Combining Philosophers
Ideas for Eurytus, E.J. Lowe and Michal Walicki
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5 ideas
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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17762
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In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
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17754
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Inductive proof depends on the choice of the ordering [Walicki]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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8297
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Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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8266
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Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe]
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8302
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Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe]
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