|
18431
|
Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards]
|
|
Full Idea:
Simons's 'nuclear' option blends features of the substratum and bundle theories. First we have tropes collected by virtue of their internal relations, forming the essential kernel or nucleus. This nucleus then bears the non-essential tropes.
|
|
From:
report of Peter Simons (Particulars in Particular Clothing [1994], p.567) by Douglas Edwards - Properties 3.5
|
|
A reaction:
[compression of Edwards's summary] This strikes me as being a remarkably good theory. I am not sure of the ontological status of properties, such that they can (unaided) combine to make part of an object. What binds the non-essentials?
|
|
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.
|