Authors/Aristotle/metaphysics/l10

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Chapter 1

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METHAPHISICE ARISTOTILIS LIBER DECIMUS Aristotle Metaphysics Book 10 (I)
[1052α] [15] τὸ ἓν ὅτι μὲν λέγεται πολλαχῶς, ἐν τοῖς περὶ τοῦ ποσαχῶς διῃρημένοις εἴρηται πρότερον: πλεοναχῶς δὲ λεγομένου οἱ συγκεφαλαιούμενοι τρόποι εἰσὶ τέτταρες τῶν πρώτων καὶ καθ᾽ αὑτὰ λεγομένων ἓν ἀλλὰ μὴ κατὰ συμβεβηκός. τό τε γὰρ συνεχὲς ἢ ἁπλῶς ἢ μάλιστά γε [20] τὸ φύσει καὶ μὴ ἁφῇ μηδὲ δεσμῷ (καὶ τούτων μᾶλλον ἓν καὶ πρότερον οὗ ἀδιαιρετωτέρα ἡ κίνησις καὶ μᾶλλον ἁπλῆ): > Unum quia multis modis dicitur, in divisis de quotiens dictum est prius. Multipliciter vero dicto capitales modi sunt quatuor primorum et secundum se dictorum unum sed non secundum accidens. Continuum enim, aut simpliciter aut maxime quod natura et non tactu nec ligatione; et horum magis unum et prius cuius indivisibilior motus est et magis simplex. Chapter 1. WE have said previously, in our distinction of the various meanings of words, that one has several meanings; the things that are directly and of their own nature and not accidentally called one may be summarized under four heads, though the word is used in more senses. (1) There is the continuous, either in general, or especially that which is continuous by nature and not by contact nor by being together; and of these, that has more unity and is prior, whose movement is more indivisible and simpler. (2)
ἔτι τοιοῦτον καὶ μᾶλλον τὸ ὅλον καὶ ἔχον τινὰ μορφὴν καὶ εἶδος, μάλιστα δ᾽ εἴ τι φύσει τοιοῦτον καὶ μὴ βίᾳ, ὥσπερ ὅσα κόλλῃ ἢ γόμφῳ ἢ συνδέσμῳ, ἀλλὰ ἔχει ἐν αὑτῷ τὸ [25] αἴτιον αὐτῷ τοῦ συνεχὲς εἶναι. Amplius tale et magis totum et habens aliquam formam et speciem, maxime autem si quid natura est tale et non vi, ut quaecumque visco aut clauo aut coniunctione, sed habet in se quod est causa sibi ut sit continuum. That which is a whole and has a certain shape and form is one in a still higher degree; and especially if a thing is of this sort by nature, and not by force like the things which are unified by glue or nails or by being tied together, i.e. if it has in itself the cause of its continuity.
τοιοῦτον δὲ τῷ μίαν τὴν κίνησιν εἶναι καὶ ἀδιαίρετον τόπῳ καὶ χρόνῳ, ὥστε φανερόν, εἴ τι φύσει κινήσεως ἀρχὴν ἔχει τῆς πρώτης τὴν πρώτην, οἷον λέγω φορᾶς κυκλοφορίαν, ὅτι τοῦτο πρῶτον μέγεθος ἕν. τὰ μὲν δὴ οὕτως ἓν ᾗ συνεχὲς ἢ ὅλον, Tale vero in Motum unum esse et indivisibile loco et tempore. Quare palam *, si quid per naturam motus habet principium primi primum, ut puta dico lationis circulationem, quia haec prima magnitudo una. Haec quidem itaque sic unum * continuum aut totum. A thing is of this sort because its movement is one and indivisible in place and time; so that evidently if a thing has by nature a principle of movement that is of the first kind (i.e. local movement) and the first in that kind (i.e. circular movement), this is in the primary sense one extended thing. Some things, then, are one in this way, qua continuous or whole, and
τὰ δὲ ὧν ἂν ὁ λόγος [30] εἷς ᾖ, τοιαῦτα δὲ ὧν ἡ νόησις μία, τοιαῦτα δὲ ὧν ἀδιαίρετος, ἀδιαίρετος δὲ τοῦ ἀδιαιρέτου εἴδει ἢ ἀριθμῷ: ἀριθμῷ μὲν οὖν τὸ καθ᾽ ἕκαστον ἀδιαίρετον, εἴδει δὲ τὸ τῷ γνωστῷ καὶ τῇ ἐπιστήμῃ, ὥσθ᾽ ἓν ἂν εἴη πρῶτον τὸ ταῖς οὐσίαις αἴτιον τοῦ ἑνός. Haec autem, si ratio una fuerit. Talia vero sunt quorum intelligentia una, talia autem quorum indivisibilis; indivisibilis vero eius quod indivisibile specie aut numero. Numero vero singulare indivisibile, specie vero quod nosci>bili et scientie; quare unum utique erit primum quod substantiis causa unius. the other things that are one are those whose definition is one. Of this sort are the things the thought of which is one, i.e. those the thought of which is indivisible; and it is indivisible if the thing is indivisible in kind or in number. (3) In number, then, the individual is indivisible, and (4) in kind, that which in intelligibility and in knowledge is indivisible, so that that which causes substances to be one must be one in the primary sense.
λέγεται μὲν οὖν τὸ ἓν τοσαυταχῶς, τό τε [35] συνεχὲς φύσει καὶ τὸ ὅλον, καὶ τὸ καθ᾽ ἕκαστον καὶ τὸ καθόλου, πάντα δὲ ταῦτα ἓν τῷ ἀδιαίρετον εἶναι τῶν μὲν τὴν κίνησιν τῶν δὲ τὴν νόησιν ἢ τὸν λόγον. Dicitur quidem igitur unum tot modis: continuum natura et totum et singulare et universale. Omnia vero haec unum per indivisibile esse, horum quidem motum, illorum autem intelligentiam aut rationem. One , then, has all these meanings – the naturally continuous and the whole, and the individual and the universal. And all these are one because in some cases the movement, in others the thought or the definition is indivisible. [52b]
[1052β] [1] —δεῖ δὲ κατανοεῖν ὅτι οὐχ ὡσαύτως ληπτέον λέγεσθαι ποῖά τε ἓν λέγεται, καὶ τί ἐστι τὸ ἑνὶ εἶναι καὶ τίς αὐτοῦ λόγος. λέγεται μὲν γὰρ τὸ ἓν τοσαυταχῶς, καὶ ἕκαστον ἔσται ἓν τούτων, ᾧ [5] ἂν ὑπάρχῃ τις τούτων τῶν τρόπων: τὸ δὲ ἑνὶ εἶναι ὁτὲ μὲν τούτων τινὶ ἔσται, ὁτὲ δὲ ἄλλῳ ὃ καὶ μᾶλλον ἐγγὺς τῷ ὀνόματί ἐστι, τῇ δυνάμει δ᾽ ἐκεῖνα, ὥσπερ καὶ περὶ στοιχείου καὶ αἰτίου εἰ δέοι λέγειν ἐπί τε τοῖς πράγμασι διορίζοντα καὶ τοῦ ὀνόματος ὅρον ἀποδιδόντα. ἔστι μὲν γὰρ ὡς [10] στοιχεῖον τὸ πῦρ (ἔστι δ᾽ ἴσως καθ᾽ αὑτὸ καὶ τὸ ἄπειρον ἤ τι ἄλλο τοιοῦτον), ἔστι δ᾽ ὡς οὔ: οὐ γὰρ τὸ αὐτὸ πυρὶ καὶ στοιχείῳ εἶναι, ἀλλ᾽ ὡς μὲν πρᾶγμά τι καὶ φύσις τὸ πῦρ στοιχεῖον, τὸ δὲ ὄνομα σημαίνει τὸ τοδὶ συμβεβηκέναι αὐτῷ, ὅτι ἐστί τι ἐκ τούτου ὡς πρώτου ἐνυπάρχοντος. οὕτω [15] καὶ ἐπὶ αἰτίου καὶ ἑνὸς καὶ τῶν τοιούτων ἁπάντων, διὸ καὶ τὸ ἑνὶ εἶναι τὸ ἀδιαιρέτῳ ἐστὶν εἶναι, ὅπερ τόδε ὄντι καὶ ἰδίᾳ χωριστῷ ἢ τόπῳ ἢ εἴδει ἢ διανοίᾳ, ἢ καὶ τὸ ὅλῳ καὶ ἀδιαιρέτῳ, Oportet autem intelligere quia non similiter sumendum est dici qualia unum dicuntur, et quid est uni esse et quae ipsius * ratio. Dicitur enim unum tot modis, et unumquodque erit unum horum cuicumque extiterit horum aliquis modorum. Uni autem esse quandoque quidem horum alicui inerit, quandoque autem alii quod et magis propinquum nomini est, potentia vero illa. Sicut de elemento et causa, si oportet dicere * in rebus determinantem et nominis terminum reddentem. Est quidem enim ut elementum ignis (est autem forsan secundum se et infinitum aut aliquid aliud tale), est autem ut non. Non enim idem igni et elemento esse, sed ut quidem re et natura ignis elementum; nomen vero significat: eo quod hoc acciderit ipsi, quia est aliquid ex hoc ut primo inexistente. Sic et in causa et in uno et talibus omnibus. Propter quod et uni esse indivisibili est esse, quod quidem * hoc enti et inseparabili aut loco aut specie aut mente, aut et toto et determinato. But it must be observed that the questions, what sort of things are said to be one, and what it is to be one and what is the definition of it, should not be assumed to be the same. One has all these meanings, and each of the things to which one of these kinds of unity belongs will be one; but to be one will sometimes mean being one of these things, and sometimes being something else which is even nearer to the meaning of the word one while these other things approximate to its application. This is also true of element or cause , if one had both to specify the things of which it is predicable and to render the definition of the word. For in a sense fire is an element (and doubtless also the indefinite or something else of the sort is by its own nature the element), but in a sense it is not; for it is not the same thing to be fire and to be an element, but while as a particular thing with a nature of its own fire is an element, the name element means that it has this attribute, that there is something which is made of it as a primary constituent. And so with cause and one and all such terms. For this reason, too, to be one means to be indivisible, being essentially one means a this and capable of being isolated either in place, or in form or thought; or perhaps to be whole and indivisible ;
μάλιστα δὲ τὸ μέτρῳ εἶναι πρώτῳ ἑκάστου γένους καὶ κυριώτατα τοῦ ποσοῦ: ἐντεῦθεν γὰρ ἐπὶ τὰ ἄλλα ἐλήλυθεν. [20] μέτρον γάρ ἐστιν ᾧ τὸ ποσὸν γιγνώσκεται: γιγνώσκεται δὲ ἢ ἑνὶ ἢ ἀριθμῷ τὸ ποσὸν ᾗ ποσόν, ὁ δὲ ἀριθμὸς ἅπας ἑνί, ὥστε πᾶν τὸ ποσὸν γιγνώσκεται ᾗ ποσὸν τῷ ἑνί, Maxime vero in eo quod est metrum esse primum uniuscuiusque generis et maxime proprie quantitatis; hinc enim ad alia venit. Metrum etenim est quo quantitas cognoscitur; cognoscitur vero aut uno aut numero quantitas in quantum quantitas, numerus autem omnis uno. Quare omnis quantitas cognoscitur in quantum quantitas uno, but it means especially to be the first measure of a kind , and most strictly of quantity; for it is from this that it has been extended to the other categories. For measure is that by which quantity is known; and quantity qua quantity is known either by a one or by a number, and all number is known by a one . Therefore all quantity qua quantity is known by the one,
καὶ ᾧ πρώτῳ ποσὰ γιγνώσκεται, τοῦτο αὐτὸ ἕν: διὸ τὸ ἓν ἀριθμοῦ ἀρχὴ ᾗ ἀριθμός. et quo primo cognosci>tur, hoc ipsum unum; quapropter unum numeri principium secundum quod numerus. and that by which quantities are primarily known is the one itself; and so the one is the starting-point of number qua number.
ἐντεῦθεν δὲ καὶ ἐν τοῖς ἄλλοις [25] λέγεται μέτρον τε ᾧ ἕκαστον πρώτῳ γιγνώσκεται, καὶ τὸ μέτρον ἑκάστου ἕν, ἐν μήκει, ἐν πλάτει, ἐν βάθει, ἐν βάρει, ἐν τάχει (τὸ γὰρ βάρος καὶ τάχος κοινὸν ἐν τοῖς ἐναντίοις: διττὸν γὰρ ἑκάτερον αὐτῶν, οἷον βάρος τό τε ὁποσηνοῦν ἔχον ῥοπὴν καὶ τὸ ἔχον ὑπεροχὴν ῥοπῆς, καὶ τάχος τό τε ὁποσηνοῦν [30] κίνησιν ἔχον καὶ τὸ ὑπεροχὴν κινήσεως: ἔστι γάρ τι τάχος καὶ τοῦ βραδέος καὶ βάρος τοῦ κουφοτέρου). Hinc autem et in aliis dicitur metrum quo primo unumquodque cognoscitur. Et metrum uniuscuiusque unum, in longitudine, in latitudine, in profunditate, in gravitate, in velocitate. Gravitas enim et velocitas commune in contrariis; duplex enim eorum utrumque, ut grave et quod est quantamcumque habens inclinationem et quod est habens excessum inclinationis, et velocitas et quantumcumque motum habens et excessum motus; est enim velocitas quaedam et tardi et gravitas levioris. And hence in the other classes too measure means that by which each is first known, and the measure of each is a unit – in length, in breadth, in depth, in weight, in speed. (The words weight and speed are common to both contraries; for each of them has two meanings – weight means both that which has any amount of gravity and that which has an excess of gravity, and speed both that which has any amount of movement and that which has an excess of movement; for even the slow has a certain speed and the comparatively light a certain weight.)
ἐν πᾶσι δὴ τούτοις μέτρον καὶ ἀρχὴ ἕν τι καὶ ἀδιαίρετον, ἐπεὶ καὶ ἐν ταῖς γραμμαῖς χρῶνται ὡς ἀτόμῳ τῇ ποδιαίᾳ. πανταχοῦ γὰρ τὸ μέτρον ἕν τι ζητοῦσι καὶ ἀδιαίρετον: τοῦτο δὲ [35] τὸ ἁπλοῦν ἢ τῷ ποιῷ ἢ τῷ ποσῷ. ὅπου μὲν οὖν δοκεῖ μὴ εἶναι ἀφελεῖν ἢ προσθεῖναι, τοῦτο ἀκριβὲς τὸ μέτρον (διὸ τὸ τοῦ ἀριθμοῦ ἀκριβέστατον: [1053α] [1] τὴν γὰρ μονάδα τιθέασι πάντῃ ἀδιαίρετον): ἐν δὲ τοῖς ἄλλοις μιμοῦνται τὸ τοιοῦτον: ἀπὸ γὰρ σταδίου καὶ ταλάντου καὶ ἀεὶ τοῦ μείζονος λάθοι ἂν καὶ προστεθέν τι καὶ ἀφαιρεθὲν μᾶλλον ἢ ἀπὸ ἐλάττονος: [5] ὥστε ἀφ᾽ οὗ πρώτου κατὰ τὴν αἴσθησιν μὴ ἐνδέχεται, τοῦτο πάντες ποιοῦνται μέτρον καὶ ὑγρῶν καὶ ξηρῶν καὶ βάρους καὶ μεγέθους: καὶ τότ᾽ οἴονται εἰδέναι τὸ ποσόν, ὅταν εἰδῶσι διὰ τούτου τοῦ μέτρου. In omnibus autem hiis metrum et principium unum aliquid et indivisibile, quoniam et in lineis utuntur quasi indivisibili pedali. Vbique namque metrum unum aliquid quaerunt et indivisibile; hoc autem quod simplex aut quali aut quanto. vbicumque quidem igitur videtur non esse aveerre aut addere, hoc est certum metrum. Quapropter numeros certissimum; unitatem enim ponunt omnino indivisibilem. In aliis vero imitantur tale. A stadio enim et talento et semper maiore latebit utique et additum aliquid et ablatum magis quam a minore; quare a quo primo secundum sensum non contingit, hoc omnes faciunt metrum et humidorum et siccorum et gravitatis et magnitudinis; et tunc putant cognoscere quantum, quando cognoscunt per hoc metrum. In all these, then, the measure and starting-point is something one and indivisible, since even in lines we treat as indivisible the line a foot long. For everywhere we seek as the measure something one and indivisible; and this is that which is simple either in quality or in quantity. Now where it is thought impossible to take away or to add, there the measure is exact (hence that of number is [53a] most exact; for we posit the unit as indivisible in every respect); but in all other cases we imitate this sort of measure. For in the case of a furlong or a talent or of anything comparatively large any addition or subtraction might more easily escape our notice than in the case of something smaller; so that the first thing from which, as far as our perception goes, nothing can be subtracted, all men make the measure, whether of liquids or of solids, whether of weight or of size; and they think they know the quantity when they know it by means of this measure.
καὶ δὴ καὶ κίνησιν τῇ ἁπλῇ κινήσει καὶ τῇ ταχίστῃ (ὀλίγιστον γὰρ αὕτη ἔχει χρόνον): [10] διὸ ἐν τῇ ἀστρολογίᾳ τὸ τοιοῦτον ἓν ἀρχὴ καὶ μέτρον (τὴν κίνησιν γὰρ ὁμαλὴν ὑποτίθενται καὶ ταχίστην τὴν τοῦ οὐρανοῦ, πρὸς ἣν κρίνουσι τὰς ἄλλας), καὶ ἐν μουσικῇ δίεσις, ὅτι ἐλάχιστον, καὶ ἐν φωνῇ στοιχεῖον. καὶ ταῦτα πάντα ἕν τι οὕτως, οὐχ ὡς κοινόν τι τὸ ἓν ἀλλ᾽ ὥσπερ εἴρηται. Et motum autem simplici motu et velocissimo; paruissimum enim hic habet tempus. Quapropter in astrologia tale unum * principium et metrum; motum enim regularem supponunt et velocissimum eum qui > * celi, ad quem alios iudicant. Et in musica diesis, quia minimum. Et in voce elementum. Et haec omnia unum aliquid ita, non ut commune aliquid quod unum sed sicut dictum est. And indeed they know movement too by the simple movement and the quickest; for this occupies least time. And so in astronomy a one of this sort is the starting-point and measure (for they assume the movement of the heavens to be uniform and the quickest, and judge the others by reference to it), and in music the quarter-tone (because it is the least interval), and in speech the letter. And all these are ones in this sense – not that one is something predicable in the same sense of all of these, but in the sense we have mentioned.
οὐκ ἀεὶ [15] δὲ τῷ ἀριθμῷ ἓν τὸ μέτρον ἀλλ᾽ ἐνίοτε πλείω, οἷον αἱ διέσεις δύο, αἱ μὴ κατὰ τὴν ἀκοὴν ἀλλ᾽ ἐν τοῖς λόγοις, καὶ αἱ φωναὶ πλείους αἷς μετροῦμεν, καὶ ἡ διάμετρος δυσὶ μετρεῖται καὶ ἡ πλευρά, καὶ τὰ μεγέθη πάντα. οὕτω δὴ πάντων μέτρον τὸ ἕν, ὅτι γνωρίζομεν ἐξ ὧν ἐστὶν ἡ οὐσία διαιροῦντες [20] ἢ κατὰ τὸ ποσὸν ἢ κατὰ τὸ εἶδος. καὶ διὰ τοῦτο τὸ ἓν ἀδιαίρετον, ὅτι τὸ πρῶτον ἑκάστων ἀδιαίρετον. οὐχ ὁμοίως δὲ πᾶν ἀδιαίρετον, οἷον ποὺς καὶ μονάς, ἀλλὰ τὸ μὲν πάντῃ, τὸ δ᾽ εἰς ἀδιαίρετα πρὸς τὴν αἴσθησιν θετέον, ὥσπερ εἴρηται ἤδη: ἴσως γὰρ πᾶν συνεχὲς διαιρετόν. Non semper autem numero unum metrum, verum aliquando plura, ut dieses due, quae non secundum auditum sed in rationibus, et voces plures quibus mensuramus, et diameter duobus mensuratur et latus, et magnitudines omnes. Sic itaque metrum omnium quod unum, quia cognoscimus ex quibus est substantia, dividentes aut secundum quantitatem aut secundum speciem. Et ideo quod unum indivisibile, quia quod primum * singulorum indivisibile. Non similiter autem omne * indivisibile, ut pes et unitas, sed hoc quidem omnino, illud vero in indivisibilia ad sensum voluit, sicut dictum est iam; nam forsan omne continuum est divisibile. But the measure is not always one in number – sometimes there are several; e.g. the quarter-tones (not to the ear, but as determined by the ratios) are two, and the articulate sounds by which we measure are more than one, and the diagonal of the square and its side are measured by two quantities, and all spatial magnitudes reveal similar varieties of unit. Thus, then, the one is the measure of all things, because we come to know the elements in the substance by dividing the things either in respect of quantity or in respect of kind. And the one is indivisible just because the first of each class of things is indivisible. But it is not in the same way that every one is indivisible e.g. a foot and a unit; the latter is indivisible in every respect, while the former must be placed among things which are undivided to perception, as has been said already – only to perception, for doubtless every continuous thing is divisible.
ἀεὶ δὲ συγγενὲς [25] τὸ μέτρον: μεγεθῶν μὲν γὰρ μέγεθος, καὶ καθ᾽ ἕκαστον μήκους μῆκος, πλάτους πλάτος, φωνῆς φωνή, βάρους βάρος, μονάδων μονάς. οὕτω γὰρ δεῖ λαμβάνειν, ἀλλ᾽ οὐχ ὅτι ἀριθμῶν ἀριθμός: καίτοι ἔδει, εἰ ὁμοίως: ἀλλ᾽ οὐχ ὁμοίως ἀξιοῖ ἀλλ᾽ ὥσπερ εἰ μονάδων μονάδας ἀξιώσειε [30] μέτρον ἀλλὰ μὴ μονάδα: ὁ δ᾽ ἀριθμὸς πλῆθος μονάδων. Semper autem cognatum est metrum. Magnitudinum quidem enim magnitudo, et secundum unumquodque longitudinis longitudo, latitudinis latitudo, vocis vox, gravitatis gravitas, unitatum unitas. Sic enim oportet accipere, sed non quod numerorum numerus, et quidem oportebat, si similiter; sed non similiter dignificat, sed ac si unitatum unitates dignificarent metrum sed non unitatem; numerus autem pluralitas unitatum est. The measure is always homogeneous with the thing measured; the measure of spatial magnitudes is a spatial magnitude, and in particular that of length is a length, that of breadth a breadth, that of articulate sound an articulate sound, that of weight a weight, that of units a unit. (For we must state the matter so, and not say that the measure of numbers is a number; we ought indeed to say this if we were to use the corresponding form of words, but the claim does not really correspond – it is as if one claimed that the measure of units is units and not a unit; number is a plurality of units.)
καὶ τὴν ἐπιστήμην δὲ μέτρον τῶν πραγμάτων λέγομεν καὶ τὴν αἴσθησιν διὰ τὸ αὐτό, ὅτι γνωρίζομέν τι αὐταῖς, ἐπεὶ μετροῦνται μᾶλλον ἢ μετροῦσιν. ἀλλὰ συμβαίνει ἡμῖν ὥσπερ ἂν εἰ ἄλλου ἡμᾶς μετροῦντος ἐγνωρίσαμεν πηλίκοι ἐσμὲν [35] τῷ τὸν πῆχυν ἐπὶ τοσοῦτον ἡμῶν ἐπιβάλλειν. Πρωταγόρας δ᾽ ἄνθρωπόν φησι πάντων εἶναι μέτρον, ὥσπερ ἂν εἰ τὸν ἐπιστήμονα εἰπὼν ἢ τὸν αἰσθανόμενον: [1053β] [1] τούτους δ᾽ ὅτι ἔχουσιν ὁ μὲν αἴσθησιν ὁ δὲ ἐπιστήμην, ἅ φαμεν εἶναι μέτρα τῶν ὑποκειμένων. οὐθὲν δὴ λέγοντες περιττὸν φαίνονταί τι λέγειν. Et scientiam autem metrum rerum dicimus et sensum propter idem, quia cognoscimus aliquid ipsis, quoniam mensurantur magis quam mensurant. Sed accidit nobis veluti si alio nos mensurante cognoscamus quanti sumus per cubitum ad tantum nostri adicere. Protagoras vero hominem omnium ait esse metrum, > ac utique si scientem dicens aut sentientem; hos autem quia habent hic quidem sensum ille vero scientiam, quae dicimus esse metra eorum quae subiciuntur. Nihil itaque dicentes superhabundans videntur aliquid dicere. Knowledge, also, and perception, we call the measure of things for the same reason, because we come to know something by them – while as a matter of fact they are measured rather than measure other things. But it is with us as if some one else measured us and we came to know how big we are by seeing that he applied the cubit-measure to such and such a fraction of us. But Protagoras says "man is the measure of all things", as if he had said the man who knows or [53b] the man who perceives ; and these because they have respectively knowledge and perception, which we say are the measures of objects. Such thinkers are saying nothing, then, while they appear to be saying something remarkable.
ὅτι μὲν οὖν τὸ ἑνὶ εἶναι μάλιστά ἐστι κατὰ τὸ ὄνομα ἀφορίζοντι [5] μέτρον τι, καὶ κυριώτατα τοῦ ποσοῦ, εἶτα τοῦ ποιοῦ, φανερόν: ἔσται δὲ τοιοῦτον τὸ μὲν ἂν ᾖ ἀδιαίρετον κατὰ τὸ ποσόν, τὸ δὲ ἂν κατὰ τὸ ποιόν: διόπερ ἀδιαίρετον τὸ ἓν ἢ ἁπλῶς ἢ ᾗ ἕν. Quod quidem igitur uni esse maxime est secundum nomen quod determinant metrum quoddam, et maxime proprie quantitatis, deinde qualitatis, palam. Erit autem tale hoc quidem si est indivisibile secundum quantitatem, illud autem si secundum qualitatem; propter quod indivisibile est quod unum aut simpliciter aut in quantum unum. Evidently, then, unity in the strictest sense, if we define it according to the meaning of the word, is a measure, and most properly of quantity, and secondly of quality. And some things will be one if they are indivisible in quantity, and others if they are indivisible in quality; and so that which is one is indivisible, either absolutely or qua one.

Chapter 2

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κατὰ δὲ τὴν οὐσίαν καὶ τὴν φύσιν ζητητέον ποτέρως [10] ἔχει, καθάπερ ἐν τοῖς διαπορήμασιν ἐπήλθομεν τί τὸ ἕν ἐστι καὶ πῶς δεῖ περὶ αὐτοῦ λαβεῖν, πότερον ὡς οὐσίας τινὸς οὔσης αὐτοῦ τοῦ ἑνός, καθάπερ οἵ τε Πυθαγόρειοί φασι πρότερον καὶ Πλάτων ὕστερον, ἢ μᾶλλον ὑπόκειταί τις φύσις καὶ [πῶς] δεῖ γνωριμωτέρως λεχθῆναι καὶ μᾶλλον ὥσπερ οἱ [15] περὶ φύσεως: ἐκείνων γὰρ ὁ μέν τις φιλίαν εἶναί φησι τὸ ἓν ὁ δ᾽ ἀέρα ὁ δὲ τὸ ἄπειρον. Secundum substantiam vero et naturam quaerendum est utro modo se habeat, quemadmodum in dubitationibus tractavimus quid quod unum est et quomodo oportet de eo suscipere: utrum velut substantia aliqua existente ipso uno, sicut pytagorici dicunt prius et Plato posterius, aut magis supponitur aliqua natura, et quomodo oportet notius dici et magis sicut qui de natura; illorum enim alius amicitiam esse dixit quod unum, alius aerem, alius infinitum. Chapter 2. With regard to the substance and nature of the one we must ask in which of two ways it exists. This is the very question that we reviewed in our discussion of problems, viz. what the one is and how we must conceive of it, whether we must take the one itself as being a substance (as both the Pythagoreans say in earlier and Plato in later times), or there is, rather, an underlying nature and the one should be described more intelligibly and more in the manner of the physical philosophers, of whom one says the one is love, another says it is air, and another the indefinite.
εἰ δὴ μηδὲν τῶν καθόλου δυνατὸν οὐσίαν εἶναι, καθάπερ ἐν τοῖς περὶ οὐσίας καὶ περὶ τοῦ ὄντος εἴρηται λόγοις, οὐδ᾽ αὐτὸ τοῦτο οὐσίαν ὡς ἕν τι παρὰ τὰ πολλὰ δυνατὸν εἶναι (κοινὸν γάρ) ἀλλ᾽ ἢ κατηγόρημα [20] μόνον, δῆλον ὡς οὐδὲ τὸ ἕν: τὸ γὰρ ὂν καὶ τὸ ἓν καθόλου κατηγορεῖται μάλιστα πάντων. ὥστε οὔτε τὰ γένη φύσεις τινὲς καὶ οὐσίαι χωρισταὶ τῶν ἄλλων εἰσίν, οὔτε τὸ ἓν γένος ἐνδέχεται εἶναι διὰ τὰς αὐτὰς αἰτίας δι᾽ ἅσπερ οὐδὲ τὸ ὂν οὐδὲ τὴν οὐσίαν. Si itaque nullum universalium esse substantiam est possibile, sicut in sermonibus de substantia et de ente dictum est, nec ipsum hoc substantiam ut unum aliquid praeter multa possibile est esse (commune namque) sed aut predicamentum solum, palam quod neque ipsum unum. Nam ens et unum universaliter predicantur maxime de omnibus. Quare nec genera nature quaedam et substantiae separabiles ab aliis sunt, nec > unum genus contingit esse propter easdem causas propter quas quidem nec ens nec substantiam. If, then, no universal can be a substance, as has been said our discussion of substance and being, and if being itself cannot be a substance in the sense of a one apart from the many (for it is common to the many), but is only a predicate, clearly unity also cannot be a substance; for being and unity are the most universal of all predicates. Therefore, on the one hand, genera are not certain entities and substances separable from other things; and on the other hand the one cannot be a genus, for the same reasons for which being and substance cannot be genera.
ἔτι δ᾽ ὁμοίως ἐπὶ πάντων ἀναγκαῖον ἔχειν: [25] λέγεται δ᾽ ἰσαχῶς τὸ ὂν καὶ τὸ ἕν: ὥστ᾽ ἐπείπερ ἐν τοῖς ποιοῖς ἐστί τι τὸ ἓν καί τις φύσις, ὁμοίως δὲ καὶ ἐν τοῖς ποσοῖς, δῆλον ὅτι καὶ ὅλως ζητητέον τί τὸ ἕν, ὥσπερ καὶ τί τὸ ὄν, ὡς οὐχ ἱκανὸν ὅτι τοῦτο αὐτὸ ἡ φύσις αὐτοῦ. ἀλλὰ μὴν ἔν γε χρώμασίν ἐστι τὸ ἓν χρῶμα, οἷον τὸ λευκόν, εἶτα [30] τὰ ἄλλα ἐκ τούτου καὶ τοῦ μέλανος φαίνεται γιγνόμενα, τὸ δὲ μέλαν στέρησις λευκοῦ ὥσπερ καὶ φωτὸς σκότος [τοῦτο δ᾽ ἐστὶ στέρησις φωτός]: ὥστε εἰ τὰ ὄντα ἦν χρώματα, ἦν ἂν ἀριθμός τις τὰ ὄντα, ἀλλὰ τίνων; δῆλον δὴ ὅτι χρωμάτων, καὶ τὸ ἓν ἦν ἄν τι ἕν, οἷον τὸ λευκόν. ὁμοίως δὲ καὶ [35] εἰ μέλη τὰ ὄντα ἦν, ἀριθμὸς ἂν ἦν, διέσεων μέντοι, ἀλλ᾽ οὐκ ἀριθμὸς ἡ οὐσία αὐτῶν: καὶ τὸ ἓν ἦν ἄν τι οὗ ἡ οὐσία οὐ τὸ ἓν ἀλλὰ δίεσις. [1054α] [1] ὁμοίως δὲ καὶ ἐπὶ τῶν φθόγγων στοιχείων ἂν ἦν τὰ ὄντα ἀριθμός, καὶ τὸ ἓν στοιχεῖον φωνῆεν. καὶ εἰ σχήματα εὐθύγραμμα, σχημάτων ἂν ἦν ἀριθμός, καὶ τὸ ἓν τὸ τρίγωνον. ὁ δ᾽ αὐτὸς λόγος καὶ ἐπὶ τῶν ἄλλων [5] γενῶν, ὥστ᾽ εἴπερ καὶ ἐν τοῖς πάθεσι καὶ ἐν τοῖς ποιοῖς καὶ ἐν τοῖς ποσοῖς καὶ ἐν κινήσει ἀριθμῶν ὄντων καὶ ἑνός τινος ἐν ἅπασιν ὅ τε ἀριθμὸς τινῶν καὶ τὸ ἓν τὶ ἕν, ἀλλ᾽ οὐχὶ τοῦτο αὐτὸ ἡ οὐσία, καὶ ἐπὶ τῶν οὐσιῶν ἀνάγκη ὡσαύτως ἔχειν: ὁμοίως γὰρ ἔχει ἐπὶ πάντων. ὅτι μὲν οὖν τὸ ἓν ἐν [10] ἅπαντι γένει ἐστί τις φύσις, καὶ οὐδενὸς τοῦτό γ᾽ αὐτὸ ἡ φύσις τὸ ἕν, φανερόν, ἀλλ᾽ ὥσπερ ἐν χρώμασι χρῶμα ἓν ζητητέον αὐτὸ τὸ ἕν, οὕτω καὶ ἐν οὐσίᾳ οὐσίαν μίαν αὐτὸ τὸ ἕν: Adhuc autem similiter in omnibus necesse est habere. Dicitur autem equaliter ens et unum. Ergo quoniam in qualitatibus est aliquid quod unum et aliqua natura, et similiter in quantis, palam quod et totaliter quaerendum quid * quod unum, quemadmodum et quid ens, tamquam non * sufficiens quod hoc ipsum * natura ipsius. At vero et in coloribus est aliquid quod color unus, puta albus, deinde alii ex hoc et nigro videntur geniti, nigrum vero privatio albi est, ut et lucis tenebra (haec enim est privatio lucis). Quare si entia essent colores, essent utique numerus quidam entia. Sed quorum? Palam utique quia colorum; et ipsum unum esset utique * aliquid unum, puta album. Similiter autem et si melodie entia essent, numerus utique essent, diesum equidem, sed non * numerus substantia ipsorum; et ipsum unum esset utique aliquid cuius substantia non ipsum unum sed diesis. Similiter autem et in sonis elementorum utique essent entia numerus, et ipsum unum elementum vocale. Et si figure rectilinee, figurarum utique esset numerus, et ipsum unum trigonum. Eadem autem ratio et in aliis generibus. Quare siquidem in * passionibus et in qualitatibus et in quantitatibus et in motu numeris existentibus et uno aliquo in omnibus, numerusque * quorun>dam et ipsum unum aliquid unum, sed non hoc ipsius substantia: et in substantiis necesse est similiter se habere; similiter enim se habet in omnibus. Quod quidem igitur unum in omni genere est quaedam natura, et nullius natura hoc ipsum * quod unum, palam. Sed sicut in coloribus colorem unum quaerendum ipsum quod unum, sic et in substantia substantiam unam ipsum unum. Further, the position must be similar in all the kinds of unity. Now unity has just as many meanings as being ; so that since in the sphere of qualities the one is something definite – some particular kind of thing – and similarly in the sphere of quantities, clearly we must in every category ask what the one is, as we must ask what the existent is, since it is not enough to say that its nature is just to be one or existent. But in colours the one is a colour, e.g. white, and then the other colours are observed to be produced out of this and black, and black is the privation of white, as darkness of light. Therefore if all existent things were colours, existent things would have been a number, indeed, but of what? Clearly of colours; and the one would have been a particular one , i.e. white. And similarly if all existing things were tunes, they would have been a number, but a number of quarter-tones, and their essence would not have been number; and the one would have been something whose substance was not to be one but to [54a] be the quarter-tone. And similarly if all existent things had been articulate sounds, they would have been a number of letters, and the one would have been a vowel. And if all existent things were rectilinear figures, they would have been a number of figures, and the one would have been the triangle. And the same argument applies to all other classes. Since, therefore, while there are numbers and a one both in affections and in qualities and in quantities and in movement, in all cases the number is a number of particular things and the one is one something, and its substance is not just to be one, the same must be true of substances also; for it is true of all cases alike. That the one, then, in every class is a definite thing, and in no case is its nature just this, unity, is evident; but as in colours the one-itself which we must seek is one colour, so too in substance the one-itself is one substance.
ὅτι δὲ ταὐτὸ σημαίνει πως τὸ ἓν καὶ τὸ ὄν, δῆλον τῷ τε παρακολουθεῖν ἰσαχῶς ταῖς κατηγορίαις καὶ μὴ εἶναι ἐν [15] μηδεμιᾷ (οἷον οὔτ᾽ ἐν τῇ τί ἐστιν οὔτ᾽ ἐν τῇ ποῖον, ἀλλ᾽ ὁμοίως ἔχει ὥσπερ τὸ ὄν) καὶ τῷ μὴ προσκατηγορεῖσθαι ἕτερόν τι τὸ εἷς ἄνθρωπος τοῦ ἄνθρωπος (ὥσπερ οὐδὲ τὸ εἶναι παρὰ τὸ τί ἢ ποῖον ἢ πόσον) καὶ <τῷ εἶναι> τὸ ἑνὶ εἶναι τὸ ἑκάστῳ εἶναι. [20] Quia vero idem significant aliqualiter unum et ens, palam per assequi equaliter cathegorias * et quia non sunt in nulla una (ut neque in quid est neque in quale, sed similiter se habet sicut ens) et per hoc quod ‘unus homo’ non predicat alterum aliquid ab homine (quemadmodum nec esse praeter quid aut quale aut quantum) et uni esse id quod unicuique esse. That in a sense unity means the same as being is clear from the facts that its meanings correspond to the categories one to one, and it is not comprised within any category (e.g. it is comprised neither in what a thing is nor in quality, but is related to them just as being is); that in one man nothing more is predicated than in man (just as being is nothing apart from substance or quality or quantity); and that to be one is just to be a particular thing.

Chapter 3

Greek Latin English
ἀντίκειται δὲ τὸ ἓν καὶ τὰ πολλὰ κατὰ πλείους τρόπους, ὧν ἕνα τὸ ἓν καὶ τὸ πλῆθος ὡς ἀδιαίρετον καὶ διαιρετόν: τὸ μὲν γὰρ ἢ διῃρημένον ἢ διαιρετὸν πλῆθός τι λέγεται, τὸ δὲ ἀδιαίρετον ἢ μὴ διῃρημένον ἕν. Opponuntur autem unum et multa secundum plures modos, quorum uno unum et multitudo * ut indivisibile et divisibile. Quod quidem enim aut divisum aut divisibile multitudo quaedam dicitur, indivisibile vero aut non divisum unum. Chapter 3. The one and the many are opposed in several ways, of which one is the opposition of the one and plurality as indivisible and divisible; for that which is either divided or divisible is called a plurality, and that which is indivisible or not divided is called one.
ἐπεὶ οὖν αἱ ἀντιθέσεις τετραχῶς, καὶ τούτων κατὰ στέρησιν λέγεται θάτερον, [25] ἐναντία ἂν εἴη καὶ οὔτε ὡς ἀντίφασις οὔτε ὡς τὰ πρός τι λεγόμενα. Quoniam ergo * quatuor modis oppositiones *, et horum secundum privationem dicitur alterum, contraria utique erunt et neque ut contradictio neque ut ad aliquid dicta. Now since opposition is of four kinds, and one of these two terms is privative in meaning, they must be contraries, and neither contradictory nor correlative in meaning.
λέγεται δὲ ἐκ τοῦ ἐναντίου καὶ δηλοῦται τὸ ἕν, ἐκ τοῦ διαιρετοῦ τὸ ἀδιαίρετον, διὰ τὸ μᾶλλον αἰσθητὸν τὸ πλῆθος εἶναι καὶ τὸ διαιρετὸν ἢ τὸ ἀδιαίρετον, ὥστε τῷ λόγῳ πρότερον τὸ πλῆθος τοῦ ἀδιαιρέτου διὰ τὴν αἴσθησιν. Dicitur autem ex contrario et ostenditur ipsum unum, ex divisibili indivisibile, propter magis sensibilem multitudinem esse et divisibile quam indivisibile. Quare ratione prior multitudo indivisibili propter sensum. And the one derives its name and its explanation from its contrary, the indivisible from the divisible, because plurality and the divisible is more perceptible than the indivisible, so that in definition plurality is prior to the indivisible, because of the conditions of perception.
ἔστι δὲ τοῦ [30] μὲν ἑνός, ὥσπερ καὶ ἐν τῇ διαιρέσει τῶν ἐναντίων διεγράψαμεν, τὸ ταὐτὸ καὶ ὅμοιον καὶ ἴσον, τοῦ δὲ πλήθους τὸ ἕτερον καὶ ἀνόμοιον καὶ ἄνισον. Est autem unius quidem, sicut et in divisione contrariorum descripsimus, idem et simile et equale; pluralitatis vero diversum et dissimile et inequale. To the one belong, as we indicated graphically in our distinction of the contraries, the same and the like and the equal, and to plurality belong the other and the unlike and the unequal.
λεγομένου δὲ τοῦ ταὐτοῦ πολλαχῶς, ἕνα μὲν τρόπον κατ᾽ ἀριθμὸν λέγομεν ἐνίοτε αὐτό, τὸ δ᾽ ἐὰν καὶ λόγῳ καὶ ἀριθμῷ ἓν ᾖ, οἷον [35] σὺ σαυτῷ καὶ τῷ εἴδει καὶ τῇ ὕλῃ ἕν: ἔτι δ᾽ ἐὰν ὁ λόγος ὁ τῆς πρώτης οὐσίας εἷς ᾖ, [1054β] [1] οἷον αἱ ἴσαι γραμμαὶ εὐθεῖαι αἱ αὐταί, καὶ τὰ ἴσα καὶ ἰσογώνια τετράγωνα, καίτοι πλείω: ἀλλ᾽ ἐν τούτοις ἡ ἰσότης ἑνότης. > Dicto vero eodem multipliciter. Uno quidem modo secundum numerum, quod dicimus aliquando ipsum. Hoc autem si ratione et numero unum fuerit, ut tu tibi ipsi et specie et materia unum. Amplius autem si ratio prime substantiae una fuerit, ut equales lineae recte eaedem, et equalia et isogonia tetragona, et etiam plura; sed in hiis equalitas unitas. The same has several meanings; (1) we sometimes mean the same numerically ; again, (2) we call a thing the same if it is one both in definition and in number, e.g. you are one with yourself both in form and in matter; and again, (3) if the definition of its primary [54b] essence is one; e.g. equal straight lines are the same, and so are equal and equal-angled quadrilaterals; there are many such, but in these equality constitutes unity.
ὅμοια δὲ ἐὰν μὴ ταὐτὰ ἁπλῶς ὄντα, μηδὲ κατὰ τὴν οὐσίαν ἀδιάφορα τὴν [5] συγκειμένην, κατὰ τὸ εἶδος ταὐτὰ ᾖ, ὥσπερ τὸ μεῖζον τετράγωνον τῷ μικρῷ ὅμοιον, καὶ αἱ ἄνισοι εὐθεῖαι: αὗται γὰρ ὅμοιαι μέν, αἱ αὐταὶ δὲ ἁπλῶς οὔ. τὰ δὲ ἐὰν τὸ αὐτὸ εἶδος ἔχοντα, ἐν οἷς τὸ μᾶλλον καὶ ἧττον ἐγγίγνεται, μήτε μᾶλλον ᾖ μήτε ἧττον. τὰ δὲ ἐὰν ᾖ τὸ αὐτὸ πάθος καὶ ἓν [10] τῷ εἴδει, οἷον τὸ λευκόν, σφόδρα καὶ ἧττον, ὅμοιά φασιν εἶναι ὅτι ἓν τὸ εἶδος αὐτῶν. τὰ δὲ ἐὰν πλείω ἔχῃ ταὐτὰ ἢ ἕτερα, ἢ ἁπλῶς ἢ τὰ πρόχειρα, οἷον καττίτερος ἀργύρῳ ᾗ λευκόν, χρυσὸς δὲ πυρὶ ᾗ ξανθὸν καὶ πυρρόν. Similia vero si non sint eadem simpliciter entia nec secundum substantiam indifferentia subiectam, * secundum speciem eadem sint, ut maius tetragonum minori simile, et inequales recte; hae namque similes quidem, eaedem vero simpliciter non. Alia si eandem speciem habentia, in quibus magis et minus fit, nec magis sint nec minus. Alia si sit eadem passio et una specie, ut album, valde et minus, similia dicunt esse quia una species ipsorum. Alia si plura habent eadem quam altera, aut simpliciter aut quae in promptu, ut stagnum argento vel auro ignis aut rubicundum et rufum *. Things are like if, not being absolutely the same, nor without difference in respect of their concrete substance, they are the same in form; e.g. the larger square is like the smaller, and unequal straight lines are like; they are like, but not absolutely the same. Other things are like, if, having the same form, and being things in which difference of degree is possible, they have no difference of degree. Other things, if they have a quality that is in form one and same – e.g. whiteness – in a greater or less degree, are called like because their form is one. Other things are called like if the qualities they have in common are more numerous than those in which they differ – either the qualities in general or the prominent qualities; e.g. tin is like silver, qua white, and gold is like fire, qua yellow and red.
ὥστε δῆλον ὅτι καὶ τὸ ἕτερον καὶ τὸ ἀνόμοιον πολλαχῶς λέγεται. καὶ [15] τὸ μὲν ἄλλο ἀντικειμένως καὶ τὸ ταὐτό, διὸ ἅπαν πρὸς ἅπαν ἢ ταὐτὸ ἢ ἄλλο: τὸ δ᾽ ἐὰν μὴ καὶ ἡ ὕλη καὶ ὁ λόγος εἷς, διὸ σὺ καὶ ὁ πλησίον ἕτερος: τὸ δὲ τρίτον ὡς τὰ ἐν τοῖς μαθηματικοῖς. τὸ μὲν οὖν ἕτερον ἢ ταὐτὸ διὰ τοῦτο πᾶν πρὸς πᾶν λέγεται, ὅσα λέγεται ἓν καὶ ὄν: οὐ γὰρ [20] ἀντίφασίς ἐστι τοῦ ταὐτοῦ, διὸ οὐ λέγεται ἐπὶ τῶν μὴ ὄντων (τὸ δὲ μὴ ταὐτὸ λέγεται), ἐπὶ δὲ τῶν ὄντων πάντων: ἢ γὰρ ἓν ἢ οὐχ ἓν πέφυχ᾽ ὅσα ὂν καὶ ἕν. τὸ μὲν οὖν ἕτερον καὶ ταὐτὸν οὕτως ἀντίκειται, Quare palam quod diversum et dissimile multipliciter dicitur. Et hoc quidem aliud opposite et idem, propter quod omne ad omne aut idem aut aliud. Hoc autem si non et materia et ratio una, quapropter et tu et propinquus diversus. Tertium autem * ut quae * in mathematicis. Diversum quidem igitur > aut idem propter hoc omne ad omne dicitur, quaecumque dicuntur * unum et ens; non enim contradictio est ipsius eiusdem, quapropter non dicitur in non entibus * (non idem autem dicitur). In entibus vero omnibus; aut enim unum aut non unum aptum natum et ens et unum. Diversum quidem igitur et idem ita opponuntur. Evidently, then, other and unlike also have several meanings. And the other in one sense is the opposite of the same (so that everything is either the same as or other than everything else). In another sense things are other unless both their matter and their definition are one (so that you are other than your neighbour). The other in the third sense is exemplified in the objects of mathematics. Other or the same can therefore be predicated of everything with regard to everything else – but only if the things are one and existent, for other is not the contradictory of the same ; which is why it is not predicated of non-existent things (while not the same is so predicated). It is predicated of all existing things; for everything that is existent and one is by its very nature either one or not one with anything else.
διαφορὰ δὲ καὶ ἑτερότης ἄλλο. τὸ μὲν γὰρ ἕτερον καὶ οὗ ἕτερον οὐκ ἀνάγκη εἶναι τινὶ ἕτερον: [25] πᾶν γὰρ ἢ ἕτερον ἢ ταὐτὸ ὅ τι ἂν ᾖ ὄν: τὸ δὲ διάφορον τινὸς τινὶ διάφορον, ὥστε ἀνάγκη ταὐτό τι εἶναι ᾧ διαφέρουσιν. τοῦτο δὲ τὸ ταὐτὸ γένος ἢ εἶδος: πᾶν γὰρ τὸ διαφέρον διαφέρει ἢ γένει ἢ εἴδει, γένει μὲν ὧν μὴ ἔστι κοινὴ ἡ ὕλη μηδὲ γένεσις εἰς ἄλληλα, οἷον ὅσων ἄλλο σχῆμα τῆς κατηγορίας, [30] εἴδει δὲ ὧν τὸ αὐτὸ γένος (λέγεται δὲ γένος ὃ ἄμφω τὸ αὐτὸ λέγονται κατὰ τὴν οὐσίαν τὰ διάφορα). τὰ δ᾽ ἐναντία διάφορα, καὶ ἡ ἐναντίωσις διαφορά τις. Differentia vero et diversitas aliud. Diversum enim et a quo est diversum non necesse aliquo esse diversum; omne namque aut diversum aut idem quodcumque est ens. Differens vero ab aliquo aliquo * differens, quare necesse ipsum idem aliquid esse * quo differunt. Hoc autem ipsum idem: * genus aut species. Omne namque differens differt aut genere aut specie. Genere quidem quorum non est communis materia nec generatio ad invicem, ut quorumcumque alia figura cathegorie. Specie vero quorum idem est genus. Dicitur autem genus * quod ambo idem dicuntur secundum substantiam differentia. Contraria vero differentia *, et contrarietas differentia quaedam. The other, then, and the same are thus opposed. But difference is not the same as otherness. For the other and that which it is other than need not be other in some definite respect (for everything that is existent is either other or the same), but that which is different is different from some particular thing in some particular respect, so that there must be something identical whereby they differ. And this identical thing is genus or species; for everything that differs differs either in genus or in species, in genus if the things have not their matter in common and are not generated out of each other (i.e. if they belong to different figures of predication), and in species if they have the same genus ( genus meaning that identical thing which is essentially predicated of both the different things). Contraries are different, and contrariety is a kind of difference.
ὅτι δὲ καλῶς τοῦτο ὑποτιθέμεθα, δῆλον ἐκ τῆς ἐπαγωγῆς: πάντα γὰρ διαφέροντα φαίνεται καὶ ταῦτα, οὐ μόνον ἕτερα [35] ὄντα ἀλλὰ τὰ μὲν τὸ γένος ἕτερα τὰ δ᾽ ἐν τῇ αὐτῇ συστοιχίᾳ τῆς κατηγορίας, [1055α] [1] ὥστ᾽ ἐν ταὐτῷ γένει καὶ ταὐτὰ τῷ γένει. διώρισται δ᾽ ἐν ἄλλοις ποῖα τῷ γένει ταὐτὰ ἢ ἕτερα. Quod autem hoc bene supponimus, palam ex inductione. Omnia enim differentia videntur et haec, non solum diversa entia sed haec quidem genere diversa, haec autem in eadem coelementatione cathegorie, quare in eodem genere et eadem specie. Determinatum autem est in aliis quae sunt genere eadem aut diversa. That we are right in this supposition is shown by induction. For all of these too are seen to be different; they are not merely other, but some are other in genus, [55a] and others are in the same line of predication, and therefore in the same genus, and the same in genus. We have distinguished elsewhere what sort of things are the same or other in genus.

Chapter 4

Greek Latin English
ἐπεὶ δὲ διαφέρειν ἐνδέχεται ἀλλήλων τὰ διαφέροντα πλεῖον καὶ ἔλαττον, ἔστι τις καὶ μεγίστη διαφορά, Quoniam autem differre contingit ab invicem differentia plus et minus, est aliqua et maxima differentia, Chapter 4. Since things which differ may differ from one another more or less, there is also a greatest difference,
καὶ ταύτην [5] λέγω ἐναντίωσιν. ὅτι δ᾽ ἡ μεγίστη ἐστὶ διαφορά, δῆλον ἐκ τῆς ἐπαγωγῆς. τὰ μὲν γὰρ γένει διαφέροντα οὐκ ἔχει ὁδὸν εἰς ἄλληλα, ἀλλ᾽ ἀπέχει πλέον καὶ ἀσύμβλητα: τοῖς δ᾽ εἴδει διαφέρουσιν αἱ γενέσεις ἐκ τῶν ἐναντίων εἰσὶν ὡς ἐσχάτων, τὸ δὲ τῶν ἐσχάτων διάστημα μέγιστον, ὥστε [10] καὶ τὸ τῶν ἐναντίων. et hanc dico contrarietatem. Quia vero maxima est differentia, palam ex inductione. Genere namque differentia non habent viam in invicem, sed distant magis et inconferibiliter. Differentibus > vero specie generationes ex contrariis sunt ut ultimis, ultimorum vero distantia maxima est; quare et quae * contrariorum. and this I call contrariety. That contrariety is the greatest difference is made clear by induction. For things which differ in genus have no way to one another, but are too far distant and are not comparable; and for things that differ in species the extremes from which generation takes place are the contraries, and the distance between extremes – and therefore that between the contraries – is the greatest.
ἀλλὰ μὴν τό γε μέγιστον ἐν ἑκάστῳ γένει τέλειον. μέγιστόν τε γὰρ οὗ μὴ ἔστιν ὑπερβολή, καὶ τέλειον οὗ μὴ ἔστιν ἔξω λαβεῖν τι δυνατόν: τέλος γὰρ ἔχει ἡ τελεία διαφορά (ὥσπερ καὶ τἆλλα τῷ τέλος ἔχειν λέγεται τέλεια), τοῦ δὲ τέλους οὐθὲν ἔξω: ἔσχατον γὰρ ἐν παντὶ [15] καὶ περιέχει, διὸ οὐδὲν ἔξω τοῦ τέλους, οὐδὲ προσδεῖται οὐδενὸς τὸ τέλειον. ὅτι μὲν οὖν ἡ ἐναντιότης ἐστὶ διαφορὰ τέλειος, ἐκ τούτων δῆλον: πολλαχῶς δὲ λεγομένων τῶν ἐναντίων, ἀκολουθήσει τὸ τελείως οὕτως ὡς ἂν καὶ τὸ ἐναντίοις εἶναι ὑπάρχῃ αὐτοῖς. At vero maximum in unoquoque genere * perfectum. Maximum enim * cuius non est excessus, et perfectum cuius non est adhuc extra sumere aliquid possibile; finem enim habet perfecta differentia, sicut et alia eo quod finem habeant dicuntur perfecta. Nihil autem extra finem; ultimum enim in omni et continet. Propter quod nihil extra finem, nec eget aliquo quod perfectum *. Quod quidem igitur contrarietas est differentia perfecta, ex hiis palam. Multipliciter autem dictis contrariis, sequetur quod perfecte * sic ut utique et quod est contrariis esse extiterit ipsis. But surely that which is greatest in each class is complete. For that is greatest which cannot be exceeded, and that is complete beyond which nothing can be found. For the complete difference marks the end of a series (just as the other things which are called complete are so called because they have attained an end), and beyond the end there is nothing; for in everything it is the extreme and includes all else, and therefore there is nothing beyond the end, and the complete needs nothing further. From this, then, it is clear that contrariety is complete difference; and as contraries are so called in several senses, their modes of completeness will answer to the various modes of contrariety which attach to the contraries.
τούτων δὲ ὄντων φανερὸν ὅτι οὐκ ἐνδέχεται [20] ἑνὶ πλείω ἐναντία εἶναι (οὔτε γὰρ τοῦ ἐσχάτου ἐσχατώτερον εἴη ἄν τι, οὔτε τοῦ ἑνὸς διαστήματος πλείω δυοῖν ἔσχατα), Hiis autem entibus palam quod non contingit plura uni contraria esse; nec enim ultimo ulterius erit utique aliquid, nec distantie unius plura sunt quam duo ultima. This being so, it is clear that one thing have more than one contrary (for neither can there be anything more extreme than the extreme, nor can there be more than two extremes for the one interval),
ὅλως τε εἰ ἔστιν ἡ ἐναντιότης διαφορά, ἡ δὲ διαφορὰ δυοῖν, ὥστε καὶ ἡ τέλειος. Totaliter autem si est contrarietas differentia, differentia vero duorum, quare et perfecta. and, to put the matter generally, this is clear if contrariety is a difference, and if difference, and therefore also the complete difference, must be between two things.
ἀνάγκη δὲ καὶ τοὺς ἄλλους ὅρους ἀληθεῖς εἶναι τῶν ἐναντίων. καὶ γὰρ πλεῖστον διαφέρει ἡ τέλειος [25] διαφορά (τῶν τε γὰρ γένει διαφερόντων οὐκ ἔστιν ἐξωτέρω λαβεῖν καὶ τῶν εἴδει: δέδεικται γὰρ ὅτι πρὸς τὰ ἔξω τοῦ γένους οὐκ ἔστι διαφορά, τούτων δ᾽ αὕτη μεγίστη), καὶ τὰ ἐν ταὐτῷ γένει πλεῖστον διαφέροντα ἐναντία (μεγίστη γὰρ διαφορὰ τούτων ἡ τέλειος), καὶ τὰ ἐν τῷ αὐτῷ δεκτικῷ πλεῖστον [30] διαφέροντα ἐναντία (ἡ γὰρ ὕλη ἡ αὐτὴ τοῖς ἐναντίοις) καὶ τὰ ὑπὸ τὴν αὐτὴν δύναμιν πλεῖστον διαφέροντα (καὶ γὰρ ἡ ἐπιστήμη περὶ ἓν γένος ἡ μία): ἐν οἷς ἡ τελεία διαφορὰ μεγίστη. Necesse autem et alios terminos esse veros contrariorum. Et enim plurimum differt perfecta differentia; genere namque differentibus non est magis extra accipere et hiis quae specie; ostensum est enim quia ad ea quae sunt extra genus non est differentia, horum autem haec * maxima. Et in eodem genere plurimum differentia contraria *; maxima namque differentia horum * quae perfecta. Et quae in eodem susceptivo plurimum differentia; eadem enim est materia contrariis. Et quae * sub > eadem potentia plurimum * differentia; et enim scientia circa unum genus quae una, in quibus perfecta differentia maxima. And the other commonly accepted definitions of contraries are also necessarily true. For not only is (1) the complete difference the greatest difference (for we can get no difference beyond it of things differing either in genus or in species; for it has been shown that there is no difference between anything and the things outside its genus, and among the things which differ in species the complete difference is the greatest); but also (2) the things in the same genus which differ most are contrary (for the complete difference is the greatest difference between species of the same genus); and (3) the things in the same receptive material which differ most are contrary (for the matter is the same for contraries); and (4) of the things which fall under the same faculty the most different are contrary (for one science deals with one class of things, and in these the complete difference is the greatest).
πρώτη δὲ ἐναντίωσις ἕξις καὶ στέρησίς ἐστιν: οὐ πᾶσα δὲ στέρησις (πολλαχῶς γὰρ λέγεται ἡ στέρησις) [35] ἀλλ᾽ ἥτις ἂν τελεία ᾖ. Prima vero contrarietas habitus et privatio est; sed non omnis privatio (multipliciter enim dicitur privatio) sed quaecumquae perfecta fuerit. The primary contrariety is that between positive state and privation – not every privation, however (for privation has several meanings), but that which is complete.
τὰ δ᾽ ἄλλα ἐναντία κατὰ ταῦτα λεχθήσεται, τὰ μὲν τῷ ἔχειν τὰ δὲ τῷ ποιεῖν ἢ ποιητικὰ εἶναι τὰ δὲ τῷ λήψεις εἶναι καὶ ἀποβολαὶ τούτων ἢ ἄλλων ἐναντίων. Alia autem contraria secundum haec dicentur, haec quidem per habere illa vero per facere aut factiva esse, alia autem per acceptiones esse et abiectiones horum aut aliorum contrariorum. And the other contraries must be called so with reference to these, some because they possess these, others because they produce or tend to produce them, others because they are acquisitions or losses of these or of other contraries.
εἰ δὴ ἀντίκειται μὲν ἀντίφασις καὶ στέρησις καὶ ἐναντιότης καὶ τὰ πρός τι, [1055β] [1] τούτων δὲ πρῶτον ἀντίφασις, ἀντιφάσεως δὲ μηδέν ἐστι μεταξύ, τῶν δὲ ἐναντίων ἐνδέχεται, ὅτι μὲν οὐ ταὐτὸν ἀντίφασις καὶ τἀναντία δῆλον: Si igitur opponuntur contradictio et privatio et contrarietas et ad aliquid, horum autem primum contradictio, contradictionis autem nihil est medium, contrariorum autem contingit: quod quidem non idem contradictio et contraria, palam. Now if the kinds of opposition are contradiction and priva[55b]tion and contrariety and relation, and of these the first is contradiction, and contradiction admits of no intermediate, while contraries admit of one, clearly contradiction and contrariety are not the same.
ἡ δὲ στέρησις ἀντίφασίς τίς ἐστιν: ἢ γὰρ τὸ ἀδύνατον ὅλως ἔχειν, [5] ἢ ὃ ἂν πεφυκὸς ἔχειν μὴ ἔχῃ, ἐστέρηται ἢ ὅλως ἢ πὼς ἀφορισθέν (πολλαχῶς γὰρ ἤδη τοῦτο λέγομεν, ὥσπερ διῄρηται ἡμῖν ἐν ἄλλοις), ὥστ᾽ ἐστὶν ἡ στέρησις ἀντίφασίς τις ἢ ἀδυναμία διορισθεῖσα ἢ συνειλημμένη τῷ δεκτικῷ: διὸ ἀντιφάσεως μὲν οὐκ ἔστι μεταξύ, στερήσεως δέ τινος ἔστιν: ἴσον [10] μὲν γὰρ ἢ οὐκ ἴσον πᾶν, ἴσον δ᾽ ἢ ἄνισον οὐ πᾶν, ἀλλ᾽ εἴπερ, μόνον ἐν τῷ δεκτικῷ τοῦ ἴσου. Privatio vero contradictio quaedam est. Aut enim quod impossibile est totaliter habere, aut si quod aptum natum * habere non habeat, privatum est aut totaliter aut aliqualiter determinatum *; multipliciter enim iam hoc dicimus, sicut divisum est a nobis in aliis. Ergo privatio quaedam est contradictio aut impotentia determinata aut concepta cum susceptivo. Quapropter contradictionis quidem non est medium, sed privationis alicuius est; equale namque aut non equale omne, equale vero aut inequale non omne, nisi solum in susceptivo equalitatis. But privation is a kind of contradiction; for what suffers privation, either in general or in some determinate way, either that which is quite incapable of having some attribute or that which, being of such a nature as to have it, has it not; here we have already a variety of meanings, which have been distinguished elsewhere. Privation, therefore, is a contradiction or incapacity which is determinate or taken along with the receptive material. This is the reason why, while contradiction does not admit of an intermediate, privation sometimes does; for everything is equal or not equal, but not everything is equal or unequal, or if it is, it is only within the sphere of that which is receptive of equality.
εἰ δὴ αἱ γενέσεις τῇ ὕλῃ ἐκ τῶν ἐναντίων, γίγνονται δὲ ἢ ἐκ τοῦ εἴδους καὶ τῆς τοῦ εἴδους ἕξεως ἢ ἐκ στερήσεώς τινος τοῦ εἴδους καὶ τῆς μορφῆς, δῆλον ὅτι ἡ μὲν ἐναντίωσις στέρησις ἂν εἴη πᾶσα, Si itaque generationes ipsi materie ex contrariis, fiuntque aut ex specie et ex speciei habitu aut privatione aliqua * speciei et forme, palam quia contrarietas privatio quaedam utique erit omnis. If, then, the comings-to-be which happen to the matter start from the contraries, and proceed either from the form and the possession of the form or from a privation of the form or shape, clearly all contrariety must be privation,
ἡ δὲ στέρησις [15] ἴσως οὐ πᾶσα ἐναντιότης (αἴτιον δ᾽ ὅτι πολλαχῶς ἐνδέχεται ἐστερῆσθαι τὸ ἐστερημένον): ἐξ ὧν γὰρ αἱ μεταβολαὶ ἐσχάτων, ἐναντία ταῦτα. Privatio vero non omnis forsan contrarietas. Causa vero quia multipliciter contingit privari privatum; ex quibus enim permutationes extremis, contraria haec *. but presumably not all privation is contrariety (the reason being that that has suffered privation may have suffered it in several ways); for it is only the extremes from which changes proceed that are contraries.
φανερὸν δὲ καὶ διὰ τῆς ἐπαγωγῆς. πᾶσα γὰρ ἐναντίωσις ἔχει στέρησιν θάτερον τῶν ἐναντίων, ἀλλ᾽ οὐχ ὁμοίως πάντα: ἀνισότης μὲν γὰρ ἰσότητος ἀνομοιότης [20] δὲ ὁμοιότητος κακία δὲ ἀρετῆς, Palam autem et per inductionem. > Omnis enim contrarietas habet privationem alterius contrariorum, sed non similiter omnia; nam inequalitas equalitatis et dissimilitudo similitudinis et malitia virtutis. And this is obvious also by induction. For every contrariety involves, as one of its terms, a privation, but not all cases are alike; inequality is the privation of equality and unlikeness of likeness, and on the other hand vice is the privation of virtue.
διαφέρει δὲ ὥσπερ εἴρηται: τὸ μὲν γὰρ ἐὰν μόνον ᾖ ἐστερημένον, τὸ δ᾽ ἐὰν ἢ ποτὲ ἢ ἔν τινι, οἷον ἂν ἐν ἡλικίᾳ τινὶ ἢ τῷ κυρίῳ, ἢ πάντῃ: διὸ τῶν μὲν ἔστι μεταξύ, καὶ ἔστιν οὔτε ἀγαθὸς ἄνθρωπος οὔτε κακός, τῶν δὲ οὐκ ἔστιν, ἀλλ᾽ ἀνάγκη εἶναι ἢ περιττὸν ἢ [25] ἄρτιον. ἔτι τὰ μὲν ἔχει τὸ ὑποκείμενον ὡρισμένον, τὰ δ᾽ οὔ. ὥστε φανερὸν ὅτι ἀεὶ θάτερον τῶν ἐναντίων λέγεται κατὰ στέρησιν: Differt autem ut dictum est: hoc quidem enim si solum sit privatum, hoc autem si est aut quando aut in quo, ut si in etate aliqua aut principali aut omni. Quapropter horum quidem est medium, et est neque bonus homo neque malus, aliorum vero non est, sed necesse esse aut parem aut imparem. amplius alia quidem habent subiectum determinatum, alia autem non. Quare palam quia semper alterum contrariorum dicitur secundum privationem. But the cases differ in a way already described; in one case we mean simply that the thing has suffered privation, in another case that it has done so either at a certain time or in a certain part (e.g. at a certain age or in the dominant part), or throughout. This is why in some cases there is a mean (there are men who are neither good nor bad), and in others there is not (a number must be either odd or even). Further, some contraries have their subject defined, others have not. Therefore it is evident that one of the contraries is always privative;
ἀπόχρη δὲ κἂν τὰ πρῶτα καὶ τὰ γένη τῶν ἐναντίων, οἷον τὸ ἓν καὶ τὰ πολλά: τὰ γὰρ ἄλλα εἰς ταῦτα ἀνάγεται. [30] Sufficit autem et si prima et genera contrariorum, puta unum et multa; alia namque ad haec reducuntur. but it is enough if this is true of the first – i.e. the generic – contraries, e.g. the one and the many; for the others can be reduced to these.

Chapter 5

Greek Latin English
ἐπεὶ δὲ ἓν ἑνὶ ἐναντίον, ἀπορήσειεν ἄν τις πῶς ἀντίκειται τὸ ἓν καὶ τὰ πολλά, καὶ τὸ ἴσον τῷ μεγάλῳ καὶ τῷ μικρῷ. Quoniam autem unum uni contrarium est, dubitabit aliquis quomodo opponuntur unum et multa, et equale magno et parvo. Chapter 5. Since one thing has one contrary, we might raise the question how the one is opposed to the many, and the equal to the great and the small.
εἰ γὰρ τὸ πότερον ἀεὶ ἐν ἀντιθέσει λέγομεν, οἷον πότερον λευκὸν ἢ μέλαν, καὶ πότερον λευκὸν ἢ οὐ λευκόν (πότερον δὲ ἄνθρωπος ἢ λευκὸν οὐ λέγομεν, ἐὰν μὴ ἐξ [35] ὑποθέσεως καὶ ζητοῦντες οἷον πότερον ἦλθε Κλέων ἢ Σωκράτης—ἀλλ᾽ οὐκ ἀνάγκη ἐν οὐδενὶ γένει τοῦτο: ἀλλὰ καὶ τοῦτο ἐκεῖθεν ἐλήλυθεν: τὰ γὰρ ἀντικείμενα μόνα οὐκ ἐνδέχεται ἅμα ὑπάρχειν, ᾧ καὶ ἐνταῦθα χρῆται ἐν τῷ πότερος ἦλθεν: [1056α] [1] εἰ γὰρ ἅμα ἐνεδέχετο, γελοῖον τὸ ἐρώτημα: εἰ δέ, καὶ οὕτως ὁμοίως ἐμπίπτει εἰς ἀντίθεσιν, εἰς τὸ ἓν ἢ πολλά, οἷον πότερον ἀμφότεροι ἦλθον ἢ ἅτερος): ‘Utrum’ enim semper in oppositione dicimus, ut utrum album aut nigrum, et utrum album aut non album. utrum vero homo aut album non dicimus, nisi ex suppositione, et quaerentes puta utrum venit cleon aut Socrates — Sed non > necesse in neque uno genere hoc. Sed et hoc inde venit; nam opposita sola non contingit simul existere, quo et hic utitur in eo quod uter venit; si enim simul contingeret, ridiculosa foret interrogatio. Si vero, et ita similiter incidet in oppositionem, in id quod unum aut multa, ut utrum ambo venerunt aut alter. For if we used the word whether only in an antithesis such as whether it is white or black , or whether it is white or not white (we do not ask whether it is a man or white ), unless we are proceeding on a prior assumption and asking something such as whether it was Cleon or Socrates that came as this is not a necessary disjunction in any class of things; yet even this is an extension from the case of opposites; for opposites alone cannot be present together; and we assume this incompatibility here too in asking which of the two [56a] came; for if they might both have come, the question would have been absurd; but if they might, even so this falls just as much into an antithesis, that of the one or many , i.e. whether both came or one of the two.
εἰ δὴ ἐν τοῖς ἀντικειμένοις ἀεὶ τοῦ ποτέρου ἡ ζήτησις, λέγεται δὲ πότερον μεῖζον [5] ἢ ἔλαττον ἢ ἴσον, τίς ἐστιν ἡ ἀντίθεσις πρὸς ταῦτα τοῦ ἴσου; οὔτε γὰρ θατέρῳ μόνῳ ἐναντίον οὔτ᾽ ἀμφοῖν: τί γὰρ μᾶλλον τῷ μείζονι ἢ τῷ ἐλάττονι; Si itaque in oppositis semper est ipsius ‘utrum’ interrogatio, dicitur autem utrum maius aut minus aut equale, aliqua est oppositio ad haec equalis. Non enim alteri soli contrarium nec ambobus; quid enim magis aut maiori aut minori? If, then, the question whether is always concerned with opposites, and we can ask whether it is greater or less or equal , what is the opposition of the equal to the other two? It is not contrary either to one alone or to both; for why should it be contrary to the greater rather than to the less?
ἔτι τῷ ἀνίσῳ ἐναντίον τὸ ἴσον, ὥστε πλείοσιν ἔσται ἢ ἑνί. εἰ δὲ τὸ ἄνισον σημαίνει τὸ αὐτὸ ἅμα ἀμφοῖν, εἴη μὲν ἂν ἀντικείμενον ἀμφοῖν Amplius inequali contrarium est equale. Quare in pluribus erit aut uno. Si vero inequale significat idem simul amborum, erit quidem utique oppositum ambobus. Further, the equal is contrary to the unequal. Therefore if it is contrary to the greater and the less, it will be contrary to more things than one. But if the unequal means the same as both the greater and the less together, the equal will be opposite to both
[10] (καὶ ἡ ἀπορία βοηθεῖ τοῖς φάσκουσι τὸ ἄνισον δυάδα εἶναι), Et dubitatio iuvat dicentes inequale dualitatem esse. (and the difficulty supports those who say the unequal is a two ),
ἀλλὰ συμβαίνει ἓν δυοῖν ἐναντίον: ὅπερ ἀδύνατον. Sed accidit unum duobus contrarium, quod est impossibile. but it follows that one thing is contrary to two others, which is impossible.
ἔτι τὸ μὲν ἴσον μεταξὺ φαίνεται μεγάλου καὶ μικροῦ, ἐναντίωσις δὲ μεταξὺ οὐδεμία οὔτε φαίνεται οὔτε ἐκ τοῦ ὁρισμοῦ δυνατόν: οὐ γὰρ ἂν εἴη τελεία μεταξύ τινος οὖσα, ἀλλὰ μᾶλλον [15] ἔχει ἀεὶ ἑαυτῆς τι μεταξύ. λείπεται δὴ ἢ ὡς ἀπόφασιν ἀντικεῖσθαι ἢ ὡς στέρησιν. Amplius equale quidem medium videtur esse magni et parui. Contrariatio autem intermedia neque videtur nec ex diffinitione possibile ; non enim utique erit perfecta mediatio alicuius existens, sed magis habet semper suimet aliquod medium. Again, the equal is evidently intermediate between the great and the small, but no contrariety is either observed to be intermediate, or, from its definition, can be so; for it would not be complete if it were intermediate between any two things, but rather it always has something intermediate between its own terms.
θατέρου μὲν δὴ οὐκ ἐνδέχεται (τί γὰρ μᾶλλον τοῦ μεγάλου ἢ μικροῦ;): ἀμφοῖν ἄρα ἀπόφασις στερητική, διὸ καὶ πρὸς ἀμφότερα τὸ πότερον λέγεται, πρὸς δὲ θάτερον οὔ (οἷον πότερον μεῖζον ἢ ἴσον, ἢ πότερον ἴσον ἢ [20] ἔλαττον), ἀλλ᾽ ἀεὶ τρία. Restat igitur aut ut negationem opponi aut ut privationem. Alterius quidem itaque non contingit; quid enim magis magni aut parvi? Amborum igitur negatio privativa . Quapropter ad ambo \jtrum’ dicitur, ad alterum vero non (ut utrum maius aut equale, aut utrum equale aut minus), sed semper tria. It remains, then, that it is opposed either as negation or as privation. It cannot be the negation or privation of one of the two; for why of the great rather than of the small? It is, then, the privative negation of both. This is why whether is said with reference to both, not to one of the two (e.g. whether it is greater or equal or whether it is equal or less ); there are always three cases.
οὐ στέρησις δὲ ἐξ ἀνάγκης: οὐ γὰρ πᾶν ἴσον ὃ μὴ μεῖζον ἢ ἔλαττον, ἀλλ᾽ ἐν οἷς πέφυκεν ἐκεῖνα. ἔστι δὴ τὸ ἴσον τὸ μήτε μέγα μήτε μικρόν, πεφυκὸς δὲ ἢ μέγα ἢ μικρὸν εἶναι: καὶ ἀντίκειται ἀμφοῖν ὡς ἀπόφασις στερητική, Non privatio autem ex necessitate; non enim omne equale quod > non maius aut minus, sed in quibus aptum natum est esse. Est itaque equale quod neque * magnum neque parvum, aptum natum magnum aut parvum esse. Et opponitur ambobus ut negatio privativa. But it is not a necessary privation; for not everything which is not greater or less is equal, but only the things which are of such a nature as to have these attributes. The equal, then, is that which is neither great nor small but is naturally fitted to be either great or small; and it is opposed to both as a privative negation
διὸ καὶ μεταξύ ἐστιν. καὶ τὸ μήτε [25] ἀγαθὸν μήτε κακὸν ἀντίκειται ἀμφοῖν, ἀλλ᾽ ἀνώνυμον: πολλαχῶς γὰρ λέγεται ἑκάτερον καὶ οὐκ ἔστιν ἓν τὸ δεκτικόν, ἀλλὰ μᾶλλον τὸ μήτε λευκὸν μήτε μέλαν. ἓν δὲ οὐδὲ τοῦτο λέγεται, ἀλλ᾽ ὡρισμένα πως ἐφ᾽ ὧν λέγεται στερητικῶς ἡ ἀπόφασις αὕτη: ἀνάγκη γὰρ ἢ φαιὸν ἢ [30] ὠχρὸν εἶναι ἢ τοιοῦτόν τι ἄλλο. Quapropter et medium est. Et quod neque malum neque bonum opponitur ambobus, sed innominatum; multipliciter enim dicitur utrumque et non est unum susceptivum. Sed magis quod neque album neque nigrum. Unum vero non hoc dicitur, sed determinati aliqualiter colores in quibus dicitur privative negatio haec; nam necesse aut pallidum aut rubeum esse aut tale aliquid aliud. (and therefore is also intermediate). And that which is neither good nor bad is opposed to both, but has no name; for each of these has several meanings and the recipient subject is not one; but that which is neither white nor black has more claim to unity. Yet even this has not one name, though the colours of which this negation is privatively predicated are in a way limited; for they must be either grey or yellow or something else of the kind.
ὥστε οὐκ ὀρθῶς ἐπιτιμῶσιν οἱ νομίζοντες ὁμοίως λέγεσθαι πάντα, ὥστε ἔσεσθαι ὑποδήματος καὶ χειρὸς μεταξὺ τὸ μήτε ὑπόδημα μήτε χεῖρα, ἔπειπερ καὶ τὸ μήτε ἀγαθὸν μήτε κακὸν τοῦ ἀγαθοῦ καὶ τοῦ κακοῦ, ὡς πάντων ἐσομένου τινὸς μεταξύ. οὐκ ἀνάγκη [35] δὲ τοῦτο συμβαίνειν. ἡ μὲν γὰρ ἀντικειμένων συναπόφασίς ἐστιν ὧν ἔστι μεταξύ τι καὶ διάστημά τι πέφυκεν εἶναι: [1056β] [1] τῶν δ᾽ οὐκ ἔστι διαφορά: ἐν ἄλλῳ γὰρ γένει ὧν αἱ συναποφάσεις, ὥστ᾽ οὐχ ἓν τὸ ὑποκείμενον. Quare non recte increpant opinantes similiter dici omnia, ut sit * calcei et manus medium quod neque calceus neque manus, quoniam quidem et quod neque bonum neque malum boni et mali, tamquam omnium futuro aliquo medio. Non * necesse autem hoc accidere. Haec quidem enim oppositorum connegatio est quo rum est medium ahquod et distantia aliqua * nata est esse, horum autem non est differentia; nam in alio genere quorum connegationes, quare non unum quod subicitur. Therefore it is an incorrect criticism that is passed by those who think that all such phrases are used in the same way, so that that which is neither a shoe nor a hand would be intermediate between a shoe and a hand, since that which is neither good nor bad is intermediate between the good and the bad – as if there must be an intermediate in all cases. But this does not necessarily follow. For the one phrase is a joint denial of opposites between which there is an intermediate and a certain natural [56b] interval; but between the other two there is no difference ; for the things, the denials of which are combined, belong to different classes, so that the substratum is not one.

Chapter 6

Greek Latin English
ὁμοίως δὲ καὶ περὶ τοῦ ἑνὸς καὶ τῶν πολλῶν ἀπορήσειεν ἄν τις. εἰ γὰρ τὰ πολλὰ τῷ ἑνὶ ἁπλῶς ἀντίκειται, [5] συμβαίνει ἔνια ἀδύνατα. Similiter autem et de uno et multis dubitabit utique aliquis. Nam si multa simpliciter uni opponuntur, accidunt quaedam impossibilia *. Chapter 6. We might raise similar questions about the one and the many. For if the many are absolutely opposed to the one, certain impossible results follow.
τὸ γὰρ ἓν ὀλίγον ἢ ὀλίγα ἔσται: τὰ γὰρ πολλὰ καὶ τοῖς ὀλίγοις ἀντίκειται. ἔτι τὰ δύο πολλά, εἴπερ τὸ διπλάσιον πολλαπλάσιον λέγεται δὲ κατὰ τὰ δύο: ὥστε τὸ ἓν ὀλίγον: πρὸς τί γὰρ πολλὰ τὰ δύο εἰ μὴ πρὸς ἕν τε καὶ τὸ ὀλίγον; οὐθὲν γάρ ἐστιν ἔλαττον. Nam unum * paucum aut pauca erit; nam multa et paucis opponuntur. Amplius ipsa duo sunt multa, si duplex * multiplex, dicitur autem secundum duo. Quare unum * paucum; ad quid enim sunt multa ipsa duo nisi ad > unum et paucum? Nihil enim est minus. One will then be few, whether few be treated here as singular or plural; for the many are opposed also to the few. Further, two will be many, since the double is multiple and double derives its meaning from two ; therefore one will be few; for what is that in comparison with which two are many, except one, which must therefore be few? For there is nothing fewer.
[10] ἔτι εἰ ὡς ἐν μήκει τὸ μακρὸν καὶ βραχύ, οὕτως ἐν πλήθει τὸ πολὺ καὶ ὀλίγον, καὶ ὃ ἂν ᾖ πολὺ καὶ πολλά, καὶ τὰ πολλὰ πολύ (εἰ μή τι ἄρα διαφέρει ἐν συνεχεῖ εὐορίστῳ), τὸ ὀλίγον πλῆθός τι ἔσται. ὥστε τὸ ἓν πλῆθός τι, εἴπερ καὶ ὀλίγον: τοῦτο δ᾽ ἀνάγκη, εἰ τὰ δύο πολλά. Amplius si ut in longitudine productum et breue, sic in multitudine multum et paucum, et quodcumque fuerit multum et multa, et multa multum (si non aliquid forte differat in continuo bene terminabili): paucum multitudo quaedam erit. Quare unum multitudo quaedam est, siquidem et paucum. Hoc autem necesse, si duo sunt multa. Further, if the much and the little are in plurality what the long and the short are in length, and whatever is much is also many, and the many are much (unless, indeed, there is a difference in the case of an easily-bounded continuum), the little (or few) will be a plurality. Therefore one is a plurality if it is few; and this it must be, if two are many.
[15] ἴσως τὰ πολλὰ λέγεται μέν πως καὶ [τὸ] πολύ, ἀλλ᾽ ὡς διαφέρον, οἷον ὕδωρ πολύ, πολλὰ δ᾽ οὔ. ἀλλ᾽ ὅσα διαιρετά, ἐν τούτοις λέγεται, Sed forsan multa dicuntur quidem ut et multum, sed ut differens; velut ydor id est aqua multum, multa autem non. Sed quaecumque divisa, in hiis dicitur. But perhaps, while the many are in a sense said to be also much , it is with a difference; e.g. water is much but not many. But many is applied to the things that are divisible;
ἕνα μὲν τρόπον ἐὰν ᾖ πλῆθος ἔχον ὑπεροχὴν ἢ ἁπλῶς ἢ πρός τι (καὶ τὸ ὀλίγον ὡσαύτως πλῆθος ἔχον ἔλλειψιν), τὸ δὲ ὡς ἀριθμός, ὃ καὶ ἀντίκειται τῷ ἑνὶ [20] μόνον. οὕτως γὰρ λέγομεν ἓν ἢ πολλά, ὥσπερ εἴ τις εἴποι ἓν καὶ ἕνα ἢ λευκὸν καὶ λευκά, καὶ τὰ μεμετρημένα πρὸς τὸ μέτρον [καὶ τὸ μετρητόν]: οὕτως καὶ τὰ πολλαπλάσια λέγεται: πολλὰ γὰρ ἕκαστος ὁ ἀριθμὸς ὅτι ἕνα καὶ ὅτι μετρητὸς ἑνὶ ἕκαστος, καὶ ὡς τὸ ἀντικείμενον τῷ ἑνί, οὐ τῷ [25] ὀλίγῳ. οὕτω μὲν οὖν ἐστὶ πολλὰ καὶ τὰ δύο, ὡς δὲ πλῆθος ἔχον ὑπεροχὴν ἢ πρός τι ἢ ἁπλῶς οὐκ ἔστιν, ἀλλὰ πρῶτον. ὀλίγα δ᾽ ἁπλῶς τὰ δύο: πλῆθος γάρ ἐστιν ἔλλειψιν ἔχον πρῶτον Uno quidem modo si fuerit multitudo habens excedentiam aut simpliciter aut ad aliquid; et paucum similiter multitudo defectum habens. Hoc autem ut numerus, quod et opponitur uni solum. Ita enim dicimus * unum aut multa, ut si quis dicat unum et una aut album et alba, et mensurata ad metrum et mensurabile. Sic et multiplicia dicuntur. Multa enim unusquisque numerus quia unum et quia mensurabilis uno unusquisque, et ut quod oppo>nitur uni, non pauco. Sic igitur sunt multa et ipsa duo, ut autem multitudo habens excedentiam aut ad aliquid aut simpliciter non sunt. Sed primum pauca simpliciter ipsa duo; multitudo enim est defectum habens prima. in the one sense it means a plurality which is excessive either absolutely or relatively (while few is similarly a plurality which is deficient), and in another sense it means number, in which sense alone it is opposed to the one. For we say one or many , just as if one were to say one and ones or white thing and white things , or to compare the things that have been measured with the measure. It is in this sense also that multiples are so called. For each number is said to be many because it consists of ones and because each number is measurable by one; and it is many as that which is opposed to one, not to the few. In this sense, then, even two is many-not, however, in the sense of a plurality which is excessive either relatively or absolutely; it is the first plurality. But without qualification two is few; for it is first plurality which is deficient
(διὸ καὶ οὐκ ὀρθῶς ἀπέστη Ἀναξαγόρας εἰπὼν ὅτι ὁμοῦ πάντα χρήματα ἦν ἄπειρα καὶ πλήθει καὶ μικρότητι, [30] ἔδει δ᾽ εἰπεῖν ἀντὶ τοῦ "καὶ μικρότητι""καὶ ὀλιγότητι": οὐ γὰρ ἄπειρα), ἐπεὶ τὸ ὀλίγον οὐ διὰ τὸ ἕν, ὥσπερ τινές φασιν, ἀλλὰ διὰ τὰ δύο. Quapropter non recte destitit Anaxagoras cum dixisset quia simul omnes res erant, infinite et multitudine et parvuitate, oportebat autem dicere pro * ‘et paruitate’ ‘et paucitate’. Non enim infinite, quoniam paucum non propter unum, ut quidam dicunt, sed propter duo. (for this reason Anaxagoras was not right in leaving the subject with the statement that "all things were together, boundless both in plurality and in smallness" – where for "and in smallness" he should have said "and in fewness"; for they could not have been boundless in fewness), since it is not one, as some say, but two, that make a few.
ἀντίκειται δὴ τὸ ἓν καὶ τὰ πολλὰ τὰ ἐν ἀριθμοῖς ὡς μέτρον μετρητῷ: ταῦτα δὲ ὡς τὰ πρός τι, ὅσα μὴ καθ᾽ αὑτὰ τῶν πρός τι. διῄρηται δ᾽ [35] ἡμῖν ἐν ἄλλοις ὅτι διχῶς λέγεται τὰ πρός τι, τὰ μὲν ὡς ἐναντία, τὰ δ᾽ ὡς ἐπιστήμη πρὸς ἐπιστητόν, τῷ λέγεσθαί τι ἄλλο πρὸς αὐτό. Opponitur itaque unum multis ut metrum mensurabili; haec autem ut quae ad aliquid, quaecumque non secundum se eorum quae * ad aliquid. Divisum autem est a nobis in aliis quia dupliciter dicuntur quae ad aliquid, alia namque ut contraria, alia ut scientia ad scibile, quia dicitur aliquid aliud ad ipsum. The one is opposed then to the many in numbers as measure to thing measurable; and these are opposed as are the relatives which are not from their very nature relatives. We have distinguished elsewhere the two senses in which relatives are so called: – (1) as contraries; (2) as knowledge to thing known, a term being called relative [57a] because another is relative to it.
[1057α] [1] τὸ δὲ ἓν ἔλαττον εἶναι τινός, οἷον τοῖν δυοῖν, οὐδὲν κωλύει: οὐ γάρ, εἰ ἔλαττον, καὶ ὀλίγον. τὸ δὲ πλῆθος οἷον γένος ἐστὶ τοῦ ἀριθμοῦ: ἔστι γὰρ ἀριθμὸς πλῆθος ἑνὶ μετρητόν, καὶ ἀντίκειταί πως τὸ ἓν καὶ ἀριθμός, οὐχ ὡς [5] ἐναντίον ἀλλ᾽ ὥσπερ εἴρηται τῶν πρός τι ἔνια: ᾗ γὰρ μέτρον τὸ δὲ μετρητόν, ταύτῃ ἀντίκειται, διὸ οὐ πᾶν ὃ ἂν ᾖ ἓν ἀριθμός ἐστιν, οἷον εἴ τι ἀδιαίρετόν ἐστιν. Unum autem esse minus aliquo, puta duobus, nihil prohibet; non enim si minus, et paucum. Multitudo autem quasi genus est numeri; est enim numerus multitudo uno mensurabilis. Et opponuntur aliqualiter unum et numerus, non ut contrarium sed sicut dictum est eorum quae ad aliquid quaedam; in quantum enim metrum, hoc * autem mensurabile: sic opponuntur. Quapropter non omne quodcumque fuerit unum numerus est, puta si quid indivisum est. There is nothing to prevent one from being fewer than something, e.g. than two; for if one is fewer, it is not therefore few. Plurality is as it were the class to which number belongs; for number is plurality measurable by one, and one and number are in a sense opposed, not as contrary, but as we have said some relative terms are opposed; for inasmuch as one is measure and the other measurable, they are opposed. This is why not everything that is one is a number; i.e. if the thing is indivisible it is not a number.
ὁμοίως δὲ λεγομένη ἡ ἐπιστήμη πρὸς τὸ ἐπιστητὸν οὐχ ὁμοίως ἀποδίδωσιν. δόξειε μὲν γὰρ ἂν μέτρον ἡ ἐπιστήμη εἶναι τὸ δὲ ἐπιστητὸν [10] τὸ μετρούμενον, συμβαίνει δὲ ἐπιστήμην μὲν πᾶσαν ἐπιστητὸν εἶναι τὸ δὲ ἐπιστητὸν μὴ πᾶν ἐπιστήμην, ὅτι τρόπον τινὰ ἡ ἐπιστήμη μετρεῖται τῷ ἐπιστητῷ. Similiter autem dicta scientia ad scibile, non similiter assignatur. Videbitur enim utique scientia metrum esse, scibile vero quod mensuratur; accidit autem scientiam quidem omnem scibile esse, scibile vero non omne scientiam, quia modo quodam scientia mensuratur scibili. But though knowledge is similarly spoken of as relative to the knowable, the relation does not work out similarly; for while knowledge might be thought to be the measure, and the knowable the thing measured, the fact that all knowledge is knowable, but not all that is knowable is knowledge, because in a sense knowledge is measured by the knowable.
τὸ δὲ πλῆθος οὔτε τῷ ὀλίγῳ ἐναντίον—ἀλλὰ τούτῳ μὲν τὸ πολὺ ὡς ὑπερέχον πλῆθος ὑπερεχομένῳ πλήθει—οὔτε τῷ ἑνὶ πάντως: ἀλλὰ τὸ μὲν [15] ὥσπερ εἴρηται, ὅτι διαιρετὸν τὸ δ᾽ ἀδιαίρετον, τὸ δ᾽ ὡς πρός τι ὥσπερ ἡ ἐπιστήμη ἐπιστητῷ, ἐὰν ᾖ ἀριθμὸς τὸ δ᾽ ἓν μέτρον. Multitudo autem nec pauco est contraria — Sed huic quidem mul>tum sicut excedens multitudo excesse multitudini — * neque ipsi uni omni modo; sed hoc quidem ut dictum est, quia divisibile illud vero indivisibile, hoc * ut ad aliquid ut scientia scibili, si fuerit numerus * unum vero metrum. Plurality is contrary neither to the few (the many being contrary to this as excessive plurality to plurality exceeded), nor to the one in every sense; but in the one sense these are contrary, as has been said, because the former is divisible and the latter indivisible, while in another sense they are relative as knowledge is to knowable, if plurality is number and the one is a measure.

Chapter 7

Greek Latin English
ἐπεὶ δὲ τῶν ἐναντίων ἐνδέχεται εἶναί τι μεταξὺ καὶ ἐνίων ἔστιν, ἀνάγκη ἐκ τῶν ἐναντίων εἶναι τὰ μεταξύ. Quoniam autem contrariorum contingit aliquid medium esse et quorundam est, necesse ex contrariis esse media. Chapter 7. Since contraries admit of an intermediate and in some cases have it, intermediates must be composed of the contraries.
πάντα [20] γὰρ τὰ μεταξὺ ἐν τῷ αὐτῷ γένει ἐστὶ καὶ ὧν ἐστὶ μεταξύ. μεταξὺ μὲν γὰρ ταῦτα λέγομεν εἰς ὅσα μεταβάλλειν ἀνάγκη πρότερον τὸ μεταβάλλον (οἷον ἀπὸ τῆς ὑπάτης ἐπὶ τὴν νήτην εἰ μεταβαίνοι τῷ ὀλιγίστῳ, ἥξει πρότερον εἰς τοὺς μεταξὺ φθόγγους, καὶ ἐν χρώμασιν εἰ [ἥξει] ἐκ τοῦ λευκοῦ [25] εἰς τὸ μέλαν, πρότερον ἥξει εἰς τὸ φοινικοῦν καὶ φαιὸν ἢ εἰς τὸ μέλαν: ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων): μεταβάλλειν δ᾽ ἐξ ἄλλου γένους εἰς ἄλλο γένος οὐκ ἔστιν ἀλλ᾽ ἢ κατὰ συμβεβηκός, οἷον ἐκ χρώματος εἰς σχῆμα. ἀνάγκη ἄρα τὰ μεταξὺ καὶ αὑτοῖς καὶ ὧν μεταξύ εἰσιν ἐν τῷ αὐτῷ γένει [30] εἶναι. Omnia namque media in eodem sunt genere et quorum sunt media. Media enim haec dicimus in quaecumque permutari prius est necesse quod permutatur, ut ab ypate in netem si transit per minimam rationem, veniet prius ad medios sonos. Et in coloribus si veniet ex albo in nigrum, prius veniet ad puniceum et plumbeum quam ad nigrum. Similiter autem et in aliis. * permutari vero ex alio genere in aliud genus non est nisi secundum accidens, ut ex colore in figuram. Necesse est ergo media et quorum sunt media in eodem genere esse. For (1) all intermediates are in the same genus as the things between which they stand. For we call those things intermediates, into which that which changes must change first; e.g. if we were to pass from the highest string to the lowest by the smallest intervals, we should come sooner to the intermediate notes, and in colours if we were to pass from white to black, we should come sooner to crimson and grey than to black; and similarly in all other cases. But to change from one genus to another genus is not possible except in an incidental way, as from colour to figure. Intermediates, then, must be in the same genus both as one another and as the things they stand between.
ἀλλὰ μὴν πάντα γε τὰ μεταξύ ἐστιν ἀντικειμένων τινῶν: ἐκ τούτων γὰρ μόνων καθ᾽ αὑτὰ ἔστι μεταβάλλειν (διὸ ἀδύνατον εἶναι μεταξὺ μὴ ἀντικειμένων: εἴη γὰρ ἂν μεταβολὴ καὶ μὴ ἐξ ἀντικειμένων). At vero omnia media sunt oppositorum quorundam; ex hiis enim solis secundum se est permutari. Quapropter impossibile est esse media non oppositorum; esset enim permutatio et non ex oppositis. But (2) all intermediates stand between opposites of some kind; for only between these can change take place in virtue of their own nature (so that an intermediate is impossible between things which are not opposite; for then there would be change which was not from one opposite towards the other).
τῶν δ᾽ ἀντικειμένων ἀντιφάσεως μὲν οὐκ ἔστι μεταξύ (τοῦτο γάρ ἐστιν ἀντίφασις, [35] ἀντίθεσις ἧς ὁτῳοῦν θάτερον μόριον πάρεστιν, οὐκ ἐχούσης οὐθὲν μεταξύ), τῶν δὲ λοιπῶν τὰ μὲν πρός τι τὰ δὲ στέρησις τὰ δὲ ἐναντία ἐστίν. τῶν δὲ πρός τι ὅσα μὴ ἐναντία, οὐκ ἔχει μεταξύ: αἴτιον δ᾽ ὅτι οὐκ ἐν τῷ αὐτῷ γένει ἐστίν. [1057β] [1] τί γὰρ ἐπιστήμης καὶ ἐπιστητοῦ μεταξύ; ἀλλὰ μεγάλου καὶ μικροῦ. Oppositorum vero contradictionis quidem medium non est; hoc enim est contradictio: oppositio cuius cuicumque altera pars adest, * non habentis nullum medium. Ceterorum vero alia ad aliquid alia privatio alia contraria. Eorum autem quae ad aliquid quaecumque non * contraria, non habent media; causa vero quia non in eodem genere sunt. Quid enim scientie et scibilis medium? Sed * magni et parvi. Of opposites, contradictories admit of no middle term; for this is what contradiction is – an opposition, one or other side of which must attach to anything whatever, i.e. which has no intermediate. Of other opposites, some are relative, others privative, others contrary. Of relative terms, those which are not contrary have no intermediate; the reason is that they are not in the same genus. For what intermediate could there be between [57b] knowledge and knowable? But between great and small there is one. (3)
εἰ δ᾽ ἐστὶν ἐν ταὐτῷ γένει τὰ μεταξύ, ὥσπερ δέδεικται, καὶ μεταξὺ ἐναντίων, ἀνάγκη αὐτὰ συγκεῖσθαι ἐκ τούτων τῶν ἐναντίων. Si vero sunt in eodem genere media, ut ostensum est, et media contrariorum, necesse ipsa componi ex hiis contrariis. If intermediates are in the same genus, as has been shown, and stand between contraries, they must be composed of these contraries.
ἢ γὰρ ἔσται τι γένος αὐτῶν ἢ οὐθέν. καὶ εἰ μὲν [5] γένος ἔσται οὕτως ὥστ᾽ εἶναι πρότερόν τι τῶν ἐναντίων, αἱ διαφοραὶ πρότεραι ἐναντίαι ἔσονται αἱ ποιήσουσαι τὰ ἐναντία εἴδη ὡς γένους: ἐκ γὰρ τοῦ γένους καὶ τῶν διαφορῶν τὰ εἴδη (οἷον εἰ τὸ λευκὸν καὶ μέλαν ἐναντία, ἔστι δὲ τὸ μὲν διακριτικὸν χρῶμα τὸ δὲ συγκριτικὸν χρῶμα, αὗται αἱ διαφοραί, [10] τὸ διακριτικὸν καὶ συγκριτικόν, πρότεραι: ὥστε ταῦτα ἐναντία ἀλλήλοις πρότερα). Nam aut erit aliquod genus ipsorum aut nullum. Et si quidem > genus erit ita ut sit prius aliquid contrariis *, differentie priores contrarie erunt facientes contrarias species ut generis; ex genere enim et differentiis species. Ut si album et nigrum contraria *, est autem hoc quidem disgregativus color illud vero congregativus color: hae differentiae, congregativum et disgregativum, priores; quare haec contraria * invicem priora. At vero contrarie differentia magis sunt contraria. For either there will be a genus including the contraries or there will be none. And if (a) there is to be a genus in such a way that it is something prior to the contraries, the differentiae which constituted the contrary species-of-a-genus will be contraries prior to the species; for species are composed of the genus and the differentiae. (E.g. if white and black are contraries, and one is a piercing colour and the other a compressing colour, these differentiae – piercing and compressing – are prior; so that these are prior contraries of one another.) But, again, the species which differ contrariwise are the more truly contrary species.
ἀλλὰ μὴν τά γε ἐναντίως διαφέροντα μᾶλλον ἐναντία): καὶ τὰ λοιπὰ καὶ τὰ μεταξὺ ἐκ τοῦ γένους ἔσται καὶ τῶν διαφορῶν (οἷον ὅσα χρώματα τοῦ λευκοῦ καὶ μέλανός ἐστι μεταξύ, ταῦτα δεῖ ἔκ τε τοῦ γένους λέγεσθαι [15] —ἔστι δὲ γένος τὸ χρῶμα—καὶ ἐκ διαφορῶν τινῶν: αὗται δὲ οὐκ ἔσονται τὰ πρῶτα ἐναντία: εἰ δὲ μή, ἔσται ἕκαστον ἢ λευκὸν ἢ μέλαν: ἕτεραι ἄρα: μεταξὺ ἄρα τῶν πρώτων ἐναντίων αὗται ἔσονται, Et reliqua et media ex genere erunt et differentiis, ut quicumque colores albi et nigri sunt medii, oportet hos ex genere dici (est autem genus color) et ex differentiis quibusdam. Hae vero non erunt prima contraria; si autem non, erit unusquisque aut albus aut niger. Altere igitur; media ergo primorum contrariorum hae erunt. And the other species, i.e. the intermediates, must be composed of their genus and their differentiae. (E.g. all colours which are between white and black must be said to be composed of the genus, i.e. colour, and certain differentiae. But these differentiae will not be the primary contraries; otherwise every colour would be either white or black. They are different, then, from the primary contraries; and therefore they will be between the primary contraries;
αἱ πρῶται δὲ διαφοραὶ τὸ διακριτικὸν καὶ συγκριτικόν): ὥστε ταῦτα πρῶτα ζητητέον [20] ὅσα ἐναντία μὴ ἐν γένει, ἐκ τίνος τὰ μεταξὺ αὐτῶν (ἀνάγκη γὰρ τὰ ἐν τῷ αὐτῷ γένει ἐκ τῶν ἀσυνθέτων τῷ γένει συγκεῖσθαι ἢ ἀσύνθετα εἶναι). τὰ μὲν οὖν ἐναντία ἀσύνθετα ἐξ ἀλλήλων, ὥστε ἀρχαί: τὰ δὲ μεταξὺ ἢ πάντα ἢ οὐθέν. ἐκ δὲ τῶν ἐναντίων γίγνεταί τι, ὥστ᾽ ἔσται μεταβολὴ εἰς τοῦτο [25] πρὶν ἢ εἰς αὐτά: ἑκατέρου γὰρ καὶ ἧττον ἔσται καὶ μᾶλλον. μεταξὺ ἄρα ἔσται καὶ τοῦτο τῶν ἐναντίων. καὶ τἆλλα ἄρα πάντα σύνθετα τὰ μεταξύ: τὸ γὰρ τοῦ μὲν μᾶλλον τοῦ δ᾽ ἧττον σύνθετόν πως ἐξ ἐκείνων ὧν λέγεται εἶναι τοῦ μὲν μᾶλλον τοῦ δ᾽ ἧττον. ἐπεὶ δ᾽ οὐκ ἔστιν ἕτερα πρότερα ὁμογενῆ [30] τῶν ἐναντίων, ἅπαντ᾽ ἂν ἐκ τῶν ἐναντίων εἴη τὰ μεταξύ, ὥστε καὶ τὰ κάτω πάντα, καὶ τἀναντία καὶ τὰ μεταξύ, ἐκ τῶν πρώτων ἐναντίων ἔσονται. Primae autem differentiae disgregativum et congregativum. Quare hoc primum * quaerendum: quaecumque * contraria non * in genere, ex quo * media ipsorum? Necesse enim quae sunt in eodem genere ex incompositis genere componi aut incomposita esse. Contraria namque incomposita sunt ex * invicem; quare * principia. Quae autem * intermedia: aut omnia aut nullum. Ex contrariis vero fit aliquid, quare erit > transmutatio in hoc prius quam in ipsa; utriusque enim et minus erit et magis. Medium igitur erit et hoc contrariorum. Et alia igitur omnia composita quae * media; nam quod huius quidem magis illius vero minus compositum est aliqualiter ex illis quorum dicitur esse huius quidem magis illius vero minus. Quoniam autem non sunt altera priora eiusdem generis contrariis, omnia utique ex contrarus media erunt. quare et inferiora omnia, et contraria et media, ex primis contrariis erunt. the primary differentiae are piercing and compressing .) Therefore it is (b) with regard to these contraries which do not fall within a genus that we must first ask of what their intermediates are composed. (For things which are in the same genus must be composed of terms in which the genus is not an element, or else be themselves incomposite.) Now contraries do not involve one another in their composition, and are therefore first principles; but the intermediates are either all incomposite, or none of them. But there is something compounded out of the contraries, so that there can be a change from a contrary to it sooner than to the other contrary; for it will have less of the quality in question than the one contrary and more than the other. This also, then, will come between the contraries. All the other intermediates also, therefore, are composite; for that which has more of a quality than one thing and less than another is compounded somehow out of the things than which it is said to have more and less respectively of the quality. And since there are no other things prior to the contraries and homogeneous with the intermediates, all intermediates must be compounded out of the contraries. Therefore also all the inferior classes, both the contraries and their intermediates, will be compounded out of the primary contraries.
ὅτι μὲν οὖν τὰ μεταξὺ ἔν τε ταὐτῷ γένει πάντα καὶ μεταξὺ ἐναντίων καὶ σύγκειται ἐκ τῶν ἐναντίων πάντα, δῆλον. [35] Quod quidem igitur media et in eodem genere omnia et intermedia contrariorum et componuntur ex contrariis omnia, palam. Clearly, then, intermediates are (1) all in the same genus and (2) intermediate between contraries, and (3) all compounded out of the contraries.

Chapter 8

Greek Latin English
τὸ δ᾽ ἕτερον τῷ εἴδει τινὸς τὶ ἕτερόν ἐστι, καὶ δεῖ τοῦτο ἀμφοῖν ὑπάρχειν: οἷον εἰ ζῷον ἕτερον τῷ εἴδει, ἄμφω ζῷα. ἀνάγκη ἄρα ἐν γένει τῷ αὐτῷ εἶναι τὰ ἕτερα τῷ εἴδει: τὸ γὰρ τοιοῦτο γένος καλῶ ὃ ἄμφω ἓν ταὐτὸ λέγεται, μὴ κατὰ συμβεβηκὸς ἔχον διαφοράν, [1058α] [1] εἴτε ὡς ὕλη ὂν εἴτε ἄλλως. οὐ μόνον γὰρ δεῖ τὸ κοινὸν ὑπάρχειν, οἷον ἄμφω ζῷα, ἀλλὰ καὶ ἕτερον ἑκατέρῳ τοῦτο αὐτὸ τὸ ζῷον, οἷον τὸ μὲν ἵππον τὸ δὲ ἄνθρωπον, διὸ τοῦτο τὸ κοινὸν ἕτερον ἀλλήλων [5] ἐστὶ τῷ εἴδει. ἔσται δὴ καθ᾽ αὑτὰ τὸ μὲν τοιονδὶ ζῷον τὸ δὲ τοιονδί, οἷον τὸ μὲν ἵππος τὸ δ᾽ ἄνθρωπος. ἀνάγκη ἄρα τὴν διαφορὰν ταύτην ἑτερότητα τοῦ γένους εἶναι. λέγω γὰρ γένους [8] διαφορὰν ἑτερότητα ἣ ἕτερον ποιεῖ τοῦτο αὐτό. Diversum autem specie alicuius aliquid diversum est, et oportet hoc ambobus inesse; ut si animal diversum est specie, ambo * animalia. Necesse ergo in eodem genere esse diversa specie. Tale enim genus voco quod ambo unum et idem dicuntur, non secundum accidens habens differentiam, sive ut materia ens sive aliter. Non solum enim oportet commune existere, puta ambo animalia, sed et alterum utrilibet hoc ipsum animal, ut hoc quidem equum illud vero hominem. Propter quod hoc quod commune diversum ab invicem est specie. Erit itaque secundum se hoc quidem tale animal illud vero tale *, ut hoc quidem equus illud vero homo. Necesse ergo differentiam hanc diversitatem esse generis. Dico enim generis differentiam diversitatem quae diversum facit hoc ipsum. Chapter 8. That which is other in species is other than something in something, and this must belong to both; e.g. if it is an animal other in species, both are animals. The things, then, which are other in species must be in the same genus. For by genus I mean that one identical thing which is predicated of both and is differentiated in no merely acci[58a]dental way, whether conceived as matter or otherwise. For not only must the common nature attach to the different things, e.g. not only must both be animals, but this very animality must also be different for each (e.g. in the one case equinity, in the other humanity), and so this common nature is specifically different for each from what it is for the other. One, then, will be in virtue of its own nature one sort of animal, and the other another, e.g. one a horse and the other a man. This difference, then, must be an otherness of the genus. For I give the name of difference in the genus an otherness which makes the genus itself other.
ἐναντίωσις τοίνυν ἔσται αὕτη (δῆλον δὲ καὶ ἐκ τῆς ἐπαγωγῆς): πάντα [10] γὰρ διαιρεῖται τοῖς ἀντικειμένοις, > Contrarietas igitur erit haec; palam autem et ex inductione. omnia enim dividuntur oppositis, This, then, will be a contrariety (as can be shown also by induction). For all things are divided by opposites,
καὶ ὅτι τὰ ἐναντία ἐν ταὐτῷ γένει, δέδεικται: ἡ γὰρ ἐναντιότης ἦν διαφορὰ τελεία, ἡ δὲ διαφορὰ ἡ εἴδει πᾶσα τινὸς τί, ὥστε τοῦτο τὸ αὐτό τε καὶ γένος ἐπ᾽ ἀμφοῖν (διὸ καὶ ἐν τῇ αὐτῇ συστοιχίᾳ πάντα τὰ ἐναντία τῆς κατηγορίας ὅσα εἴδει διάφορα καὶ μὴ γένει, [15] ἕτερά τε ἀλλήλων μάλιστα—τελεία γὰρ ἡ διαφορά—καὶ ἅμα ἀλλήλοις οὐ γίγνεται). ἡ ἄρα διαφορὰ ἐναντίωσίς ἐστιν. τοῦτο ἄρα ἐστὶ τὸ ἑτέροις εἶναι τῷ εἴδει, τὸ ἐν ταὐτῷ γένει ὄντα ἐναντίωσιν ἔχειν ἄτομα ὄντα (ταὐτὰ δὲ τῷ εἴδει ὅσα μὴ ἔχει ἐναντίωσιν ἄτομα ὄντα): ἐν γὰρ τῇ διαιρέσει καὶ [20] ἐν τοῖς μεταξὺ γίγνονται ἐναντιώσεις πρὶν εἰς τὰ ἄτομα ἐλθεῖν: et quod contraria in eodem genere sunt, ostensum est. Nam contrarietas erat differentia perfecta. Differentia vero quae specie omnis alicuius aliquid *, quare hoc idemque et genus * in ambobus. Quare et in eadem coelementatione omnia * contraria cathegorie quaecumque * specie differentia et non genere, diversaque * ab invicem maxime; perfecta enim * difterentia, et simul * invicem non fit. Ergo differentia contrarietas est. Hoc enim est diversis esse specie: in eodem genere entia contrarietatem habere, entia individua. Eadem vero specie quaecumque non habent contrarietatem, individua entia. In divisione enim et in mediis fiunt contrarietates priusquam ad individua perveniatur. and it has been proved that contraries are in the same genus. For contrariety was seen to be complete difference; and all difference in species is a difference from something in something; so that this is the same for both and is their genus. (Hence also all contraries which are different in species and not in genus are in the same line of predication, and other than one another in the highest degree – for the difference is complete – , and cannot be present along with one another.) The difference, then, is a contrariety. This, then, is what it is to be other in species – to have a contrariety, being in the same genus and being indivisible (and those things are the same in species which have no contrariety, being indivisible); we say being indivisible , for in the process of division contrarieties arise in the intermediate stages before we come to the indivisibles.
ὥστε φανερὸν ὅτι πρὸς τὸ καλούμενον γένος οὔτε ταὐτὸν οὔτε ἕτερον τῷ εἴδει οὐθέν ἐστι τῶν ὡς γένους εἰδῶν (προσηκόντως: ἡ γὰρ ὕλη ἀποφάσει δηλοῦται, τὸ δὲ γένος ὕλη οὗ λέγεται γένος—μὴ ὡς τὸ τῶν Ἡρακλειδῶν ἀλλ᾽ ὡς τὸ [25] ἐν τῇ φύσει), οὐδὲ πρὸς τὰ μὴ ἐν ταὐτῷ γένει, ἀλλὰ διοίσει τῷ γένει ἐκείνων, εἴδει δὲ τῶν ἐν ταὐτῷ γένει. ἐναντίωσιν γὰρ ἀνάγκη εἶναι τὴν διαφορὰν οὗ διαφέρει εἴδει: αὕτη δὲ ὑπάρχει τοῖς ἐν ταὐτῷ γένει οὖσι μόνοις. Quare palam quia ad id quod vocatur genus nec idem nec diversum specie nihil est eorum quae conveniunt ut generis specierum. Nam materia negatione ostenditur, genus autem materia quod dicitur genus, non ut quod * Eraclitorum sed ut * in natura. Neque ad ea quae non in eodem genere, sed * different genere ab illis, specie vero ab eis quae in eodem genere. Contrarietatem enim necesse est esse differentiam, non differre specie; haec autem inest in eodem genere existentibus solis. Evidently, therefore, with reference to that which is called the genus, none of the species-of-a-genus is either the same as it or other than it in species (and this is fitting; for the matter is indicated by negation, and the genus is the matter of that of which it is called the genus, not in the sense in which we speak of the genus or family of the Heraclidae, but in that in which the genus is an element in a thing's nature), nor is it so with reference to things which are not in the same genus, but it will differ in genus from them, and in species from things in the same genus. For a thing's difference from that from which it differs in species must be a contrariety; and this belongs only to things in the same genus.

Chapter 9

Greek Latin English
ἀπορήσειε δ᾽ ἄν τις διὰ τί γυνὴ ἀνδρὸς οὐκ εἴδει διαφέρει, [30] ἐναντίου τοῦ θήλεος καὶ τοῦ ἄρρενος ὄντος τῆς δὲ διαφορᾶς ἐναντιώσεως, οὐδὲ ζῷον θῆλυ καὶ ἄρρεν ἕτερον τῷ εἴδει: καίτοι καθ᾽ αὑτὸ τοῦ ζῴου αὕτη ἡ διαφορὰ καὶ οὐχ ὡς λευκότης ἢ μελανία ἀλλ᾽ ᾗ ζῷον καὶ τὸ θῆλυ καὶ τὸ ἄρρεν ὑπάρχει. ἔστι δ᾽ ἡ ἀπορία αὕτη σχεδὸν ἡ αὐτὴ καὶ διὰ [35] τί ἡ μὲν ποιεῖ τῷ εἴδει ἕτερα ἐναντίωσις ἡ δ᾽ οὔ, οἷον τὸ πεζὸν καὶ τὸ πτερωτόν, λευκότης δὲ καὶ μελανία οὔ. > Dubitabit autem utique aliquis quare femina a viro non specie differt, contrario feminino et masculino existente, diffe rentia autem contrarietate. Neque animal masculinum et femininum diversum est specie, quamvis secundum se animalis haec sit differentia et non ut albedo aut nigredo sed in quantum animal femininum et masculinum inest. Est autem dubitatio haec fere eadem et quare haec quidem contrarietas facit specie diversa haec autem non, ut ambulativum et volativum, sed albedo et nigredo non. Chapter 9. One might raise the question, why woman does not differ from man in species, when female and male are contrary and their difference is a contrariety; and why a female and a male animal are not different in species, though this difference belongs to animal in virtue of its own nature, and not as paleness or darkness does; both female and male belong to it qua animal. This question is almost the same as the other, why one contrariety makes things different in species and another does not, e.g. with feet and with wings do, but paleness and darkness do not.
ἢ ὅτι τὰ μὲν οἰκεῖα πάθη τοῦ γένους τὰ δ᾽ ἧττον; καὶ ἐπειδή ἐστι τὸ μὲν λόγος τὸ δ᾽ ὕλη, [1058β] [1] ὅσαι μὲν ἐν τῷ λόγῳ εἰσὶν ἐναντιότητες εἴδει ποιοῦσι διαφοράν, ὅσαι δ᾽ ἐν τῷ συνειλημμένῳ τῇ ὕλῃ οὐ ποιοῦσιν. διὸ ἀνθρώπου λευκότης οὐ ποιεῖ οὐδὲ μελανία, οὐδὲ τοῦ λευκοῦ ἀνθρώπου ἔστι διαφορὰ κατ᾽ εἶδος πρὸς [5] μέλανα ἄνθρωπον, οὐδ᾽ ἂν ὄνομα ἓν τεθῇ. ὡς ὕλη γὰρ ὁ ἄνθρωπος, οὐ ποιεῖ δὲ διαφορὰν ἡ ὕλη: οὐδ᾽ ἀνθρώπου γὰρ εἴδη εἰσὶν οἱ ἄνθρωποι διὰ τοῦτο, καίτοι ἕτεραι αἱ σάρκες καὶ τὰ ὀστᾶ ἐξ ὧν ὅδε καὶ ὅδε: ἀλλὰ τὸ σύνολον ἕτερον μέν, εἴδει δ᾽ οὐχ ἕτερον, ὅτι ἐν τῷ λόγῳ οὐκ ἔστιν ἐναντίωσις. τοῦτο δ᾽ [10] ἐστὶ τὸ ἔσχατον ἄτομον: ὁ δὲ Καλλίας ἐστὶν ὁ λόγος μετὰ τῆς ὕλης: καὶ ὁ λευκὸς δὴ ἄνθρωπος, ὅτι Καλλίας λευκός: κατὰ συμβεβηκὸς οὖν ὁ ἄνθρωπος. οὐδὲ χαλκοῦς δὴ κύκλος καὶ ξύλινος: οὐδὲ τρίγωνον χαλκοῦν καὶ κύκλος ξύλινος, οὐ διὰ τὴν ὕλην εἴδει διαφέρουσιν ἀλλ᾽ ὅτι ἐν τῷ λόγῳ [15] ἔνεστιν ἐναντίωσις. πότερον δ᾽ ἡ ὕλη οὐ ποιεῖ ἕτερα τῷ εἴδει, οὖσά πως ἑτέρα, ἢ ἔστιν ὡς ποιεῖ; διὰ τί γὰρ ὁδὶ ὁ ἵππος τουδὶ <τοῦ> ἀνθρώπου ἕτερος τῷ εἴδει; καίτοι σὺν τῇ ὕλῃ οἱ λόγοι αὐτῶν. ἢ ὅτι ἔνεστιν ἐν τῷ λόγῳ ἐναντίωσις; καὶ γὰρ τοῦ λευκοῦ ἀνθρώπου καὶ μέλανος ἵππου, καὶ ἔστι γε [20] εἴδει, ἀλλ᾽ οὐχ ᾗ ὁ μὲν λευκὸς ὁ δὲ μέλας, ἐπεὶ καὶ εἰ ἄμφω λευκὰ ἦν, ὅμως ἂν ἦν εἴδει ἕτερα. Aut quia haec quidem sunt propriae passiones generis illa vero minus. Quoniam * est hoc quidem ratio hoc autem materia, quaecumque quidem in ratione sunt contrarietates specie faciunt differentiam, quae vero in concepto cum materia non faciunt. Quapropter hominis albedo non facit nec nigredo, nec albi hominis est differentia secundum speciem ad nigrum hominem, nec si nomen imponatur. Ut materia enim homo, non facit autem differentiam materia; non enim hominis species sunt homines propter hoc, quamvis diverse * carnes et ossa ex quibus hic et hic. Sed simul totum diversum quidem, specie vero non diversum, quia in ratione non est contrarietas. Hoc autem est ultimum individuum. Callias vero est ratio cum materia; et albus itaque homo, quia Callias albus; secundum accidens ergo homo albus. Nec ereus itaque circulus et ligneus; nec triangulus ereus et circulus ligneus non propter materiam > specie differunt, sed quia in ratione inest contrarietas. Vtrum autem materia non facit diversa specie, ens aliqualiter, aut est ut facit? Propter quid enim hic equus ab hoc homine diversus est specie? Equidem rationes ipsorum * cum materia. Aut quia est in ratione contrarietas. Et enim albi hominis et nigri equi diversitas est specie, sed non in quantum hic albus et ille niger; quoniam et si ambo albi essent, tamen essent specie diversa. Perhaps it is because the former are modifications peculiar to the genus, and the latter are less so. And since one [58b] element is definition and one is matter, contrarieties which are in the definition make a difference in species, but those which are in the thing taken as including its matter do not make one. And so paleness in a man, or darkness, does not make one, nor is there a difference in species between the pale man and the dark man, not even if each of them be denoted by one word. For man is here being considered on his material side, and matter does not create a difference; for it does not make individual men species of man, though the flesh and the bones of which this man and that man consist are other. The concrete thing is other, but not other in species, because in the definition there is no contrariety. This is the ultimate indivisible kind. Callias is definition + matter, the pale man, then, is so also, because it is the individual Callias that is pale; man, then, is pale only incidentally. Neither do a brazen and a wooden circle, then, differ in species; and if a brazen triangle and a wooden circle differ in species, it is not because of the matter, but because there is a contrariety in the definition. But does the matter not make things other in species, when it is other in a certain way, or is there a sense in which it does? For why is this horse other than this man in species, although their matter is included with their definitions? Doubtless because there is a contrariety in the definition. For while there is a contrariety also between pale man and dark horse, and it is a contrariety in species, it does not depend on the paleness of the one and the darkness of the other, since even if both had been pale, yet they would have been other in species.
τὸ δὲ ἄρρεν καὶ θῆλυ τοῦ ζῴου οἰκεῖα μὲν πάθη, ἀλλ᾽ οὐ κατὰ τὴν οὐσίαν ἀλλ᾽ ἐν τῇ ὕλῃ καὶ τῷ σώματι, διὸ τὸ αὐτὸ σπέρμα θῆλυ ἢ ἄρρεν γίγνεται παθόν τι πάθος. Masculinum vero et femina animalis proprie sunt passiones, sed non secundum substantiam, verum in materia et corpore. Propter quod idem sperma femina aut masculum fit patiens passionem aliquam. But male and female, while they are modifications peculiar to animal , are so not in virtue of its essence but in the matter, ie. the body. This is why the same seed becomes female or male by being acted on in a certain way.
τί μὲν οὖν ἐστὶ τὸ τῷ εἴδει ἕτερον [25] εἶναι, καὶ διὰ τί τὰ μὲν διαφέρει εἴδει τὰ δ᾽ οὔ, εἴρηται. Quid quidem igitur est esse diversum specie, et quare alia differunt specie * alia non, dictum est. We have stated, then, what it is to be other in species, and why some things differ in species and others do not.

Chapter 10

Greek Latin English
ἐπειδὴ δὲ τὰ ἐναντία ἕτερα τῷ εἴδει, τὸ δὲ φθαρτὸν καὶ τὸ ἄφθαρτον ἐναντία (στέρησις γὰρ ἀδυναμία διωρισμένη), ἀνάγκη ἕτερον εἶναι τῷ γένει τὸ φθαρτὸν καὶ τὸ ἄφθαρτον. Quoniam vero contraria * diversa specie, * corruptibile autem et incorruptibile contraria (privatio enim est impotentia determinata), necesse diversum esse genere corruptibile et incorruptibile. Chapter 10. Since contraries are other in form, and the perishable and the imperishable are contraries (for privation is a determinate incapacity), the perishable and the imperishable must be different in kind.
νῦν μὲν οὖν ἐπ᾽ αὐτῶν εἰρήκαμεν τῶν καθόλου [30] ὀνομάτων, ὥστε δόξειεν ἂν οὐκ ἀναγκαῖον εἶναι ὁτιοῦν ἄφθαρτον καὶ φθαρτὸν ἕτερα εἶναι τῷ εἴδει, ὥσπερ οὐδὲ λευκὸν καὶ μέλαν (τὸ γὰρ αὐτὸ ἐνδέχεται εἶναι, καὶ ἅμα, ἐὰν ᾖ τῶν καθόλου, ὥσπερ ὁ ἄνθρωπος εἴη ἂν καὶ λευκὸς καὶ μέλας, καὶ τῶν καθ᾽ ἕκαστον: εἴη γὰρ ἄν, μὴ ἅμα, ὁ αὐτὸς [35] λευκὸς καὶ μέλας: καίτοι ἐναντίον τὸ λευκὸν τῷ μέλανι): Nunc ergo diximus de hiis universalibus nominibus, ut autem videbitur non necesse esse quodcumque incorruptibile et corruptibile diversa specie esse, quemadmodum neque album et nigrum, idem enim contingit esse, et simul, si fuerit universalium, quemadmodum homo erit utique et albus et niger, et singularium; erit enim, non simul, idem * albus et niger. * equidem album contrarium nigro. Now so far we have spoken of the general terms themselves, so that it might be thought not to be necessary that every imperishable thing should be different from every perishable thing in form, just as not every pale thing is different in form from every dark thing. For the same thing can be both, and even at the same time if it is a universal (e.g. man can be both pale and dark), and if it is an individual it can still be both; for the same man can be, though not at the same time, pale and dark. Yet pale is contrary to dark.
ἀλλὰ τῶν ἐναντίων τὰ μὲν κατὰ συμβεβηκὸς ὑπάρχει ἐνίοις, οἷον καὶ τὰ νῦν εἰρημένα καὶ ἄλλα πολλά, τὰ δὲ ἀδύνατον, ὧν ἐστὶ καὶ τὸ φθαρτὸν καὶ τὸ ἄφθαρτον: [1059α] [1] οὐδὲν γάρ ἐστι φθαρτὸν κατὰ συμβεβηκός: τὸ μὲν γὰρ συμβεβηκὸς ἐνδέχεται μὴ ὑπάρχειν, τὸ δὲ φθαρτὸν τῶν ἐξ ἀνάγκης ὑπαρχόντων ἐστὶν οἷς ὑπάρχει: ἢ ἔσται τὸ αὐτὸ καὶ ἓν φθαρτὸν [5] καὶ ἄφθαρτον, εἰ ἐνδέχεται μὴ ὑπάρχειν αὐτῷ τὸ φθαρτόν. ἢ τὴν οὐσίαν ἄρα ἢ ἐν τῇ οὐσίᾳ ἀνάγκη ὑπάρχειν τὸ φθαρτὸν ἑκάστῳ τῶν φθαρτῶν. ὁ δ᾽ αὐτὸς λόγος καὶ περὶ τοῦ ἀφθάρτου: τῶν γὰρ ἐξ ἀνάγκης ὑπαρχόντων ἄμφω. ᾗ ἄρα καὶ καθ᾽ ὃ πρῶτον τὸ μὲν φθαρτὸν τὸ δ᾽ ἄφθαρτον, [10] ἔχει ἀντίθεσιν, ὥστε ἀνάγκη γένει ἕτερα εἶναι. > Sed contrariorum haec quidem secundum accidens insunt quibusdam, ut quae nunc dicta sunt et alia multa, haec autem impossibile, quorum est et corruptibile et incorruptibile. nihil enim est corruptibile secundum accidens. Nam accidens contingit non existere, et corruptibile ex necessitate existentium est quibus inest; aut erit idem et unum corruptibile et incorruptibile, si contingit non existere * ipsi corruptibile. Aut * substantiam igitur aut in substantia necesse est inesse corruptibile unicuique corruptibilium. Eadem vero ratio et de incorruptibili *; ex necessitate enim existentium ambo sunt. In quantum igitur et secundum quod primum hoc quidem corruptibile hoc autem incorruptibile, habet oppositionem, unde necesse genere esse diversa. But while some contraries belong to certain things by accident (e.g. both those now mentioned and many others), others cannot, and among these are perishable and [59a] imperishable . For nothing is by accident perishable. For what is accidental is capable of not being present, but perishableness is one of the attributes that belong of necessity to the things to which they belong; or else one and the same thing may be perishable and imperishable, if perishableness is capable of not belonging to it. Perishableness then must either be the essence or be present in the essence of each perishable thing. The same account holds good for imperishableness also; for both are attributes which are present of necessity. The characteristics, then, in respect of which and in direct consequence of which one thing is perishable and another imperishable, are opposite, so that the things must be different in kind.
φανερὸν τοίνυν ὅτι οὐκ ἐνδέχεται εἶναι εἴδη τοιαῦτα οἷα λέγουσί τινες: ἔσται γὰρ καὶ ἄνθρωπος ὁ μὲν φθαρτὸς ὁ δ᾽ ἄφθαρτος. καίτοι τῷ εἴδει ταὐτὰ λέγεται εἶναι τὰ εἴδη τοῖς τισὶ καὶ οὐχ ὁμώνυμα: τὰ δὲ γένει ἕτερα πλεῖον διέστηκεν ἢ τὰ εἴδει. Palam igitur quod non contingit esse species tales quales dicunt quidam; erit enim homo hic quidem corruptibilis hic autem incorruptibilis. Equidem specie eadem dicuntur esse species ipsis quibusdam et non equivoca. Diversa vero genere plus distant quam quae specie. Evidently, then, there cannot be Forms such as some maintain, for then one man would be perishable and another imperishable. Yet the Forms are said to be the same in form with the individuals and not merely to have the same name; but things which differ in kind are farther apart than those which differ in form.


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