Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Catherine Z. Elgin and Thoralf Skolem

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9 ideas

2. Reason / A. Nature of Reason / 6. Coherence

8616	How can multiple statements, none of which is tenable, conjoin to yield a tenable conclusion? [Elgin]

8617	Statements that are consistent, cotenable and supportive are roughly true [Elgin]

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 / 8. Critique of Set Theory

13536

Skolem did not believe in the existence of uncountable sets [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]

13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification

8618	Coherence is a justification if truth is its best explanation (not skill in creating fiction) [Elgin]

14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction

20653

Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]