|
17263
|
Why do rationalists accept Sufficient Reason, when it denies the existence of fundamental facts? [Correia/Schnieder]
|
|
Full Idea:
What is most puzzling about the rationalist tradition is the steadfast certainty with which the Principle of Sufficient Reason was often accepted, since it in effect denies that there are fundamental facts.
|
|
From:
Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 2.2)
|
|
A reaction:
A very simple and interesting observation. The principle implies either a circle of reasons, or an infinite regress of reasons. Nothing can be labelled as 'primitive' or 'foundational' or 'given'. The principle is irrational!
|
|
17270
|
Is existential dependence by grounding, or do grounding claims arise from existential dependence? [Correia/Schnieder]
|
|
Full Idea:
We may take existential dependence to be a relation induced by certain cases of grounding, but one may also think that facts about existential dependence are prior to corresponding ground claims, and in fact ground those claims.
|
|
From:
Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 4.3)
|
|
A reaction:
I would vote for grounding, since dependence seems more abstract, and seems to demand explanation, whereas grounding seems more like a feature of reality, and to resist further intrinsic explanation (on the whole).
|
|
17267
|
The identity of two facts may depend on how 'fine-grained' we think facts are [Correia/Schnieder]
|
|
Full Idea:
There is a disagreement on the issue of factual identity, concerning the 'granularity' of facts, the question of how fine-grained they are.
|
|
From:
Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 3.3)
|
|
A reaction:
If they are very fine-grained, then no two descriptions of a supposed fact will capture the same details. If we go broadbrush, facts become fuzzy and less helpful. 'Fact' was never going to be a clear term.
|
|
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.
|