12314
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Audience-relative explanation, or metaphysical explanation based on information? [Stanford]
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Full Idea:
Rather than an 'interest-relative' notion of explanation (Putnam), it can be informational content which makes an explanation, which is an 'audience-invariant' contraint, which is not pragmatic, but mainly epistemological and also partly metaphysical.
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From:
Michael Stanford (Explanation: the state of play [1991], p.172)
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A reaction:
[compressed summary of Ruben 1990] Examples given are that Rome burning explains Nero fiddling, even if no one ever says so, and learning that George III had porphyria explains his madness.
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13165
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Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]
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Full Idea:
Geometry does not ask 'why?' ..When from the exterior angle equalling two opposite interior angles it is shown that the interior angles make two right angles, this is not a causal demonstration. With no exterior angle they still equal two right angles.
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From:
Proclus (Commentary on Euclid's 'Elements' [c.452], p.161-2), quoted by Paolo Mancosu - Explanation in Mathematics §5
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A reaction:
A very nice example. It is hard to imagine how one might demonstrate the cause of the angles making two right angles. If you walk, turn left x°, then turn left y°, then turn left z°, and x+y+z=180°, you end up going in the original direction.
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9569
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The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]
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Full Idea:
It is unsurprising that geometry was discovered in the necessity of Nile land measurement, since everything in the world of generation goes from imperfection to perfection. They would naturally pass from sense-perception to calculation, and so to reason.
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From:
Proclus (Commentary on Euclid's 'Elements' [c.452]), quoted by Charles Chihara - A Structural Account of Mathematics 9.12 n55
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A reaction:
The last sentence is the core of my view on abstraction, that it proceeds by moving through levels of abstraction, approaching more and more general truths.
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