Combining Philosophers

All the ideas for Hermarchus, Samuel Alexander and Thoralf Skolem

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9 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Axiomatising set theory makes it all relative [Skolem]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Skolem did not believe in the existence of uncountable sets [Skolem]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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
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
Mathematician want performable operations, not propositions about objects [Skolem]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
To be is to have causal powers [Alexander,S]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
Epiphenomenalism makes the mind totally pointless [Alexander,S]
Epiphenomenalism is like a pointless nobleman, kept for show, but soon to be abolished [Alexander,S]
25. Social Practice / F. Life Issues / 6. Animal Rights
Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]