Timeline for What is the status of the extreme value theorem in forms of constructive mathematics, such as Smooth Infinitesimal Analysis?
Current License: CC BY-SA 3.0
9 events
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| Oct 12, 2021 at 13:36 | history | edited | Paul Taylor |
added newly created tag
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| Aug 20, 2014 at 8:02 | comment | added | Mikhail Katz | @MattF., first of all thanks for your answer. As far as the question title is concerned, I think the change is fine. Arguably "constructive" can be used in the sense of "relying on an intuitionistic logic". The identification of "constructive" and "computational" is one of the cornerstones of Bishop's approach but one may be allowed to hold alternative opinions. For an analysis of Bishop's ideology see arxiv.org/abs/1110.5456 In fact your comment could be the subject of a separate question if you wish to pursue it. | |
| Aug 20, 2014 at 1:20 | comment | added | user44143 | @Paul Taylor, I liked the question better before, since I would not call SIA constructive. 1) SIA is not computational. 2) SIA contradicts theorems of Bishop-style mathematics like $x^2=0 \rightarrow x=0$. 3) SIA relies on infinitesimals which can not be exhibited in a way that violates Bishop's principles of "make every concept affirmative" and "avoid pseudo-generality". I like constructively and I like SIA, but let's keep the concepts separate! | |
| Aug 18, 2014 at 2:38 | answer | added | user44143 | timeline score: 4 | |
| Aug 17, 2014 at 21:42 | history | edited | Nate Eldredge | CC BY-SA 3.0 |
Fix typo in title, to improve searchability
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| Aug 17, 2014 at 8:59 | comment | added | Paul Taylor | Please excuse my liberty in generalising your question slightly. | |
| Aug 17, 2014 at 8:58 | history | edited | Paul Taylor | CC BY-SA 3.0 |
Generalised the question and spelt out the TLA.
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| Aug 17, 2014 at 8:52 | answer | added | Paul Taylor | timeline score: 5 | |
| Aug 13, 2014 at 7:39 | history | asked | Mikhail Katz | CC BY-SA 3.0 |