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Ideas for 'Introduction to Russell's Theory of Types', 'Philosophy of Mathematics' and 'Tractatus Logico-Philosophicus'

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11 ideas

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
18156 Modern axioms of geometry do not need the real numbers [Bostock]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
18097 The Peano Axioms describe a unique structure [Bostock]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
18153 A number is a repeated operation [Wittgenstein]
18160 The concept of number is just what all numbers have in common [Wittgenstein]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
18149 There are many criteria for the identity of numbers [Bostock]
18148 Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock]
18145 Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
18143 Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
18161 The theory of classes is superfluous in mathematics [Wittgenstein]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
18116 Numbers can't be positions, if nothing decides what position a given number has [Bostock]
18117 Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock]