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All the ideas for 'poems', 'Cours d'Analyse' and 'Events'

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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?
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
9413 An event is a change in or to an object [Lombard, by Mumford]
     Full Idea: Lombard holds that an event is a change in or to an object.
     From: report of Lawrence B. Lombard (Events [1986]) by Stephen Mumford - Laws in Nature 2.1
     A reaction: This strikes me as more plausible than Davidson's view that events are primitive, or Kim's that they are exemplifications of properties. Events then exist just insofar as we wish to (or are able to) discriminate them.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
6017 Nomos is king [Pindar]
     Full Idea: Nomos is king.
     From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture
     A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed.