Combining Philosophers

All the ideas for Augustin-Louis Cauchy, Andreas Osiander and N.L. Wilson

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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?

14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations

15282	Facts should be deducible from the theory and initial conditions, and prefer the simpler theory [Osiander, by Harré/Madden]
	Full Idea: The two positivist criteria for a scientific theory are that the facts must be deducible from the theory together with initial conditions, and if there is more than one theory the simplest must be chosen.
	From: report of Andreas Osiander (Preface to 'De Revolutionibus' [1543]) by Harré,R./Madden,E.H. - Causal Powers 7.I
	A reaction: Harré and Madden cite this as a famous early statement of positivism. It seems to combine Hempel and Lewis very concisely. Wrong, of course. It does not, though, appear to mention 'laws'.

19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity

6316	We translate in a way that makes the largest possible number of statements true [Wilson,NL]
	Full Idea: We select as designatum that individual which will make the largest possible number of statements true.
	From: N.L. Wilson (Substances without Substrata [1959]), quoted by Willard Quine - Word and Object II.§13 n
	A reaction: From the Quine's reference, it sounds as if Wilson was the originator of the well-known principle of charity, later taken up by Davidson. If so, he should be famous, because it strikes me as a piece of fundamental and important wisdom.