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19542
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It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew]
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Full Idea:
The proposition that understanding does not involve knowledge is widespread (for example, in discussions of what philosophy aims at), but hardly withstands scrutiny. If you do not know how a jet engine works, you do not understand how it works.
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From:
Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.24)
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A reaction:
This seems a bit disingenuous. As in 'Theaetetus', knowing the million parts of a jet engine is not to understand it. More strongly - how could knowledge of an infinity of separate propositional truths amount to understanding on their own?
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19541
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Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew]
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Full Idea:
If we say our cognitive aim is to get knowledge, the opposing views are the naturalistic view that what matters is just true belief (or just 'getting by'), or that there are rival epistemic goods such as understanding and wisdom.
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From:
Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.17)
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A reaction:
[compressed summary] I'm a fan of understanding. The accumulation of propositional knowledge would relish knowing the mass of every grain of sand on a beach. If you say the propositions should be 'important', other values are invoked.
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19539
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If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew]
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Full Idea:
If knowledge is indeed unanalyzable, that could be seen as a liberation of justification to assume importance in its own right.
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From:
Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.11)
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A reaction:
[They cite Kvanvig 2003:192 and Greco 2010:9-] See Scruton's Idea 3897. I suspect that we should just give up discussing 'knowledge', which is a woolly and uninformative term, and focus on where the real epistemological action is.
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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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