Combining Texts

All the ideas for 'fragments/reports', 'talk' and 'Commentary on Euclid's 'Elements''

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4 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined

23367	Even pointing a finger should only be done for a reason [Epictetus]
	Full Idea: Philosophy says it is not right even to stretch out a finger without some reason.
	From: Epictetus (fragments/reports [c.57], 15)
	A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!).

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

9916	Convention, yes! Arbitrary, no! [Poincaré, by Putnam]
	Full Idea: Poincaré once exclaimed, 'Convention, yes! Arbitrary, no!'.
	From: report of Henri Poincaré (talk [1901]) by Hilary Putnam - Models and Reality
	A reaction: An interesting view. It mustn't be assumed that conventions are not rooted in something. Maybe a sort of pragmatism is implied.

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.