Combining Philosophers
Ideas for Rescher,N/Oppenheim,P, B Russell/AN Whitehead and Solon
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8 ideas
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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10037
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'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
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10025
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Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
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8683
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Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
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10093
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The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
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8691
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The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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10305
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In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
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8684
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Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
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8746
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To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro]
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