Combining Philosophers

All the ideas for Augustin-Louis Cauchy, Wilhelm Dilthey and Proclus

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6 ideas

1. Philosophy / H. Continental Philosophy / 3. Hermeneutics

5437	The claim of hermeneutics to give knowledge through understanding is challenged by positivism [Mautner on Dilthey]
	Full Idea: The claim of hermeneutics to give understanding instead of explanation can be seen as part of the theory of knowledge, but it seems to be incompatible with the most accepted aspects of positivism.
	From: comment on Wilhelm Dilthey (works [1883]) by Thomas Mautner - Penguin Dictionary of Philosophy p.248
	A reaction: So much the worse for positivism. The same conflict occurs in modern philosophy of mind. God can be a positivist if he likes, but we must settle for hermeneutics for a lot of our knowledge. We are discussing method, not ontology.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals

18085	Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
	Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit.
	From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
	A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits

18084	When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
	Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others.
	From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
	A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction?

14. Science / D. Explanation / 1. Explanation / d. Explaining people

5436	Natural science seeks explanation; human sciences seek understanding [Dilthey, by Mautner]
	Full Idea: In the natural sciences we seek for causes and ask for explanation (erklären), but in the human or cultural sciences we seek understanding (verstehen) by means of interpretation.
	From: report of Wilhelm Dilthey (works [1883]) by Thomas Mautner - Penguin Dictionary of Philosophy p.144
	A reaction: This seems a nice distinction. The prospects of finding the causes or explanations of Shakespeare's plays don't look good, and when you have explained the causes of a chemical reaction you probably have all you need.

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.