Combining Philosophers
Ideas for Hermarchus, Baruch de Spinoza and Michael D. Resnik
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10 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
17185
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Mathematics deals with the essences and properties of forms [Spinoza]
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6304
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Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
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6. Mathematics / A. Nature of Mathematics / 2. Geometry
17222
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The sum of its angles follows from a triangle's nature [Spinoza]
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17197
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The idea of a triangle involves truths about it, so those are part of its essence [Spinoza]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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
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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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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