Combining Texts

All the ideas for 'Syntactic Structure', 'The Theory of Transfinite Numbers' and 'Mathematics: Form and Function'

expand these ideas     |    start again     |     specify just one area for these texts

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5 ideas

2. Reason / F. Fallacies / 8. Category Mistake / c. Category mistake as semantic

18009

Chomsky established the view that category mistakes are well-formed but meaningless [Chomsky, by Magidor]

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

9616	A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]

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

18189

ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities

15896

Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]

19. Language / C. Assigning Meanings / 1. Syntax

18007

Syntax is independent of semantics; sentences can be well formed but meaningless [Chomsky, by Magidor]