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Headword: Μόνον καὶ ἓν διαφέρει
Adler number: mu,1232
Translated headword: monad and one differ
Vetting Status: high
Translation:
"[...] the monad [is] that which exists in things noetic, but the one [is that which exists] among the sensible numbers.[1] And while the monad is apprehended in accordance with equality and proportion, the dyad [sc. is taken] in accordance with excess and deficiency."[2]
Greek Original:
Μόνον καὶ ἓν διαφέρει: μονὰς ἡ ἐν τοῖς νοητοῖς οὖσα, ἓν δὲ τὸ ἐν τοῖς αἰσθητοῖς ἀριθμοῖς. καὶ ἡ μὲν μονὰς κατὰ τὴν ἰσότητα καὶ μέτρον λαμβάνεται, ἡ δὲ δυὰς καθ' ὑπερβολὴν καὶ ἔλλειψιν.
Notes:
The headword phrase summarises the following quoted text (on which see below), with slight variation in the first of the two terms being contrasted: μόνον is the neuter nominative, vocative, and accusative (and masculine accusative) singular form of the adjective μόνος, -η, -ον ("alone, solitary"; see LSJ s.v. The other term, ἕν ("one"), is the neuter form of the numeral adjective εἷς and μία , masculine and feminine gender, respectively (see LSJ s.v. and Smyth §347).
[1] The importance of the difference between noetic (pure, ideal, intelligible, abstract) and aesthetic (sensible, tangible, concrete) numbers to Greek philosophy and mathematics is explained by Klein (p. 10 and pp. 46-51).
[2] Together with the headword phrase, this quotation approximates the Life of Pythagoras in Photius, Bibliotheca 249.438b33-8. The Suda omits that part of Photius' entry attributing the distinction between noetic and aesthetic numbers to the followers of Pythagoras (C6 BCE); cf. pi 3120, pi 3121, pi 3123, pi 3124, and OCD(4) s.v. But Aristotle, Metaphysics 987a19-20 (web address 1), asserts that the Pythagoreans had no such distinction; they maintained that number was the being (τὰ οὐσία , "essence") of all things. Indeed he claims that the distinction is Platonic in origin. At Metaphysics 987b7-11 (web address 2) he points to Plato's separation of numbers as Forms or Ideas from sensible things and further to his mentor's having posited a realm of "mathematical entities" intermediate between noetic and aesthetic being; cf. Metaphysics 987b14-18 (web address 2) and Burkert, pp. 30-1.
References:
H.W. Smyth, Greek Grammar, Cambridge, MA: Harvard University Press, 1956
J. Klein, Greek Mathematical Thought and the Origin of Algebra, trans. E. Brann, Cambridge, MA: M.I.T. Press, 1968
W. Burkert, Lore and Science in Ancient Pythagoreanism, trans. E.L. Minar, Jr., Cambridge, MA: Harvard University Press, 1972
Associated internet addresses:
Web address 1,
Web address 2
Keywords: biography; definition; dialects, grammar, and etymology; mathematics; philosophy
Translated by: Ronald Allen on 3 January 2009@00:39:14.
Vetted by:
Catharine Roth (tweaks and cosmetics) on 4 January 2009@20:00:10.
David Whitehead (tweaks and cosmetics) on 5 January 2009@03:08:37.
David Whitehead on 27 May 2013@04:07:17.
David Whitehead on 9 August 2014@09:02:17.
Catharine Roth (cosmeticule) on 20 December 2014@00:59:24.
David Whitehead (coding) on 18 May 2016@09:55:11.

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