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All the ideas for 'Mahaprajnaparamitashastra', 'Cours d'Analyse' and 'Prescriptivism'

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5 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 / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism

2854	Prescriptivism says 'ought' without commitment to act is insincere, or weakly used [Hooker,B]
	Full Idea: Prescriptivism holds that if you think one 'ought' to do a certain kind of act, and yet you are not committed to doing that act in the relevant circumstances, then you either spoke insincerely, or are using the word 'ought' in a weak sense.
	From: Brad W. Hooker (Prescriptivism [1995], p.640)
	A reaction: So that's an 'ought', but not a 'genuine ought', then? (No True Scotsman move). Someone ought to rescue that drowning child, but I can't be bothered.

23. Ethics / B. Contract Ethics / 2. Golden Rule

2856	Universal moral judgements imply the Golden Rule ('do as you would be done by') [Hooker,B]
	Full Idea: Prescriptivity is especially important if moral judgements are universalizable, for then we can employ golden rule-style reasoning ('do as you would be done by').
	From: Brad W. Hooker (Prescriptivism [1995], p.640)

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').