Combining Texts
Ideas for
'Individuals without Sortals', 'Principia Mathematica' and 'Idealism: a critical survey'
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12 ideas
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 / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
17518
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Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
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17516
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If counting needs a sortal, what of things which fall under two sortals? [Ayers]
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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 / 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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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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