Combining Texts

All the ideas for 'Clitophon', 'Commentary on Euclid's 'Elements'' and 'Letters to Leibniz 1'

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

---

4 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 / f. Altruism

1590	The just man does not harm his enemies, but benefits everyone [Plato]
	Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone.
	From: Plato (Clitophon [c.372 BCE], 410b)
	A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus.

26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws

17009	I won't object if someone shows that gravity consistently arises from the action of matter [Newton]
	Full Idea: If someone explains gravity along with all its laws by the action of some subtle matter, and shows that the motion of the planets and comets will not be disturbed by this matter, I shall be far from objecting.
	From: Isaac Newton (Letters to Leibniz 1 [1693], 1693.10.16)
	A reaction: Important if you think that Newton is the hero of the descriptive regularity theory of laws. Newton probably thought laws came from God, but he wouldn't object to Leibniz's view, that God planted the laws within the matter.