Combining Texts
Ideas for
'works', 'Introduction to Mathematical Philosophy' and 'Causation and Explanation'
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12 ideas
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
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14427
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We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
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14428
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Members define a unique class, whereas defining characteristics are numerous [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
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14447
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Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell]
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14440
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We may assume that there are infinite collections, as there is no logical reason against them [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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14443
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The British parliament has one representative selected from each constituency [Russell]
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14445
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Choice shows that if any two cardinals are not equal, one must be the greater [Russell]
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14444
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Choice is equivalent to the proposition that every class is well-ordered [Russell]
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14446
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We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
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14459
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Reducibility: a family of functions is equivalent to a single type of function [Russell]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
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14461
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Propositions about classes can be reduced to propositions about their defining functions [Russell]
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4. Formal Logic / F. Set Theory ST / 7. Natural Sets
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8469
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Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein]
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
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8745
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Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell]
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