Combining Texts

All the ideas for 'Set Theory and related topics (2nd ed)', 'Remarks on axiomatised set theory' and 'Questions on Aristotle's Physics'

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9 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 / C. Structure of Objects / 4. Quantity of an Object

16678

Without magnitude a thing would retain its parts, but they would have no location [Buridan]

9. Objects / E. Objects over Time / 8. Continuity of Rivers

16793

A thing is (less properly) the same over time if each part is succeeded by another [Buridan]

14. Science / A. Basis of Science / 2. Demonstration

16577

Induction is not demonstration, because not all of the instances can be observed [Buridan]

14. Science / C. Induction / 2. Aims of Induction

16576

Science is based on induction, for general truths about fire, rhubarb and magnets [Buridan]