Combining Philosophers

Ideas for Giordano Bruno, Kit Fine and Jos A. Benardete

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4 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

3326	Set theory attempts to reduce the 'is' of predication to mathematics [Benardete,JA]
	Full Idea: Set theory offers the promise of a complete mathematization of the 'is' of predication.
	From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.13)

3327	The set of Greeks is included in the set of men, but isn't a member of it [Benardete,JA]
	Full Idea: Set inclusion is sharply distinguished from set membership (as the set of Greeks is found to be included in, but not a member of, the set of men).
	From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.13)

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

3335	The standard Z-F Intuition version of set theory has about ten agreed axioms [Benardete,JA, by PG]
	Full Idea: Zermelo proposed seven axioms for set theory, with Fraenkel adding others, to produce the standard Z-F Intuition.
	From: report of José A. Benardete (Metaphysics: the logical approach [1989], Ch.17) by PG - Db (ideas)

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets

10565	There is no stage at which we can take all the sets to have been generated [Fine,K]
	Full Idea: There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new.
	From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)