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14. Science / D. Explanation / 2. Types of Explanation / l. Explanation by proof

[proofs which also reveal why something is true]

5 ideas
Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
Reductio proofs do not seem to be very explanatory [Colyvan]
Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan]
Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan]