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'', 'Introduction to the Philosophy of Mathematics' and 'Actualism and Possible Worlds'
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6 ideas
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
17939
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Mathematics can reveal structural similarities in diverse systems [Colyvan]
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14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
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Mathematics can show why some surprising events have to occur [Colyvan]
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14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
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Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
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Reductio proofs do not seem to be very explanatory [Colyvan]
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17935
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If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan]
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17942
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Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan]
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