Combining Philosophers
Ideas for Roger Fry, Michael D. Resnik and George Cantor
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9 ideas
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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9992
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The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
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10232
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Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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18176
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Pure mathematics is pure set theory [Cantor]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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6300
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Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
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6303
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Sets are positions in patterns [Resnik]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
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6295
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There are too many mathematical objects for them all to be mental or physical [Resnik]
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6296
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Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
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6301
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Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
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6302
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Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
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