Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Principia Mathematica' and 'The Boundary Stones of Thought'
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15 ideas
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
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18803
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Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
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9542
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The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
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18814
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'Absolute necessity' would have to rest on S5 [Rumfitt]
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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
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18798
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It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt]
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18799
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Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt]
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
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17884
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Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
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17893
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'Reflection principles' say the whole truth about sets can't be captured [Koellner]
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18830
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Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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18843
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The iterated conception of set requires continual increase in axiom strength [Rumfitt]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
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18836
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A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt]
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18837
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A set can be determinate, because of its concept, and still have vague membership [Rumfitt]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
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18845
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If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
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21720
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Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead]
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
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10044
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Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro]
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18208
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We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead]
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