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Search results for mu,1232 in Adler number:
Headword:
*mo/non
kai\
e(\n
diafe/rei
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:*mo/non kai\ e(\n diafe/rei: mona\s h( e)n toi=s nohtoi=s ou)=sa, e(\n de\ to\ e)n toi=s ai)sqhtoi=s a)riqmoi=s. kai\ h( me\n mona\s kata\ th\n i)so/thta kai\ me/tron lamba/netai, h( de\ dua\s kaq' u(perbolh\n kai\ e)/lleiyin.
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:
mo/non is the neuter nominative, vocative, and accusative (and masculine accusative) singular form of the adjective
mo/nos, -h, -on ("alone, solitary"; see LSJ s.v. The other term,
e(/n ("one"), is the neuter form of the numeral adjective
ei(=s and
mi/a, masculine and feminine gender, respectively (see LSJ s.v. and Smyth ยง347).
[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 (
ta\ ou)si/a, "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:
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