Combining Texts

Ideas for 'Classical Cosmology (frags)', 'Replies on 'Limits of Abstraction'' and 'Constructibility and Mathematical Existence'

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2 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)

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

8758	We could talk of open sentences, instead of sets [Chihara, by Shapiro]
	Full Idea: Chihara's programme is to replace talk of sets with talk of open sentences. Instead of speaking of the set of all cats, we talk about the open sentence 'x is a cat'.
	From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2
	A reaction: As Shapiro points out, this is following up Russell's view that sets should be replaced with talk of properties. Chihara is expressing it more linguistically. I'm in favour of any attempt to get rid of sets.