Combining Philosophers

Ideas for Michael Burke, Pierre-Joseph Proudhon and Michael Dummett

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4 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
10537 The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9193 ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
9194 The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10542 To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett]