Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Commentary on Euclid's 'Elements'' and 'Goodness and Choice'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

5 ideas

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.

22. Metaethics / B. Value / 2. Values / b. Successful function

22381	Being a good father seems to depend on intentions, rather than actual abilities [Foot]
	Full Idea: Being a good father, or daughter, or friend seems to depend on one's intentions, rather than on such things as cleverness and strength.
	From: Philippa Foot (Goodness and Choice [1961], p.138)
	A reaction: Not sure about that. In wartime a good father might need to be actually brave, and in times of hardship be actually economically successful. 'He meant well, but he was a hopeless father'?

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

7903	The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
	Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
	From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
	A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').

26. Natural Theory / A. Speculations on Nature / 3. Natural Function

22380	Some words, such as 'knife', have a meaning which involves its function [Foot]
	Full Idea: The word 'knife' names an object in respect of its function. That is not to say (simply) that it names an object which has a function, but also that the function is involved in the meaning of the word.
	From: Philippa Foot (Goodness and Choice [1961], p.134)
	A reaction: It seems faintly possible that someone (a child, perhaps) could know the word and recognise the object, but not know what the object is for. Ditto with other things which have functional names.