Combining Philosophers

All the ideas for Proclus, Amos and Carl Friedrich Gauss

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4 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite

10855	Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss]
	Full Idea: I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits ...which are permitted to increase without bound.
	From: Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7

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.

29. Religion / B. Monotheistic Religion / 2. Judaism

7604	Amos was the first prophet to emphasise justice and compassion [Amos, by Armstrong,K]
	Full Idea: Amos was the first prophet to emphasise social justice and compassion.
	From: report of Amos (30: Book of Amos [c.740 BCE]) by Karen Armstrong - A History of God
	A reaction: It increasingly strikes me that early religious thinkers were actually working out the rules for good community living, but seeing them through the distorting spectacles of religion as a means to post-life salvation.