Combining Texts

All the ideas for 'Clitophon', 'Cours d'Analyse' and 'The Myth of the Given'

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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?

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism

8790	The 'doctrine of the given' is correct; some beliefs or statements are self-justifying [Chisholm]
	Full Idea: In my opinion, the 'doctrine of the given' is correct in saying that there are some beliefs or statements which are 'self-justifying' and that among such beliefs are statements some of which concern appearances or 'ways of being appeared to'.
	From: Roderick Chisholm (The Myth of the Given [1964], §12)
	A reaction: To boldly assert that they are 'self-justifying' invites a landslide of criticisms, pointing at a regress. It might be better to say they are self-evident, or intuitively known, or primitive, or true by the natural light of reason.

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.