Combining Texts

All the ideas for 'Intellectual Norms and Foundations of Mind', 'An Axiomatization of Set Theory' and 'Models and Reality'

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7 ideas

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

13655

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

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

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size

15943

Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]

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

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

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

13672

All the axioms for mathematics presuppose set theory [Neumann]

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

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

26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws

14349

If there are no finks or antidotes at the fundamental level, the laws can't be ceteris paribus [Burge, by Corry]