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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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7667
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There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin]
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Full Idea:
Diderot is among the first to preach that there are two men: the artificial man, who belongs in society and seeks to please, and the violent, bold, criminal instinct of a man who wishes to break out (and, if controlled, is responsible for works of genius.
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From:
report of Denis Diderot (works [1769], Ch.3) by Isaiah Berlin - The Roots of Romanticism
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A reaction:
This has an obvious ancestor in Plato's picture (esp. in 'Phaedrus') of the two conflicting sides to the psuché, which seem to be reason and emotion. In Diderot, though, the suppressed man has virtues, which Plato would deny.
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5888
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Souls are born, since they are sensitive and inherited, so they must perish [Panaetius, by Cicero]
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Full Idea:
Panaetius says that whatever is born must perish, and souls are clearly born, as shown by the resemblance of children to their parents in disposition as well as body; also, anything sensible of pain is susceptible to sickness, and hence perishes.
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From:
report of Panaetius (fragments/reports [c.145 BCE]) by M. Tullius Cicero - Tusculan Disputations I.xxxii
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A reaction:
These seem to be rather good arguments. If we actually observe what someone's soul is like (through character) it seems rooted in a family and culture, and it certainly seems susceptible to disease. An empirical approach.
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