Combining Texts

All the ideas for 'Letters to Thomasius', 'Remarks on axiomatised set theory' and 'Set Theory and related topics (2nd ed)'

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7 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes

8920	Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]

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

17879

Axiomatising set theory makes it all relative [Skolem]

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]

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]

9. Objects / D. Essence of Objects / 1. Essences of Objects

13432

The essence of a circle is the equality of its radii [Leibniz]

27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement

12696

Bodies are recreated in motion, and don't exist in intervening instants [Leibniz]