4 ideas
| 18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
| Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors. | |
| From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6 |
| 18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
| Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits. | |
| From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts. |
| 7628 | Broad rejects the inferential component of the representative theory [Broad, by Maund] |
| Full Idea: Broad, one of the most important modern defenders of the representative theory of perception, explicitly rejects the inferential component of the theory. | |
| From: report of C.D. Broad (Mind and Its Place in Nature [1925]) by Barry Maund - Perception Ch.1 | |
| A reaction: Since the supposed inferences happen much too quickly to be conscious, it is hard to see how we could distinguish an inference from an interpretation mechanism. Personally I interpret things long before the question of truth arises. |
| 7636 | It can't be more rational to believe in natural laws than miracles if the laws are not rational [Ishaq on Hume] |
| Full Idea: In Hume's argument against miracles, how can it be more rational to believe the laws than the miracles, if the laws themselves are not based on reason? | |
| From: comment on David Hume (Of Miracles [1748]) by Atif Ishaq - talk | |
| A reaction: A very nice question. Hume never presents his argument with such an overt reliance on reason. But if the argument says you are in the 'habit' of expecting no anomalies in the laws, what is to prevent you changing the habit of a lifetime? |