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'Action', 'Principia Mathematica' and 'Number Determiners, Numbers, Arithmetic'
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17 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9998
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What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber]
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10002
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'2 + 2 = 4' can be read as either singular or plural [Hofweber]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
18248
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A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
18152
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Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10003
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Why is arithmetic hard to learn, but then becomes easy? [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
10008
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Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
10005
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Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
10000
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We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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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10037
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'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
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
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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10006
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First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
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
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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