Combining Texts
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'works', 'Philosophy of Mathematics' and 'Things qua Truthmakers'
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8 ideas
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
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9646
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There is no limit to how many ways something can be proved in mathematics [Brown,JR]
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9647
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Computers played an essential role in proving the four-colour theorem of maps [Brown,JR]
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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 / 6. Mathematics as Set Theory / b. Mathematics is not set theory
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9643
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Set theory may represent all of mathematics, without actually being mathematics [Brown,JR]
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9644
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When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
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9625
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To see a structure in something, we must already have the idea of the structure [Brown,JR]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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9628
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Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR]
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