5 ideas
| 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. |
| 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? |
| 7441 | Experiences are defined by their causal role, and causal roles belong to physical states [Lewis] |
| Full Idea: The definitive characteristic of any experience is its causal role, its most typical causes and effects; but we materialists believe that these causal roles which belong by analytic necessity to experiences belong in fact to certain physical states. | |
| From: David Lewis (An Argument for the Identity Theory [1966], §I) | |
| A reaction: This is the Causal version of functionalism, which Armstrong also developed. The word 'typical' leads later to a teleological element in the theory (e.g. in Lycan). There are other things to say about mental states than just their causal role. |
| 7442 | 'Pain' contingently names the state that occupies the causal role of pain [Lewis] |
| Full Idea: On my theory, 'pain' is a contingent name - that is, a name with different denotations in different possible worlds - since in any world, 'pain' names whatever state happens in that world to occupy the causal role definitive of pain. | |
| From: David Lewis (An Argument for the Identity Theory [1966], §II n6) | |
| A reaction: Better to say that 'pain' (like 'sound') is ambiguous. It is indiscriminately used by English-speakers to mean [1] the raw quale that we experience when damaged, and [2] whatever it is that leads to pain behaviour. Maybe frogs have 2 but not 1. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |