Combining Philosophers

Ideas for Protagoras, Cratylus and Ian Rumfitt

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5 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

18830

Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt]

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

18843

The iterated conception of set requires continual increase in axiom strength [Rumfitt]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I

18836

A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt]

18837

A set can be determinate, because of its concept, and still have vague membership [Rumfitt]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI

18845

If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt]