Combining Texts
Ideas for
'Three Varieties of Knowledge', 'Introducing the Philosophy of Mathematics' and 'Principia Mathematica'
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12 ideas
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 / B. Propositional Logic PL / 3. Truth Tables
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8713
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In classical/realist logic the connectives are defined by truth-tables [Friend]
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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
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8708
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Double negation elimination is not valid in intuitionist logic [Friend]
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4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
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8694
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Free logic was developed for fictional or non-existent objects [Friend]
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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
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8665
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A 'proper subset' of A contains only members of A, but not all of them [Friend]
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8672
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A 'powerset' is all the subsets of a set [Friend]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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8677
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Set theory makes a minimum ontological claim, that the empty set exists [Friend]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
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8666
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Infinite sets correspond one-to-one with a subset [Friend]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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8682
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Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend]
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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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