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All the ideas for 'Mahaprajnaparamitashastra', 'Elusive Knowledge' and 'Cours d'Analyse'

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8 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?

11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs

12899	The timid student has knowledge without belief, lacking confidence in their correct answer [Lewis]
	Full Idea: I allow knowledge without belief, as in the case of the timid student who knows the answer but has no confidence that he has it right, and so does not believe what he knows.
	From: David Lewis (Elusive Knowledge [1996], p.429)
	A reaction: [He cites Woozley 1953 for the timid student] I don't accept this example (since my views on knowledge are rather traditional, I find). Why would the student give that answer if they didn't believe it? Sustained timid correctness never happens.

11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism

12897	To say S knows P, but cannot eliminate not-P, sounds like a contradiction [Lewis]
	Full Idea: If you claim that S knows that P, and yet grant that S cannot eliminate a certain possibility of not-P, it certainly seems as if you have granted that S does not after all know that P. To speak of fallible knowledge just sounds contradictory.
	From: David Lewis (Elusive Knowledge [1996], p.419)
	A reaction: Starting from this point, fallibilism seems to be a rather bold move. The only sensible response seems to be to relax the requirement that not-P must be eliminable. Best: in one epistemic context P, in another not-P.

13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification

12898	Justification is neither sufficient nor necessary for knowledge [Lewis]
	Full Idea: I don't agree that the mark of knowledge is justification, first because justification isn't sufficient - your true opinion that you will lose the lottery isn't knowledge, whatever the odds; and also not necessary - for what supports perception or memory?
	From: David Lewis (Elusive Knowledge [1996])
	A reaction: I don't think I agree. The point about the lottery is that an overwhelming reason will never get you to knowing that you won't win. But good reasons are coherent, not statistical. If perceptions are dubious, justification must be available.

13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism

12895	Knowing is context-sensitive because the domain of quantification varies [Lewis, by Cohen,S]
	Full Idea: The context-sensitivity of 'knows' is a function of contextual restrictions on the domain of quantification.
	From: report of David Lewis (Elusive Knowledge [1996]) by Stewart Cohen - Contextualism Defended p.68
	A reaction: I think the shifting 'domain of quantification' is one of the most interesting features of ordinary talk. Or, more plainly. 'what are you actually talking about?' is the key question in any fruitful dialogue. Sophisticated speakers tacitly shift domain.

19562	We have knowledge if alternatives are eliminated, but appropriate alternatives depend on context [Lewis, by Cohen,S]
	Full Idea: S knows P if S's evidence eliminates every alternative. But the nature of the alternatives depends on context. So for Lewis, the context sensitivity of 'knows' is a function of contextual restrictions ln the domain of quantification.
	From: report of David Lewis (Elusive Knowledge [1996]) by Stewart Cohen - Contextualism Defended (and reply) 1
	A reaction: A typical modern attempt to 'regiment' a loose term like 'context'. That said, I like the idea. I'm struck by how the domain varies during a conversation (as in 'what we are talking about'). Domains standardly contain 'objects', though.

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

7903	The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
	Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
	From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
	A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').