Subject: Re: [HM] A question around zero
From: Luigi Borzacchini (gibi@pascal.dm.uniba.it)
Date: Mon Jan 31 2000 - 03:36:27 EST
Ralph Gainey writes:
>
> I have read that the ancient Greek language used both the definite
> and the indefinite article, unique among the contemporary cultures.
> This was said to give them an advantage in the consideration of
> early math and logic questions, such as Plato's detailed treatment
> of "the one and the many."
>
> Could someone suggest a reference for this view?
I am not an expert in the ancient Greek language, however I think that
the most famous reference for this question is Bruno Snell's book "Die
Entdeckung des Geistes" (1953, english transl. "The discovery of the mind"),
or his less famous "Der Weg zum Denken und zur Wahrheit" (Hypomnemata 57,
1978). Snell underlines the role played by the autonomous existence of a
determinative article in the genesis of the Greek philosophical lexicon,
for example to create abstract nouns from adjectives, verbs or Gods. I did
not find anything analogous about the indefinite article. As far as I know
there is not in ancient Greek an autonomous indefinite article: "a friend"
could be translated as "philos tis" or "philoon tis", where 'tis' is the
indefinite pronoun or adjective, as "eis philos", where 'eis' is the
numeral pronoun or adjective, or even simply as "philos".
>
> I am interested as well in an argument that Plato's discourse
> provides an early form of what is know as "the Russell Paradox."
>
Plato faced in almost all his dialogues the whole range of the Sophists'
paradoxes, from those concerning being and negatives, to those concerning
one/many or binary relationships. There is a great family of antinomies
whose ancestor is the "negative judgement paradox" ('the greatest quandary',
according to Plato), of Eleatic origin and forbidding the utterance of
negative judgements, which includes many further famous arguments, from the
"Meno" and "liar" paradoxes to Cantor's and Goedel's antinomical arguments.
Some occurrence of this antinomy could even be interpreted as stating
Russell's paradox, but I want to underline that it had to be a 'forced'
interpretation, because the set-theoretic style was completely stranger and
even rejected by Plato (and Aristotle), for 'ideas' and 'forms' were not
reducible to their parts: there could be no 'theoretical knowledge' of the
"heaps"!
Luigi Borzacchini
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