Combining Philosophers

All the ideas for Hermarchus, Thoralf Skolem and Augustus De Morgan

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9 ideas

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 / E. Structures of Logic / 6. Relations in Logic

17744

De Morgan started the study of relations and their properties [De Morgan, by Walicki]

13501

De Morgan found inferences involving relations, which eluded Aristotle's syllogistic [De Morgan, by Hart,WD]

5. Theory of Logic / G. Quantification / 2. Domain of Quantification

17743

De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki]

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]

25. Social Practice / F. Life Issues / 6. Animal Rights

6005	Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]