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All the ideas for 'Clitophon', 'Cours d'Analyse' and 'Two Problems for Essentialism'

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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?

22. Metaethics / B. Value / 2. Values / f. Altruism

1590	The just man does not harm his enemies, but benefits everyone [Plato]
	Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone.
	From: Plato (Clitophon [c.372 BCE], 410b)
	A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus.

26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism

5492	How can essences generate the right powers to vary with distance between objects? [Armstrong]
	Full Idea: In Newtonian physics the distance between two objects determines the attractive forces between them, but then the objects will have to be sensitive to the distance, in order to 'know' what forces to generate; but distance isn't a causal power.
	From: David M. Armstrong (Two Problems for Essentialism [2001], p.170)
	A reaction: Ellis replies that he is not troubled, because he believes in essential properties which are separate from their causal roles. Indeed, how else could you explain their causal roles? Still, distance must be mentioned when explaining gravity.