Chapter XIX.—Pythagoras’ Duality of Substances; His “Categories.”

There are, then, according to Pythagoras, two worlds: one intelligible, which has the monad for an originating principle; and the other sensible. But of this (latter) is the quaternion having the iota, the one tittle,637    Matt. v. 18. a perfect number. And there likewise is, according to the Pythagoreans, the i, the one tittle, which is chief and most dominant, and enables us to apprehend the substance of those intelligible entities which are capable of being understood through the medium of intellect and of sense. (And in this substance inhere) the nine incorporeal accidents which cannot exist without substance, viz., “quality,” and “quantity,” and “relation,” and “where,” and “when,” and “position,” and “possession,” and “action,” and “passion.” These, then, are the nine accidents (inhering in) substance, and when reckoned with these (substances), contains the perfect number, the i.  Wherefore, the universe being divided, as we said, into the intelligible and sensible world, we have also reason from the intelligible (world), in order that by reason we may behold the substance of things that are cognised by intellect, and are incorporeal and divine. But we have, he says, five senses—smelling, seeing, hearing, taste, and touch. Now, by these we arrive at a knowledge of things that are discerned by sense; and so, he says, the sensible is divided from the intelligible world. And that we have for each of these an instrument for attaining knowledge, we perceive from the following consideration. Nothing, he says, of intelligibles can be known to us from sense. For he says neither eye has seen, nor ear heard, nor any whatsoever of the other senses known that (which is cognised by mind). Neither, again, by reason is it possible to arrive at a knowledge of any of the things discernible by sense.  But one must see that a thing is white, and taste that it is sweet, and know by hearing that it is musical or out of tune. And whether any odour is fragrant or disagreeable, is the function of smell, not of reason. It is the same with objects of touch; for anything rough, or soft, or warm, or cold, it is not possible to know by hearing, but (far from it), for touch is the judge of such (sensations).  Things being thus constituted, the arrangement of things that have been made and are being made is observed to happen in conformity with numerical (combinations). For in the same manner as, commencing from monad, by an addition of monads or triads, and a collection of the succeeding numbers, we make some one very large complex whole of number; (and) then, again, from an amassed number thus formed by addition, we accomplish, by means of a certain subtraction and re-calculation, a solution of the totality of the aggregate numbers; so likewise he asserts that the world, bound by a certain arithmetical and musical chain, was, by its tension and relaxation, and by addition and subtraction, always and for ever preserved incorrupt.

[24] Δύο οὖν κατὰ τὸν Πυθαγόραν εἰσὶ κόσμοι: εἷς μὲν νοητός, ὃς ἔχει τὴν μονάδα ἀρχήν, εἷς δὲ αἰσθητός: τούτου δέ ἐστι[ν ἀρχὴ ἡ] τετρακτύς, ἔχουσα ἰῶτα, τὴν «μίαν κεραίαν», ἀριθμὸν τέλειον. καὶ ἔστι κατὰ τοὺς Πυθαγορικοὺς τὸ [ι], ἡ μία κεραία, πρώτη καὶ κυριωτάτη καὶ τ(ῶ)ν νοητῶν [καὶ τῶν αἰσθητῶν] οὐσία, νοητῶς καὶ αἰσθητῶς λαμβανομένη. [ᾗ δ' ἔστι] συμβεβηκότα γένη ἀσώματα ἐννέα, ἃ χωρὶς εἶναι τῆς οὐσίας οὐ δύναται: ποιὸν καὶ ποσὸν καὶ πρός τι καὶ ποῦ καὶ (π)ό(τ)ε καὶ κεῖσθαι καὶ ἔχειν καὶ ποιεῖν καὶ π(ά)σχειν. ἔστιν οὖν ἐννέα τὰ συμβεβηκότα τῇ οὐσίᾳ, οἷς συναριθμουμένη ἔχει τὸν τέλειον ἀριθμόν, τὸν δέκα. Διό(π)ερ διῃρημένου τοῦ παντός, ὡς εἴπομεν, εἰς νοητὸν καὶ αἰσθητὸν κόσμον, ἔχομεν καὶ ἡμεῖς ἀπὸ τοῦ νοητοῦ τὸν λόγον, ἵνα τῷ λόγῳ τὴν τῶν νοητῶν καὶ ἀσωμάτων καὶ θείων ἐποπτεύωμεν οὐσίαν. αἰσθήσεις δέ, φησίν, ἔχομεν πέντε_ὄσφρησιν, ὅρασιν, ἀκοήν, γεῦσιν καὶ ἁφήν_, [ἐν] αἷς τῶν αἰσθητῶν ἐρχόμεθα εἰς γνῶσιν. καὶ οὕτω, φησίν, ἐστὶ διῃρημένος [ὁ] αἰσθητὸς ἀπὸ τοῦ νοητοῦ κόσμου. καὶ ὅτι ἔχομεν γνώσεως ὄργανον πρὸς ἑκάτερον αὐτῶν, ἐντεῦθεν κατανοῶμεν. οὐδέν, φησί, τῶν νοητῶν γνωστὸν ἡμῖν δύναται γενέσθαι δι' αἰσθήσεως. ἐκεῖνο γὰρ «οὔτε ὀφθαλμὸς εἶδεν οὔτε οὖς ἤκουσεν» οὔτ' ἔγνω, φησί, τῶν ἄλλων αἰσθήσεων οἱαδητισοῦν. οὐδ' αὖ πάλιν, [φησί,] τῷ λόγῳ εἰς γνῶσιν τῶν αἰσθητῶν οὐχ οἷόν τε ἐλθεῖν τινος, ἀλλὰ δεῖ [ἡμᾶς] ὅτι [τι] λευκόν ἐστιν ἰδεῖν, καὶ γεύσασθαι ὅτι [τι] γλυ(κ)ύ, καὶ ὅτι [τι] ᾠδικὸν ἢ δύσηχον ἀκούσαντας εἰδέναι: (κ)αὶ εἴ τι τῶν ὀσμῶν ἐστιν εὐῶδες ἢ ἀηδές, ὀσφρήσεως ἔργον, οὐ λόγου. ὡσαύτως δὲ ἔχει καὶ τὰ τῆς ἁφῆς: σκληρὸν γὰρ ἢ ἁπαλόν, ἢ θερμὸν ἢ ψυχρὸν οὐχ οἷόν τέ ἐστιν ἀκούσαντα[ς] εἰδέναι, ἀλλὰ γὰρ τῶν τοιούτων ἐστὶ κρίσις ἡ ἁφή. Τούτων οὕτως ὑφεστηκότων ἡ διακόσμησις, [φησί,] τῶν γεγονότων καὶ γινομένων ἀριθμητικῶς γινομένη θεωρεῖται. ὃν γὰρ τρόπον ἀπὸ μονάδος ἀρξάμενο(ι) κατὰ προσθήκην (δυ)άδων ἢ τριάδων καὶ τῶν ἑξῆς ἀθροιζομένων ἀριθμῶν ἕν τι σύστημα ποιοῦμεν μέγιστον ἀριθμοῦ, εἶτα πάλιν ἀπὸ τοῦ κατὰ [τὴν] σύνθεσιν ἀθροισθέντος ἀφαιρέσει τινὶ καὶ ἀναποδισμῷ λύσιν τῶν συνεστώτων ἀριθμητικῶς ἐργαζόμεθα,