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10198
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If only two indiscernible electrons exist, future differences must still be possible [Zimmerman,DW]
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Full Idea:
If nothing existed except two electrons, which are indiscernible, it remains possible that differences will emerge later. Even if this universe has eternal symmetry, such differences are still logically, metaphysically, physically and causally possible.
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From:
Dean W. Zimmerman (Distinct Indiscernibles and the Bundle Theory [1997], p.306)
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A reaction:
The question then is whether the two electrons have hidden properties that make differences possible. Zimmerman assumes that 'laws' of an indeterministic kind will do the job. I doubt that. Can differences be discerned after the event?
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10199
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Discernible differences at different times may just be in counterparts [Zimmerman,DW]
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Full Idea:
Possible differences which may later become discernible could be treated as differences in a counterpart, which is similar to, but not identical with, the original object.
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From:
Dean W. Zimmerman (Distinct Indiscernibles and the Bundle Theory [1997], p.307)
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A reaction:
[compressed] This is a reply to Idea 10198, which implies that two things could never be indiscernible over time, because of their different possibilities. One must then decide issues about rigid designation and counterparts.
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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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14608
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A-theorists, unlike B-theorists, believe some sort of objective distinction between past, present and future [Zimmerman,DW]
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Full Idea:
To be an A-theorist is to believe in some sort of objective distinction between what is present and past and future. ..To be a B-theorist is to deny the objectivity of our talk about past, present and future.
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From:
Dean W. Zimmerman (The Privileged Present: A-Theory [2008], 2)
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A reaction:
The A/B distinction originates with McTaggart. All my intuitions side with the A-theory, certainly to the extent that the present seems to be objectively privileged in some way (despite special relativity).
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