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Headword: Εἴδη
Adler number: epsiloniota,29
Translated headword: forms
Vetting Status: high
The Pythagoreans used to say that the monad and dyad and triad are principles of the forms, since those who arrange from the monad up to the tetrad produce the decad; and they also regarded it perfect and named it 'receptacle'.[1] So they said that these tetradic principles existed in everything, both in general and in particular, and in the domain of the intelligible as well as in the physical and sensible things. Now the intelligible things are a monad in all respects (for it is understood not only that their substance is lacking parts but also that their activity is at rest and in absence of movement),[2] and knowledge or objects of knowledge are also a dyad. For [this is] what according to its definition goes from something toward something, for knowledge is a transformation from what is definite toward what is definite.[3] For there is no knowledge that is indefinite; this is, in fact, how knowledge gets its name: because it leads us to [a state of] rest.[4] That which is the object of opinion and that which is physical are triads, and I call the universals 'physical things', I mean the ones that are in the domain of physical things, but not the particulars. For opinion [concerns] the universal physical things. Therefore, opinion is a triad since it starts from something, and it does not go to something in a definite way but in this way or that.
Greek Original:
Εἴδη: ὅτι ἀρχὰς τῶν εἰδῶν ἔλεγον οἱ Πυθαγόρειοι τὴν μονάδα καὶ δυάδα καὶ τριάδα, διότι οἱ ἀπὸ μονάδος συντιθέμενοι μέχρι τῆς τετράδος ποιοῦσι τὸν δέκα, ὃς αὐτοῖς καὶ τέλειος ἐνομίζετο, καὶ δεχὰς ἐπωνομάζετο. εἶναι οὖν ἔλεγον τὰς τετραδικὰς ταύτας ἀρχὰς καὶ κοινῶς ἐν πᾶσι καὶ ἰδίᾳ ἔν τε τοῖς νοητοῖς καὶ ἐν τοῖς φυσικοῖς καὶ ἐν τοῖς αἰσθητοῖς. κοινῶς μὲν οὖν ἐπὶ πάντων μονὰς μὲν τὰ νοητὰ [ἀμερὴς γὰρ ἐκείνων οὐ μόνον ἡ οὐσία, ἀλλὰ καὶ ἡ ἐνέργεια ἐν στάσει καὶ ἀκινησίᾳ θεωρουμένη], δυὰς δὲ καὶ ἡ ἐπιστήμη ἢ τὰ ἐπιστημονικά: ὡρισμένως γὰρ τὸ ἀπό του ἐπί τι ἔρχεται. ἡ γὰρ ἐπιστήμη μετάβασίς ἐστιν ἐξ ὡρισμένων εἰς ὡρισμένα: οὐκ ἔστι γὰρ ἐπιστήμη ἀόριστος: ἔνθεν γὰρ καὶ ἐπιστήμη ἐκλήθη, παρὰ τὸ ἐπὶ στάσιν ἡμᾶς ἄγειν. τριὰς δὲ τὰ δοξαστὰ καὶ φυσικά: φυσικὰ δέ φημι τὰ καθόλου, τὰ ἐν τοῖς φυσικοῖς, ἀλλ' οὐ τὰ καθ' ἕκαστα. τῶν γὰρ καθόλου φυσικῶν ἡ δόξα. τριὰς οὖν ἡ δόξα, διὰ τὸ ὁρμᾶν μὲν ἀπό του, μὴ ὡρισμένως δὲ ἐπί τι φέρεσθαι, ἀλλ' ἢ ὧδε ἢ ὧδε.
From John Philoponus, Commentary on Aristotle's De anima 76.9-32 Hayduck.
[1] The Pythagoreans were probably interested in the decad, which they considered as being perfect, because it can be expressed in the form of a tetraktys or succession of the numbers 1-2-3-4, represented as points arranged in a triangle. Each number would correspond to the sequence point-line-plane-solid (see Ross [1981] 144-146 and, more recently, Annas [1976] 55ff.; on the Pythagorean thesis that the number ten is perfect see Aristotle, Metaphysics 986a6ff., and Burkert's comments ad locum in his 1972 commentary). According to Aristotle's testimony, since the Pythagoreans saw that the attributes and the ratios of the musical scale were expressible in numbers, and since all other things in the whole of nature seemed to be modeled after numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things. They held the number 10 to be perfect insofar as it comprises the whole nature of numbers (Metaphysics 985b23-986a12). This account is also given by Asclepius, who, in commenting on Aristotle's Metaphysics, says: 'they (i.e. the Pythagoreans) used to call the world 'number ten', since just as the number ten is capable of receiving all the numbers, so too the world is capable of receiving all the forms' (On the Metaphysics 35.17-19). A few lines later Asclepius clarifies again why the number ten or 'decad' is called 'receptacle', but this time he uses the same word as the Suda (dechas): 'for just as the world is capable of receiving the forms, so too the number ten contains in itself all the numbers, insofar as it is a receptacle' (On the Metaphysics 38.30-32). The connection between 'decad' (δεκάς ) and 'receptacle' (δεχάς ) is also reinforced by the similarity of the words in Greek, a similarity hard to reflect in translation.
[2] Probable reference to Aristotle (see Nicomachean Ethics 1154b26-27: 'for activity belongs not only to movement but also to absence of movement').
[3] See Aristotle, Protrepticus fr.33.2: 'for knowledge is more concerned with things that are defined and ordered than with their contraries' (Oxford Translation).
[4] A play on the etymological connection between ἐπιστήμη (knowledge) and στάσις (rest). Aristotle maintains that the original acquisition of knowledge is not a case of generation or alteration; and this happens because, Aristotle argues, our thought knows and understands when it is at rest and is not active. The core of this doctrine holds that thought starts when it goes away from the permanent flux of sensation and opinion and occupies a certain condition of calm and rest (Physics 247b9-13). For the Platonic antecedents of this theory, see Plato, Phaedo 96B and Cratylus 437A.
Annas, J., Aristotle's Metaphysics. Books M and N (Oxford: Clarendon Press 1976)
Burkert, W., Lore and Science in Ancient Pythagoreanism, trans. Minar. (Cambridge MA: Harvard University Press 1972)
Ross, W.D., Aristotle's Metaphysics (Oxford: Clarendon Press 1981 reprint)
Keywords: definition; dialects, grammar, and etymology; mathematics; philosophy; science and technology
Translated by: Marcelo Boeri on 15 May 2001@08:30:47.
Vetted by:
William Hutton (Modified translation, augmented notes, added keyword, cosmetics, raised status) on 16 May 2001@10:09:28.
David Whitehead (added note and keyword; restorative and other cosmetics) on 24 December 2002@09:33:43.
David Whitehead (another keyword; tweaking) on 22 November 2012@09:30:16.
Catharine Roth (coding) on 15 June 2015@00:35:36.
David Whitehead (cosmetics) on 21 April 2016@09:03:50.
Catharine Roth (tweaked translation and notes) on 8 April 2018@20:51:24.


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