Combining Philosophers

All the ideas for Augustin-Louis Cauchy, Thomas Paine and Johann Winckelmann

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4 ideas

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?

21. Aesthetics / B. Nature of Art / 4. Art as Expression

8119	Art aims only at beauty, of form, of idea, and (above all) of expression [Winckelmann, by Tolstoy]
	Full Idea: According to Winckelmann, the law and aim of all art is beauty, independent of goodness. The three kinds of beauty are of form, of idea, and of expression (the highest aim, attainable only when the other two are present).
	From: report of Johann Winckelmann (History of Ancient Art [1764]) by Leo Tolstoy - What is Art? Ch.3
	A reaction: This sounds very like 'art for art's sake', but a hundred years earlier. This is quite a good distinction, and I particularly like the 'beauty of idea', which is often overlooked.

24. Political Theory / B. Nature of a State / 3. Constitutions

23261	A people, not government, creates a constitution, which is essential for legitimacy [Paine]
	Full Idea: A constitution is not the act of a government, but of a people constituting a government, and a government without a constitution is power without right.
	From: Thomas Paine (Rights of Man [1792], Ch.7), quoted by A.C. Grayling - The Good State 5
	A reaction: A constitution looks like the ultimate focus of a social contract (though Greeks had them long ago). It is hard to say why a government should consider itself to be sovereign if it hasn't got it in writing.