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16672
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Quantity is the quantified parts of a thing, plus location and coordination [Olivi]
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Full Idea:
Quantity refers to nothing other than the parts of the thing quantified, together with their location or position, being extrinsically coordinated with each other.
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From:
Peter John Olivi (Treatise on Quantity [1286], f. 49vb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.1
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A reaction:
I'm not sure I understand 'extrinsically'. Is there some external stretching force? God spends his time spreading out his stuff? It is nice that being spread out isn't taken for granted. We take much more for granted than they did. Motion, for example.
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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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23689
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Moral words have an inherited power from expressing attitudes in emotional situations [Stevenson,CL]
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Full Idea:
A term is moral because of the power that the word acquires, on account of its history in emotional situations, to evoke or directly express attitudes, as distinct from describing or designating them.
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From:
Charles Leslie Stevenson (Ethics and Language [1944], p.33), quoted by John Hacker-Wright - Philippa Foot's Moral Thought 1 'Ayer'
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A reaction:
Invites the question of what the words meant before they acquired this patina of historical usage. If 'good' orginally meant 'hurray!', its repeated usage doesn't seem to change that. If it was descriptive, why would that change with time?
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