Combining Philosophers

All the ideas for Proclus, William S. Jevons and Dorion Sagan

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4 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism

16567	Scientists know everything about nothing, philosophers nothing about everything [Sagan,D]
	Full Idea: The scientist learns more and more about less and less, until she knows everything about nothing, whereas a philosopher learns less and less about more and more until he knows nothing about everything.
	From: Dorion Sagan (Cosmic Apprentice [2013])
	A reaction: [Came via Twitter] Not sure if this is true, but it is too nice to miss.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

8628	I hold that algebra and number are developments of logic [Jevons]
	Full Idea: I hold that algebra is a highly developed logic, and number but logical discrimination.
	From: William S. Jevons (The Principles of Science [1879], p.156), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §15
	A reaction: Thus Frege shows that logicism was an idea that was in the air before he started writing. Riemann's geometry and Boole's logic presumably had some influence here.

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.