Combining Texts

All the ideas for 'fragments/reports', 'Remarks on axiomatised set theory' and 'Models and Reality'

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9 ideas

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

17879

Axiomatising set theory makes it all relative [Skolem]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L

9915	V = L just says all sets are constructible [Putnam]

13655

The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17878

If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]

9913	The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam]

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

17880

Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17881

Mathematician want performable operations, not propositions about objects [Skolem]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

9914	It is unfashionable, but most mathematical intuitions come from nature [Putnam]

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]