Combining Texts
Ideas for
'W.V. Quine', 'The Theory of Logical Types' and 'The Foundations of Empirical Knowledge'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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8454
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The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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8473
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The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
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23457
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Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
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21556
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Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
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21568
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A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
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