6 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? |
| 16674 | The quantity is just the matter, in that it has extended parts and is diffuse [Charleton] |
| Full Idea: The extension or quantity of a thing is merely modus materiae, or (rather) the matter itself composing that thing; insomuch as it consists not in a point, but has parts posited without parts, in respect whereof it is diffuse. | |
| From: Walter Charleton (Physiologia [1654], III.10.1.4), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.2 |
| 19701 | Fallibilism is consistent with dogmatism or scepticism, and is not alternative to them [Dougherty] |
| Full Idea: There has been a tendency to treat fallibilism as an alternative to either dogmatism or scepticism. ...But it is much better to think of fallibilism as consistent with either dogmatism or skepticism. | |
| From: Trent Dougherty (Fallibilism [2011], 'Closure') | |
| A reaction: It seems perfectly reasonably to describe oneself as a 'fallibilist dogmatist' (perhaps from the Pope?), or a 'fallibilist sceptic' (perhaps from Peter Unger?), so this idea sounds correct. |
| 19700 | It is best to see the fallibility in the reasons, rather than in the agents or the knowledge [Dougherty] |
| Full Idea: It seems best to take fallible reasons as the basic notion of fallibilism. So fallible knowers are agents who know what they know on the basis of fallible reasons. Fallible knowledge will be knowledge on basis of fallible reasons. | |
| From: Trent Dougherty (Fallibilism [2011], 'Cognates') | |
| A reaction: This is because an ideal knower would be compelled by the evidence, so if fallibilism is universal it must reside in the evidence and not in the knower (bottom p.131). |
| 19702 | We can't normally say that we know something 'but it might be false' [Dougherty] |
| Full Idea: It will ordinarily be conversationally inappropriate to say 'I know that p, but p might be false' even if it is true, since this would mislead an interlocutor to infer that that possibility was an epistemically significant one. | |
| From: Trent Dougherty (Fallibilism [2011], 'Epistemic') | |
| A reaction: This seems to imply hypocrisy when a fallibilist philosopher claims (in non-philosophical company) to know something. Fair enough. Philosophers are in a permanent state of hypocrisy about what they are really thinking. That's the fun of it. |