Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'Commentary on Euclid's 'Elements'' and 'Self-Reliance'

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4 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason

6558	A foolish consistency is the hobgoblin of little minds [Emerson]
	Full Idea: A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do.
	From: Ralph Waldo Emerson (Self-Reliance [1841], p.37)
	A reaction: A remark to warm the hearts of pragmatists, Wittgensteinians, Nietzscheans and the post-modern mob. But pay careful attention to the word "foolish". Robert Fogelin gives a very balanced view of the matter (e.g. Idea 6557).

9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined

19347	Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
	Full Idea: For individuation, substance needs three properties: independence, to separate it from other things; unity, to call it one thing, rather than an aggregate; and permanence or stability over time. Its other role is as subject for predicates.
	From: Franklin Perkins (Leibniz: Guide for the Perplexed [2007], 3.1)
	A reaction: Perkins is describing the Aristotelian view, which is taken up by Leibniz. 'Substance' is not a controversial idea, if we see that it only means that the world is full of 'things'. It is an unusual philosopher wholly totally denies that.

14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations

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.

18. Thought / E. Abstraction / 1. Abstract Thought

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.