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'works', 'Introduction to the Philosophy of Mathematics' and 'Abstract Objects'
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11 ideas
14. Science / B. Scientific Theories / 1. Scientific Theory
16971
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Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik]
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14. Science / C. Induction / 6. Bayes's Theorem
17943
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Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]
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14. Science / D. Explanation / 1. Explanation / a. Explanation
11243
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Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis]
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14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
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Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA]
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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
17938
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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 / k. Explanations by essence
12000
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Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung]
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14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
17934
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Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
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17933
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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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