of the rainbow: the connexions to be proved which these questions embody are identical generically, because all three are forms of repercussion; but specifically they are different.
τὰ δὲ τῶι τὸ ↵μέσον ὑπὸ τὸ ἕτερον μέσον εἶναι διαφέρει τῶν προβλημάτων, οἷον διὰ τί ὁ Νεῖλος φθίνοντος τοῦ μηνὸς μᾶλλον ῥεῖ; διότι χειμεριώτερος φθίνων ὁ μείς. διὰ τί δὲ χειμεριώτερος φθίνων; διότι ἡ σελήνη ἀπολείπει. ταῦτα γὰρ οὕτως ἔχει πρὸς ἄλληλα.	98a29 Other connexions that require proof only differ in that the ‘middle’ of the one is subordinate to the ‘middle’ of the other. For example: Why does the Nile rise towards the end of the month? Because towards its close the month is more stormy. Why is the month more stormy towards its close? Because the moon is waning. Here the one cause is subordinate to the other.
c16	Chapter 16
Περὶ δ᾽ αἰτίου καὶ οὗ αἴτιον ἀπορήσειε μὲν ἄν τις, ἆρα ὅτε ὑπάρχει τὸ αἰτιατόν, καὶ τὸ αἴτιον ὑπάρχει (ὥσπερ εἰ φυλλορροεῖ ἢ ἐκλείπει, καὶ τὸ αἴτιον τοῦ ἐκλείπειν ἢ φυλλορροεῖν ἔσται• οἷον εἰ τοῦτ᾽ ἔστι τὸ πλατέα ἔχειν τὰ	16 98a35 The question might be raised with regard to cause and effect whether when the effect is present the cause also is present; whether, for instance, if a plant sheds its leaves or the moon is eclipsed, there is present also the cause of the eclipse or of the fall of the leaves-the possession of broad leaves, let us say, in the latter case, in the former the earth’s interposition.
[98b]φύλλα, τοῦ δ᾽ ἐκλείπειν τὸ τὴν γῆν ἐν μέσωι εἶναι• εἰ γὰρ μὴ ὑπάρχει, ἄλλο τι ἔσται τὸ αἴτιον αὐτῶν), εἴ τε τὸ αἴτιον ὑπάρχει, ἅμα καὶ τὸ αἰτιατόν (οἷον εἰ ἐν μέσωι ἡ γῆ, ἐκλείπει, ἢ εἰ πλατύφυλλον, φυλλορροεῖ).	98b2 For, one might argue, if this cause is not present, these phenomena will have some other cause: if it is present, its effect will be at once implied by it-the eclipse by the earth’s interposition, the fall of the leaves by the possession of broad leaves; but if so, they will be logically coincident
εἰ δ᾽ οὕτως, ἅμ᾽ ↵ἂν εἴη καὶ δεικνύοιτο δι᾽ ἀλλήλων. ἔστω γὰρ τὸ φυλλορροεῖν ἐφ᾽ οὗ Α, τὸ δὲ πλατύφυλλον ἐφ᾽ οὗ Β, ἄμπελος δὲ ἐφ᾽ οὗ Γ. εἰ δὴ τῶι Β ὑπάρχει τὸ Α (πᾶν γὰρ πλατύφυλλον φυλλορροεῖ), τῶι δὲ Γ ὑπάρχει τὸ Β (πᾶσα γὰρ ἄμπελος πλατύφυλλοσ), τῶι Γ ὑπάρχει τὸ Α, καὶ πᾶσα ἄμ↵πελος φυλλορροεῖ. αἴτιον δὲ τὸ Β τὸ μέσον. ἀλλὰ καὶ ὅτι πλατύφυλλον ἡ ἄμπελος, ἔστι διὰ τοῦ φυλλορροεῖν ἀποδεῖξαι. ἔστω γὰρ τὸ μὲν Δ πλατύφυλλον, τὸ δὲ Ε τὸ φυλλορροεῖν, ἄμπελος δὲ ἐφ᾽ οὗ Ζ. τῶι δὴ Ζ ὑπάρχει τὸ Ε (φυλλορροεῖ γὰρ πᾶσα ἄμπελοσ), τῶι δὲ Ε τὸ Δ (ἅπαν ↵γὰρ τὸ φυλλορροοῦν πλατύφυλλον)• πᾶσα ἄρα ἄμπελος πλατύφυλλον.	98b4 and each capable of proof through the other. Let me illustrate: Let A be deciduous character, B the possession of broad leaves, C vine. Now if A inheres in B (for every broad-leaved plant is deciduous), and B in C (every vine possessing broad leaves); then A inheres in C (every vine is deciduous), and the middle term B is the cause. But we can also demonstrate that the vine has broad leaves because it is deciduous. Thus, let D be broad-leaved, E deciduous, F vine. Then E inheres in F (since every vine is deciduous), and D in E (for every deciduous plant has broad leaves): therefore every vine has broad leaves, and the cause is its deciduous character.
αἴτιον δὲ τὸ φυλλορροεῖν. εἰ δὲ μὴ ἐνδέχεται αἴτια εἶναι ἀλλήλων (τὸ γὰρ αἴτιον πρότερον οὗ αἴτιον, καὶ τοῦ μὲν ἐκλείπειν αἴτιον τὸ ἐν μέσωι τὴν γῆν εἶναι, τοῦ δ᾽ ἐν μέσωι τὴν γῆν εἶναι οὐκ αἴτιον τὸ ἐκλείπειν) – εἰ οὖν ἡ μὲν διὰ τοῦ αἰτίου ↵ἀπόδειξις τοῦ διὰ τί, ἡ δὲ μὴ διὰ τοῦ αἰτίου τοῦ ὅτι, ὅτι μὲν ἐν μέσωι, οἶδε, διότι δ᾽ οὔ.	98b16 If, however, they cannot each be the cause of the other (for cause is prior to effect, and the earth’s interposition is the cause of the moon’s eclipse and not the eclipse of the interposition)-if, then, demonstration through the cause is of the reasoned fact and demonstration not through the cause is of the bare fact, one who knows it through the eclipse knows the fact of the earth’s interposition but not the reasoned fact.
ὅτι δ᾽ οὐ τὸ ἐκλείπειν αἴτιον τοῦ ἐν μέσωι, ἀλλὰ τοῦτο τοῦ ἐκλείπειν, φανερόν• ἐν γὰρ τῶι λόγωι τῶι τοῦ ἐκλείπειν ἐνυπάρχει τὸ ἐν μέσωι, ὥστε δῆλον ὅτι διὰ τούτου ἐκεῖνο γνωρίζεται, ἀλλ᾽ οὐ τοῦτο δι᾽ ἐκείνου.	98b22 Moreover, that the eclipse is not the cause of the interposition, but the interposition of the eclipse, is obvious because the interposition is an element in the definition of eclipse, which shows that the eclipse is known through the interposition and not vice versa.
↵Η ἐνδέχεται ἑνὸς πλείω αἴτια εἶναι; καὶ γὰρ εἰ ἔστι τὸ αὐτὸ πλειόνων πρώτων κατηγορεῖσθαι, ἔστω τὸ Α τῶι Β πρώτωι ὑπάρχον, καὶ τῶι Γ ἄλλωι πρώτωι, καὶ ταῦτα τοῖς Δ Ε. ὑπάρξει ἄρα τὸ Α τοῖς Δ Ε• αἴτιον δὲ τῶι μὲν Δ τὸ Β, τῶι δὲ Ε τὸ Γ• ὥστε τοῦ μὲν αἰτίου ὑπάρχοντος ἀνάγκη ↵τὸ πρᾶγμα ὑπάρχειν, τοῦ δὲ πράγματος ὑπάρχοντος οὐκ ἀνάγκη πᾶν ὁ ἂν ἦι αἴτιον, ἀλλ᾽ αἴτιον μέν, οὐ μέντοι πᾶν.	98b25 On the other hand, can a single effect have more than one cause? One might argue as follows: if the same attribute is predicable of more than one thing as its primary subject, let B be a primary subject in which A inheres, and C another primary subject of A, and D and E primary subjects of B and C respectively. A will then inhere in D and E, and B will be the cause of A’s inherence in D, C of A’s inherence in E. The presence of the cause thus necessitates that of the effect, but the presence of the effect necessitates the presence not of all that may cause it but only of a cause which yet need not be the whole cause.
ἢ εἰ ἀεὶ καθόλου τὸ πρόβλημά ἐστι, καὶ τὸ αἴτιον ὅλον τι, καὶ οὗ αἴτιον, καθόλου; οἷον τὸ φυλλορροεῖν ὅλωι τινὶ ἀφωρισμένον, κἂν εἴδη αὐτοῦ ἦι, καὶ τοισδὶ καθόλου, ἢ φυτοῖς ἢ τοιοισδὶ ↵φυτοῖς• ὥστε καὶ τὸ μέσον ἴσον δεῖ εἶναι ἐπὶ τούτων καὶ οὗ αἴτιον, καὶ ἀντιστρέφειν. οἷον διὰ τί τὰ δένδρα φυλλορροεῖ; εἰ δὴ διὰ πῆξιν τοῦ ὑγροῦ, εἴτε φυλλορροεῖ δένδρον, δεῖ ὑπάρχειν πῆξιν, εἴτε πῆξις ὑπάρχει, μὴ ὁτωιοῦν ἀλλὰ δένδρωι, φυλλορροεῖν.	98b32 We may, however, suggest that if the connexion to be proved is always universal and commensurate, not only will the cause be a whole but also the effect will be universal and commensurate. For instance, deciduous character will belong exclusively to a subject which is a whole, and, if this whole has species, universally and commensurately to those species-i.e. either to all species of plant or to a single species. So in these universal and commensurate connexions the ‘middle’ and its effect must reciprocate, i.e. be convertible. Supposing, for example, that the reason why trees are deciduous is the coagulation of sap, then if a tree is deciduous, coagulation must be present, and if coagulation is present-not in any subject but in a tree-then that tree must be deciduous.
c17	Chapter 17
[99a]Πότερον δ᾽ ἐνδέχεται μὴ τὸ αὐτὸ αἴτιον εἶναι τοῦ αὐτοῦ πᾶσιν ἀλλ᾽ ἕτερον, ἢ οὔ;	17 99a1 Can the cause of an identical effect be not identical in every instance of the effect but different? Or is that impossible?
ἢ εἰ μὲν καθ᾽ αὑτὸ ἀποδέδεικται καὶ μὴ κατὰ σημεῖον ἢ συμβεβηκός, οὐχ οἷόν τε• ὁ γὰρ λόγος τοῦ ἄκρου τὸ μέσον ἐστίν• εἰ δὲ μὴ οὕτως, ἐνδέχεται.	99a2 Perhaps it is impossible if the effect is demonstrated as essential and not as inhering in virtue of a symptom or an accident-because the middle is then the definition of the major term-though possible if the demonstration is not essential.
ἔστι ↵δὲ καὶ οὗ αἴτιον καὶ ὧι σκοπεῖν κατὰ συμβεβηκός• οὐ μὴν δοκεῖ προβλήματα εἶναι. εἰ δὲ μή, ὁμοίως ἕξει τὸ μέσον• εἰ μὲν ὁμώνυμα, ὁμώνυμον τὸ μέσον, εἰ δ᾽ ὡς ἐν γένει, ὁμοίως ἕξει. οἷον διὰ τί καὶ ἐναλλὰξ ἀνάλογον; ἄλλο γὰρ αἴτιον ἐν γραμμαῖς καὶ ἀριθμοῖς καὶ τὸ αὐτό γε, ἧι μὲν ↵γραμμή, ἄλλο, ἧι δ᾽ ἔχον αὔξησιν τοιανδί, τὸ αὐτό. οὕτως ἐπὶ πάντων. τοῦ δ᾽ ὅμοιον εἶναι χρῶμα χρώματι καὶ σχῆμα σχήματι ἄλλο ἄλλωι. ὁμώνυμον γὰρ τὸ ὅμοιον ἐπὶ τούτων• ἔνθα μὲν γὰρ ἴσως τὸ ἀνάλογον ἔχειν τὰς πλευρὰς καὶ ἴσας τὰς γωνίας, ἐπὶ δὲ χρωμάτων τὸ τὴν αἴσθη↵σιν μίαν εἶναι ἤ τι ἄλλο τοιοῦτον. τὰ δὲ κατ᾽ ἀναλογίαν τὰ αὐτὰ καὶ τὸ μέσον ἕξει κατ᾽ ἀναλογίαν.	99a4 Now it is possible to consider the effect and its subject as an accidental conjunction, though such conjunctions would not be regarded as connexions demanding scientific proof. But if they are accepted as such, the middle will correspond to the extremes, and be equivocal if they are equivocal, generically one if they are generically one. Take the question why proportionals alternate. The cause when they are lines, and when they are numbers, is both different and identical; different in so far as lines are lines and not numbers, identical as involving a given determinate increment. In all proportionals this is so. Again, the cause of likeness between colour and colour is other than that between figure and figure; for likeness here is equivocal, meaning perhaps in the latter case equality of the ratios of the sides and equality of the angles, in the case of colours identity of the act of perceiving them, or something else of the sort. Again, connexions requiring proof which are identical by analogy middles also analogous.
Ἔχει δ᾽ οὕτω τὸ παρακολουθεῖν τὸ αἴτιον ἀλλήλοις καὶ οὗ αἴτιον καὶ ὧι αἴτιον• καθ᾽ ἕκαστον μὲν λαμβάνοντι τὸ οὗ αἴτιον ἐπὶ πλέον, οἷον τὸ τέτταρσιν ἴσας τὰς ἔξω ἐπὶ πλέον ἢ τρίγωνον ἢ τε↵τράγωνον, ἅπασι δὲ ἐπ᾽ ἴσον (ὅσα γὰρ τέτταρσιν ὀρθαῖς ἴσας τὰς ἔξω)• καὶ τὸ μέσον ὁμοίως. ἔστι δὲ τὸ μέσον λό- γος τοῦ πρώτου ἄκρου, διὸ πᾶσαι αἱ ἐπιστῆμαι δι᾽ ὁρισμοῦ γίγνονται. οἷον τὸ φυλλορροεῖν ἅμα ἀκολουθεῖ τῆι ἀμπέλωι καὶ ὑπερέχει, καὶ συκῆι, καὶ ὑπερέχει• ἀλλ᾽ οὐ πάντων, ↵ἀλλ᾽ ἴσον. εἰ δὴ λάβοις τὸ πρῶτον μέσον, λόγος τοῦ φυλλορροεῖν ἐστιν. ἔσται γὰρ πρῶτον μὲν ἐπὶ θάτερα μέσον, ὅτι τοιαδὶ ἅπαντα• εἶτα τούτου μέσον, ὅτι ὀπὸς πήγνυται ἤ τι ἄλλο τοιοῦτον. τί δ᾽ ἐστὶ τὸ φυλλορροεῖν; τὸ πήγνυσθαι τὸν ἐν τῆι συνάψει τοῦ σπέρματος ὀπόν.	99al7 <A name=bk99al7></A>The truth is that cause, effect, and subject are reciprocally predicable in the following way. If the species are taken severally, the effect is wider than the subject (e.g. the possession of external angles equal to four right angles is an attribute wider than triangle or are), but it is coextensive with the species taken collectively (in this instance with all figures whose external angles are equal to four right angles). And the middle likewise reciprocates, for the middle is a definition of the major; which is incidentally the reason why all the sciences are built up through definition. We may illustrate as follows. Deciduous is a universal attribute of vine, and is at the same time of wider extent than vine; and of fig, and is of wider extent than fig: but it is not wider than but coextensive with the totality of the species. Then if you take the middle which is proximate, it is a definition of deciduous. I say that, because you will first reach a middle next the subject, and a premiss asserting it of the whole subject, and after that a middle-the coagulation of sap or something of the sort-proving the connexion of the first middle with the major: but it is the coagulation of sap at the junction of leaf-stalk and stem which defines deciduous.
↵Ἐπὶ δὲ τῶν σχημάτων ὧδε ἀποδώσει ζητοῦσι τὴν παρακολούθησιν τοῦ αἰτίου καὶ οὗ αἴτιον. ἔστω τὸ Α τῶι Β ὑπάρχειν παντί, τὸ δὲ Β ἑκάστωι τῶν Δ, ἐπὶ πλέον δέ. τὸ μὲν δὴ Β καθόλου ἂν εἴη τοῖς Δ• τοῦτο γὰρ λέγω καθόλου ὧι μὴ ἀντιστρέφει, πρῶτον δὲ καθόλου ὧι ἕκαστον μὲν μὴ ἀντι↵στρέφει, ἅπαντα δὲ ἀντιστρέφει καὶ παρεκτείνει. τοῖς δὴ Δ αἴτιον τοῦ Α τὸ Β. δεῖ ἄρα τὸ Α ἐπὶ πλέον τοῦ Β ἐπεκτείνειν• εἰ δὲ μή, τί μᾶλλον αἴτιον ἔσται τοῦτο ἐκείνου; εἰ δὴ πᾶσιν ὑπάρχει τοῖς Ε τὸ Α, ἔσται τι ἐκεῖνα ἓν ἅπαντα ἄλλο τοῦ Β. εἰ γὰρ μή, πῶς ἔσται εἰπεῖν ὅτι ὧι τὸ Ε, τὸ [99b]Α παντί, ὧι δὲ τὸ Α, οὐ παντὶ τὸ Ε; διὰ τί γὰρ οὐκ ἔσται τι αἴτιον οἷον [τὸ Α] ὑπάρχει πᾶσι τοῖς Δ; ἀλλ᾽ ἆρα καὶ τὰ Ε ἔσται τι ἕν; ἐπισκέψασθαι δεῖ τοῦτο, καὶ ἔστω τὸ Γ. ἐνδέχεται δὴ τοῦ αὐτοῦ πλείω αἴτια εἶναι, ἀλλ᾽ οὐ τοῖς αὐ↵τοῖς τῶι εἴδει, οἷον τοῦ μακρόβια εἶναι τὰ μὲν τετράποδα τὸ μὴ ἔχειν χολήν, τὰ δὲ πτηνὰ τὸ ξηρὰ εἶναι ἢ ἕτερόν τι. Εἰ δὲ εἰς τὸ ἄτομον μὴ εὐθὺς ἔρχονται, καὶ μὴ μόνον ἓν τὸ μέσον ἀλλὰ πλείω, καὶ τὰ αἴτια πλείω.	99a30 If an explanation in formal terms of the inter-relation of cause and effect is demanded, we shall offer the following. Let A be an attribute of all B, and B of every species of D, but so that both A and B are wider than their respective subjects. Then B will be a universal attribute of each species of D (since I call such an attribute universal even if it is not commensurate, and I call an attribute primary universal if it is commensurate, not with each species severally but with their totality), and it extends beyond each of them taken separately. Thus, B is the cause of A’s inherence in the species of D: consequently A must be of wider extent than B; otherwise why should B be the cause of A’s inherence in D any more than A the cause of B’s inherence in D? Now if A is an attribute of all the species of E, all the species of E will be united by possessing some common cause other than B: otherwise how shall we be able to say that A is predicable of all of which E is predicable, while E is not predicable of all of which A can be predicated? I mean how can there fail to be some special cause of A's inherence in E, as there was of A's inherence in all the species of D? Then are the species of E, too, united by possessing some common cause? This cause we must look for. Let us call it C.We conclude, then, that the same effect may have more than one cause, but not in subjects specifically identical. For instance, the cause of longevity in quadrupeds is lack of bile, in birds a dry constitution-or certainly something different.
c18	Chapter 18
Πότερον δ᾽ αἴτιον τῶν μέσων, τὸ πρὸς τὸ καθόλου πρῶ↵τον ἢ τὸ πρὸς τὸ καθ᾽ ἕκαστον, τοῖς καθ᾽ ἕκαστον; δῆλον δὴ ὅτι τὰ ἐγγύτατα ἑκάστωι ὧι αἴτιον. τοῦ γὰρ τὸ πρῶτον ὑπὸ τὸ καθόλου ὑπάρχειν τοῦτο αἴτιον, οἷον τῶι Δ τὸ Γ τοῦ τὸ Β ὑπάρχειν αἴτιον. τῶι μὲν οὖν Δ τὸ Γ αἴτιον τοῦ Α, τῶι δὲ Γ τὸ Β, τούτωι δὲ αὐτό.	18 99b7 If immediate premisses are not reached at once, and there is not merely one middle but several middles, i.e. several causes; is the cause of the property’s inherence in the several species the middle which is proximate to the primary universal, or the middle which is proximate to the species? Clearly the cause is that nearest to each species severally in which it is manifested, for that is the cause of the subject’s falling under the universal. To illustrate formally: C is the cause of B’s inherence in D; hence C is the cause of A’s inherence in D, B of A’s inherence in C, while the cause of A’s inherence in B is B itself.
c19	Chapter 19
Περὶ μὲν οὖν συλλογισμοῦ καὶ ἀποδείξεως, τί τε ἑκάτερόν ἐστι καὶ πῶς γίνεται, φανερόν, ἅμα δὲ καὶ περὶ ἐπιστήμης ἀποδεικτικῆς• ταὐτὸν γάρ ἐστιν.	19 99b15 As regards syllogism and demonstration, the definition of, and the conditions required to produce each of them, are now clear, and with that also the definition of, and the conditions required to produce, demonstrative knowledge, since it is the same as demonstration.
περὶ δὲ τῶν ἀρχῶν, πῶς τε γίνονται γνώριμοι καὶ τίς ἡ γνωρίζουσα ἕξις, ἐντεῦθεν ἔσται δῆλον προαπορήσασι πρῶτον.	99b18 As to the basic premisses, how they become known and what is the developed state of knowledge of them is made clear by raising some preliminary problems.
↵Ὅτι μὲν οὖν οὐκ ἐνδέχεται ἐπίστασθαι δι᾽ ἀποδείξεως μὴ γιγνώσκοντι τὰς πρώτας ἀρχὰς τὰς ἀμέσους, εἴρηται πρότερον.	99b20 We have already said that scientific knowledge through demonstration is impossible unless a man knows the primary immediate premisses.
τῶν δ᾽ ἀμέσων τὴν γνῶσιν, καὶ πότερον ἡ αὐτή ἐστιν ἢ οὐχ ἡ αὐτή, διαπορήσειεν ἄν τις, καὶ πότερον ἐπιστήμη ἑκατέρου [ἢ οὔ], ἢ τοῦ μὲν ἐπιστήμη τοῦ δ᾽ ἕτερόν τι γέ↵νος, καὶ πότερον οὐκ ἐνοῦσαι αἱ ἕξεις ἐγγίνονται ἢ ἐνοῦσαι λελήθασιν.	99b23 But there are questions which might be raised in respect of the apprehension of these immediate premisses: one might not only ask whether it is of the same kind as the apprehension of the conclusions, but also whether there is or is not scientific knowledge of both; or scientific knowledge of the latter, and of the former a different kind of knowledge; and, further, whether the developed states of knowledge are not innate but come to be in us, or are innate but at first unnoticed.
εἰ μὲν δὴ ἔχομεν αὐτάς, ἄτοπον• συμβαίνει γὰρ ἀκριβεστέρας ἔχοντας γνώσεις ἀποδείξεως λανθάνειν.	99b26 Now it is strange if we possess them from birth; for it means that we possess apprehensions more accurate than demonstration and fail to notice them.
εἰ δὲ λαμβάνομεν μὴ ἔχοντες πρότερον, πῶς ἂν γνωρίζοιμεν καὶ μανθάνοιμεν ἐκ μὴ προϋπαρχούσης γνώσεως; ἀδύ↵νατον γάρ, ὥσπερ καὶ ἐπὶ τῆς ἀποδείξεως ἐλέγομεν.	99b28 If on the other hand we acquire them and do not previously possess them, how could we apprehend and learn without a basis of pre-existent knowledge? For that is impossible, as we used to find in the case of demonstration.
φανερὸν τοίνυν ὅτι οὔτ᾽ ἔχειν οἷόν τε, οὔτ᾽ ἀγνοοῦσι καὶ μηδεμίαν ἔχουσιν ἕξιν ἐγγίγνεσθαι.	99b30 So it emerges that neither can we possess them from birth, nor can they come to be in us if we are without knowledge of them to the extent of having no such developed state at all.
ἀνάγκη ἄρα ἔχειν μέν τινα δύναμιν, μὴ τοιαύτην δ᾽ ἔχειν ἣ ἔσται τούτων τιμιωτέρα κατ᾽ ἀκρίβειαν.	99b32 Therefore we must possess a capacity of some sort, but not such as to rank higher in accuracy than these developed states.
φαίνεται δὲ τοῦτό γε πᾶσιν ὑπάρχον τοῖς ζώιοις. ↵ἔχει γὰρ δύναμιν σύμφυτον κριτικήν, ἣν καλοῦσιν αἴσθησιν•	99b34 And this at least is an obvious characteristic of all animals, for they possess a congenital discriminative capacity which is called sense-perception.
ἐνούσης δ᾽ αἰσθήσεως τοῖς μὲν τῶν ζώιων ἐγγίγνεται μονὴ τοῦ αἰσθήματος, τοῖς δ᾽ οὐκ ἐγγίγνεται. ὅσοις μὲν οὖν μὴ ἐγγίγνεται, ἢ ὅλως ἢ περὶ ἃ μὴ ἐγγίγνεται, οὐκ ἔστι τούτοις γνῶσις ἔξω τοῦ αἰσθάνεσθαι• ἐν οἷς δ᾽ ἔνεστιν αἰσθομένοις ἔχειν [100a]ἔτι ἐν τῆι ψυχῆι.	99b36 But though sense-perception is innate in all animals, in some the sense-impression comes to persist, in others it does not. So animals in which this persistence does not come to be have either no knowledge at all outside the act of perceiving, or no knowledge of objects of which no impression persists; animals in which it does come into being have perception and can continue to retain the sense-impression in the soul:
πολλῶν δὲ τοιούτων γινομένων ἤδη διαφορά τις γίνεται, ὥστε τοῖς μὲν γίνεσθαι λόγον ἐκ τῆς τῶν τοιού- των μονῆς, τοῖς δὲ μή.	100a1 and when such persistence is frequently repeated a further distinction at once arises between those which out of the persistence of such sense-impressions develop a power of systematizing them and those which do not.
Ἐκ μὲν οὖν αἰσθήσεως γίνεται μνήμη, ὥσπερ λέγομεν, ἐκ δὲ μνήμης πολλάκις τοῦ αὐτοῦ γινομέ↵νης ἐμπειρία• αἱ γὰρ πολλαὶ μνῆμαι τῶι ἀριθμῶι ἐμπειρία μία ἐστίν. ἐκ δ᾽ ἐμπειρίας ἢ ἐκ παντὸς ἠρεμήσαντος τοῦ καθόλου ἐν τῆι ψυχῆι, τοῦ ἑνὸς παρὰ τὰ πολλά, ὁ ἂν ἐν ἅπασιν ἓν ἐνῆι ἐκείνοις τὸ αὐτό, τέχνης ἀρχὴ καὶ ἐπιστήμης, ἐὰν μὲν περὶ γένεσιν, τέχνης, ἐὰν δὲ περὶ τὸ ὄν, ἐπιστήμης. ↵οὔτε δὴ ἐνυπάρχουσιν ἀφωρισμέναι αἱ ἕξεις, οὔτ᾽ ἀπ᾽ ἄλλων ἕξεων γίνονται γνωστικωτέρων, ἀλλ᾽ ἀπὸ αἰσθήσεως, οἷον ἐν μάχηι τροπῆς γενομένης ἑνὸς στάντος ἕτερος ἔστη, εἶθ᾽ ἕτερος, ἕως ἐπὶ ἀρχὴν ἦλθεν. ἡ δὲ ψυχὴ ὑπάρχει τοιαύτη οὖσα οἵα δύνασθαι πάσχειν τοῦτο.	100a4 So out of sense-perception comes to be what we call memory, and out of frequently repeated memories of the same thing develops experience; for a number of memories constitute a single experience. From experience again-i.e. from the universal now stabilized in its entirety within the soul, the one beside the many which is a single identity within them all-originate the skill of the craftsman and the knowledge of the man of science, skill in the sphere of coming to be and science in the sphere of being. We conclude that these states of knowledge are neither innate in a determinate form, nor developed from other higher states of knowledge, but from sense-perception. It is like a rout in battle stopped by first one man making a stand and then another, until the original formation has been restored. The soul is so constituted as to be capable of this process.
ὁ δ᾽ ἐλέχθη μὲν πάλαι, ↵οὐ σαφῶς δὲ ἐλέχθη, πάλιν εἴπωμεν. στάντος γὰρ τῶν ἀδιαφόρων ἑνός, πρῶτον μὲν ἐν τῆι ψυχῆι καθόλου (καὶ γὰρ αἰσθάνεται μὲν τὸ καθ᾽ ἕκαστον, ἡ δ᾽ αἴσθησις τοῦ καθόλου [100b]ἐστίν, οἷον ἀνθρώπου, ἀλλ᾽ οὐ Καλλίου ἀνθρώπου)• πάλιν ἐν τούτοις ἵσταται, ἕως ἂν τὰ ἀμερῆ στῆι καὶ τὰ καθόλου, οἷον τοιονδὶ ζῶιον, ἕως ζῶιον, καὶ ἐν τούτωι ὡσαύτως. δῆλον δὴ ὅτι ἡμῖν τὰ πρῶτα ἐπαγωγῆι γνωρίζειν ἀναγκαῖον• καὶ γὰρ ↵ἡ αἴσθησις οὕτω τὸ καθόλου ἐμποιεῖ.	100a14 Let us now restate the account given already, though with insufficient clearness. When one of a number of logically indiscriminable particulars has made a stand, the earliest universal is present in the soul: for though the act of sense-perception is of the particular, its content is universal-is man, for example, not the man Callias. A fresh stand is made among these rudimentary universals, and the process does not cease until the indivisible concepts, the true universals, are established: e.g. such and such a species of animal is a step towards the genus animal, which by the same process is a step towards a further generalization. Thus it is clear that we must get to know the primary premisses by induction; for the method by which even sense-perception implants the universal is inductive.
Ἐπεὶ δὲ τῶν περὶ τὴν διάνοιαν ἕξεων αἷς ἀληθεύομεν αἱ μὲν ἀεὶ ἀληθεῖς εἰσιν, αἱ δὲ ἐπιδέχονται τὸ ψεῦδος, οἷον δόξα καὶ λογισμός, ἀληθῆ δ᾽ ἀεὶ ἐπιστήμη καὶ νοῦς, καὶ οὐδὲν ἐπιστήμης ἀκριβέστερον ἄλλο γένος ἢ νοῦς, αἱ δ᾽ ἀρχαὶ τῶν ἀποδείξεων γνωριμώ↵τεραι, ἐπιστήμη δ᾽ ἅπασα μετὰ λόγου ἐστί, τῶν ἀρχῶν ἐπιστήμη μὲν οὐκ ἂν εἴη, ἐπεὶ δ᾽ οὐδὲν ἀληθέστερον ἐνδέχεται εἶναι ἐπιστήμης ἢ νοῦν, νοῦς ἂν εἴη τῶν ἀρχῶν, ἔκ τε τούτων σκοποῦσι καὶ ὅτι ἀποδείξεως ἀρχὴ οὐκ ἀπόδειξις, ὥστ᾽ οὐδ᾽ ἐπιστήμης ἐπιστήμη. εἰ οὖν μηδὲν ἄλλο παρ᾽ ἐπιστήμην γέ↵νος ἔχομεν ἀληθές, νοῦς ἂν εἴη ἐπιστήμης ἀρχή. καὶ ἡ μὲν ἀρχὴ τῆς ἀρχῆς εἴη ἄν, ἡ δὲ πᾶσα ὁμοίως ἔχει πρὸς τὸ πᾶν πρᾶγμα.	100b5 Now of the thinking states by which we grasp truth, some are unfailingly true, others admit of error-opinion, for instance, and calculation, whereas scientific knowing and intuition are always true: further, no other kind of thought except intuition is more accurate than scientific knowledge, whereas primary premisses are more knowable than demonstrations, and all scientific knowledge is discursive. From these considerations it follows that there will be no scientific knowledge of the primary premisses, and since except intuition nothing can be truer than scientific knowledge, it will be intuition that apprehends the primary premisses-a result which also follows from the fact that demonstration cannot be the originative source of demonstration, nor, consequently, scientific knowledge of scientific knowledge.If, therefore, it is the only other kind of true thinking except scientific knowing, intuition will be the originative source of scientific knowledge. And the originative source of science grasps the original basic premiss, while science as a whole is similarly related as originative source to the whole body of fact.