13165
|
Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]
|
|
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.
|
|
From:
Proclus (Commentary on Euclid's 'Elements' [c.452], p.161-2), quoted by Paolo Mancosu - Explanation in Mathematics §5
|
|
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.
|
9569
|
The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]
|
|
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.
|
|
From:
Proclus (Commentary on Euclid's 'Elements' [c.452]), quoted by Charles Chihara - A Structural Account of Mathematics 9.12 n55
|
|
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.
|
20445
|
Levinas says Marxism is the replacement of individualist ethics, by solidarity and sociality [Levinas, by Critchley]
|
|
Full Idea:
For Levinas, Marxism is the absorption of the ethical in the socioeconomic, and so it is the disappearance of the face-to-face relation and the privileging of relations of solidarity and anonymous sociality, which he calls 'socialism'.
|
|
From:
report of Emmanuel Levinas (works [1956]) by Simon Critchley - Impossible Objects: interviews 1
|
|
A reaction:
Startling, if you are not used to this sort of thing. If you are in trouble, I should help you, not because you are you, or a human being, but because you are a member of my group? So what about the Good Samaritan? Or solidarity with humanity? Animals?
|