Combining Philosophers

Ideas for Epicurus, Menedemus and Ian Rumfitt

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10 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
18803 Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
12204 The logic of metaphysical necessity is S5 [Rumfitt]
18814 'Absolute necessity' would have to rest on S5 [Rumfitt]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18798 It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt]
18799 Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt]
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]