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Aristotle · Metaphysics §14.1#2

Critique of the Indefinite Dyad and Relatives as Accidents

Passage 152 of 159 · Greek

Summary

Aristotle criticizes the Platonist view that makes the "unequal" the "indefinite dyad of the great and the small," arguing that relatives like great-small and much-few are accidents rather than substances. He further shows that relatives have no independent generation or destruction, and exposes the logical flaws in deriving numbers from the few and the much.

§14.1#2οἱ δὲ τὸ ἄνισον ὡς ἕν τι, τὴν δυάδα δὲ ἀόριστον ποιοῦντες μεγάλου καὶ μικροῦ, πόρρω λίαν τῶν δοκούντων καὶ δυνατῶν λέγουσιν· πάθη τε γὰρ ταῦτα καὶ συμβεβηκότα μᾶλλον ἢ ὑποκείμενα τοῖς ἀριθμοῖς καὶ τοῖς μεγέθεσίν ἐστι, τὸ πολὺ καὶ ὀλίγον ἀριθμοῦ, καὶ μέγα καὶ μικρὸν μεγέθους, ὥσπερ ἄρτιον καὶ περιττόν, καὶ λεῖον καὶ τραχύ, καὶ εὐθὺ καὶ καμπύλον·
But those who make the unequal as some one thing, and the indefinite dyad consisting of the great and the small, speak too far from what is plausible and possible; for these are affections and accidents rather than subjects for numbers and magnitudes, much and few being of number, and great and small of magnitude, just as even and odd, smooth and rough, and straight and curved.
ἔτι δὲ πρὸς ταύτῃ τῇ ἁμαρτίᾳ καὶ πρός τι ἀνάγκη εἶναι τὸ μέγα καὶ τὸ μικρὸν καὶ ὅσα τοιαῦτα· τὸ δὲ πρός τι πάντων ἥκιστα φύσις τις ἢ οὐσία ἐστι, καὶ ὑστέρα τοῦ ποιοῦ καὶ ποσοῦ· καὶ πάθος τι τοῦ ποσοῦ τὸ πρός τι, ὥσπερ ἐλέχθη, ἀλλʼ οὐχ ὕλη, εἴ τι ἕτερον καὶ τῷ ὅλως κοινῷ πρός τι καὶ τοῖς μέρεσιν αὐτοῦ καὶ εἴδεσιν.
And in addition to this error, the great and the small and all such things must be relatives; and the relative is least of all some nature or substance, and is posterior to quality and quantity; and the relative is an affection of quantity, as was said, but not matter, if indeed there is something else that is other both for the general relative as a whole and for its parts and species.
οὐθὲν γάρ ἐστιν οὔτε μέγα οὔτε μικρόν, οὔτε πολὺ οὔτε ὀλίγον, οὔτε ὅλως πρός τι, ὃ οὐχ ἕτερόν τι ὂν πολὺ ἢ ὀλίγον ἢ μέγα ἢ μικρὸν ἢ πρός τί ἐστιν.
For there is nothing either great or small, or much or few, or in general relative, which, without being something else, is much or few or great or small or relative.
σημεῖον δʼ ὅτι ἥκιστα οὐσί τις καὶ ὄν τι τὸ πρός τι τὸ μόνου μὴ εἶναι γένεσιν αὐτοῦ μηδὲ φθορὰν μηδὲ κίνησιν ὥσπερ κατὰ τὸ ποσὸν αὔξησις καὶ φθίσις, κατὰ τὸ ποιὸν ἀλλοίωσις, κατὰ τόπον φορά, κατὰ τὴν οὐσίαν ἡ ἁπλῆ γένεσις καὶ φθορά,—ἀλλʼ οὐ κατὰ τὸ πρός τι·
And it is a sign that the relative is least of all some substance and an entity that of it alone there is no generation or destruction or motion, as there is increase and decrease in quantity, alteration in quality, locomotion in respect of place, and simple generation and destruction in respect of substance — but not in respect of the relative.
ἄνευ γὰρ τοῦ κινηθῆναι ὁτὲ μὲν μεῖζον ὁτὲ δὲ ἔλαττον ἢ ἴσον ἔσται θατέρου κινηθέντος κατὰ τὸ ποσόν.
For without being moved, it will be at one time greater and at another smaller or equal, when the other has been moved in quantity.
ἀνάγκη τε ἑκάστου ὕλην εἶναι τὸ δυνάμει τοιοῦτον, ὥστε καὶ οὐσίας· τὸ δὲ πρός τι οὔτε δυνάμει οὐσία οὔτε ἐνεργείᾳ.
And it is necessary that the matter of each thing be that which is potentially of such a nature, and so also the matter of substance; but the relative is neither potentially nor actually a substance.
ἄτοπον οὖν, μᾶλλον δὲ ἀδύνατον, τὸ οὐσίας μὴ οὐσίαν ποιεῖν στοιχεῖον καὶ πρότερον· ὕστερον γὰρ πᾶσαι αἱ κατηγορίαι.
It is therefore absurd, or rather impossible, to make that which is not a substance an element of substance and prior to it; for all the other categories are posterior.
ἔτι δὲ τὰ στοιχεῖα οὐ κατηγορεῖται καθʼ ὧν στοιχεῖα, τὸ δὲ πολὺ καὶ ὀλίγον καὶ χωρὶς καὶ ἅμα κατηγορεῖται ἀριθμοῦ, καὶ τὸ μακρὸν καὶ τὸ βραχὺ γραμμῆς, καὶ ἐπίπεδόν ἐστι καὶ πλατὺ καὶ στενόν.
Moreover, elements are not predicated of those things of which they are elements; but much and few are predicated both separately and together of number, and long and short of a line, and a plane is both wide and narrow.
εἰ δὲ δὴ καὶ ἔστι τι πλῆθος οὗ τὸ μὲν ἀεί, τὸ ὀλίγον, οἷον ἡ δυάς (εἰ γὰρ πολύ, τὸ ἓν ἂν ὀλίγον εἴη), κἂν πολὺ ἁπλῶς εἴη, οἷον ἡ δεκὰς πολύ, εἰ ταύτης μή ἐστι πλεῖον, ἢ τὰ μύρια.
And if indeed there is some multiplicity of which one part is always the "few", such as the dyad (for if it were "much", the "one" would be "few"), and another part would be "much" simply, such as the decad is "much", if there is nothing more than this, or ten thousand.
πῶς οὖν ἔσται οὕτως ἐξ ὀλίγου καὶ πολλοῦ ὁ ἀριθμός;
How then will number be thus composed of the few and the much?
ἢ γὰρ ἄμφω ἔδει κατηγορεῖσθαι ἢ μηδέτερον· νῦν δὲ τὸ ἕτερον μόνον κατηγορεῖται.
For either both ought to be predicated or neither; but now only one of the two is predicated.

Notes

  1. 1088a15τὴν δυάδα δὲ ἀόριστον ποιοῦντες μεγάλου καὶ μικροῦ — The genitive phrase μεγάλου καὶ μικροῦ depends either on δυάδα or on ἀόριστον, and is here interpreted as a genitive of material or composition, meaning "the indefinite dyad consisting of the great and the small."
  2. 1088a24εἴ τι ἕτερον καὶ τῷ ὅλως κοινῷ πρός τι καὶ τοῖς μέρεσιν αὐτοῦ καὶ εἴδεσιν — The clause starting with εἴ τι ἕτερον functions as a conditional qualification or concession to the preceding negative "but not matter." It implies the omission of an existential verb (like ἐστίν or ὑπάρχει): "even if there is some other thing [as matter] both for the general relative as a whole and for its parts and species."
  3. 1088b9εἰ γὰρ πολύ, τὸ ἓν ἂν ὀλίγον εἴη — The subject of πολύ is the "dyad" (δυάς) mentioned in the preceding clause. The conditional construction with ἄν + imperfect indicative (or optative) presents an absurd logical consequence: "for if it (the dyad) were 'much', the 'one' would be 'few'."
  4. 1088b12ἢ γὰρ ἄμφω ἔδει κατηγορεῖσθαι ἢ μηδέτερον — The imperfect impersonal verb ἔδει expresses a logical obligation or necessity that is unrealized in the actual situation ("ought to have been"), serving to point out the inconsistency in the Platonist doctrine.

Cite this passage

Aristotle, Metaphysics §14.1#2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg025.humanitext-grc2:14.1%232

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