Combining Philosophers
Ideas for Eubulides, Willard Quine and B Russell/AN Whitehead
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11 ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
3302
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Set theory is full of Platonist metaphysics, so Quine aimed to keep it separate from logic [Quine, by Benardete,JA]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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NF has no models, but just blocks the comprehension axiom, to avoid contradictions [Quine, by Dummett]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
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Quine wants V = L for a cleaner theory, despite the scepticism of most theorists [Quine, by Shapiro]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21720
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Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead]
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21717
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Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B]
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18170
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The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
21695
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The set scheme discredited by paradoxes is actually the most natural one [Quine]
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4. Formal Logic / F. Set Theory ST / 7. Natural Sets
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Russell's antinomy challenged the idea that any condition can produce a set [Quine]
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
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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3336
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Two things can never entail three things [Quine, by Benardete,JA]
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