Timeline for Au revoir, law of excluded middle?
Current License: CC BY-SA 2.5
18 events
| when toggle format | what | by | license | comment | |
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| Aug 14, 2018 at 11:35 | comment | added | Andrej Bauer | And the article was seeded by the above answer. | |
| Aug 14, 2018 at 11:21 | comment | added | j.c. | Andrej Bauer has since published a beautiful article titled "Five stages of accepting constructive mathematics" doi.org/10.1090/bull/1556 . | |
| Jul 3, 2017 at 19:48 | comment | added | მამუკა ჯიბლაძე | And, speaking of the group case itself, this would correspond to something like realizing existence of stable homotopy theory, where none of the noncommutativity phenomena are lost and yet everything becomes even more richly and beautifully commutative than before. | |
| Jul 3, 2017 at 19:42 | comment | added | მამუკა ჯიბლაძე | Stage seven: overcoming. Intuitionism offers no less (perhaps even more) fragmentary viewpoint than the "classical" one. There must be next level which restores the symmetry of the latter without smashing subtleties of the former. Within the Kübler-Ross analogy so cleverly used by @Andrej this seventh stage might correspond to somehow breaking free of the time flow asymmetry (without losing the essence of causality) since some of the most adequate semantics for intuitionism inevitably rely on irreversibility in one form or another. | |
| Jun 24, 2014 at 1:10 | comment | added | Nikos M. | elitism, elitism, elitism.. hmm what should one one infer (psychologicaly speaking) from this..? (my 2 cents :)) | |
| Jun 24, 2014 at 1:03 | comment | added | Nikos M. | i wonder if one can prove (either classicaly or otherwise) that the intended proposition behind the "5 stages" (denied, bargained, accepted etc..) is actually decidable? Else things can be very different :) ps. people may choose where to spend their time (or afford it if you like), yet do not assume for a minute that symbolic jargon (fixed by convention of a guild) is the one true path to meaning (can create many conventions expressing meaning or even meaninglessness is one willing to enumerate them all?) | |
| Jun 20, 2010 at 11:11 | comment | added | Andrej Bauer | Indeed, the five stages present a process of growth which end with the liberation from a difficult period in one's life, such as death, classical mathematics, drugs, or commutative groups. What Charles described goes in the opposite direction when an imprisoned soul finds its purpose in a crusade that turns out to be just as confining as the original prison. | |
| Jun 20, 2010 at 8:40 | comment | added | Peter LeFanu Lumsdaine | @Charles: I agree with the danger you're describing - obsession, fundamentalism... (I could be accused of it myself, some days of the week.) But I don't think it's a new stage on Andrej's list; it's stage 1, for someone going in the other direction. | |
| May 21, 2010 at 10:27 | comment | added | Charles Stewart | There seems to be a stage beyond 5, which we might call "Stockholm Syndrome", where you identify so completely with the new, frightening, more complex world that the enemy of complexity, the original simplicity, becomes your enemy: the only interesting groups are noncommutative, the only valid intuitions about formalisms are constructively well-grounded ones. We've all met stage-sixers, haven't we? | |
| May 20, 2010 at 19:03 | comment | added | Dan Piponi | Some people seem to get hung up over whether or not LEM is true. A better question is "what interesting things can I do with or without it?". There is a lot of interesting stuff you get from not using LEM, even if you believe LEM is true. Take that attitude and you can jump straight to stage 5. | |
| May 20, 2010 at 18:27 | comment | added | darij grinberg | Damn. I was 15 seconds too late. | |
| May 20, 2010 at 18:26 | comment | added | Andrej Bauer | I fixed the URLs. They should work now. | |
| May 20, 2010 at 18:26 | history | edited | darij grinberg | CC BY-SA 2.5 |
deleted 5 characters in body; added 5 characters in body
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| May 20, 2010 at 18:25 | history | edited | Andrej Bauer | CC BY-SA 2.5 |
More url fixing
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| May 20, 2010 at 17:17 | comment | added | Cam McLeman | +1, and this coming from someone who's definitely still in stage 1 in regards to not using the principle of the excluded middle. At least I now know what stage I'm in. | |
| May 20, 2010 at 16:45 | comment | added | lambdafunctor | I intended to put a 'not' in front of the original sentence 'p or ~p', and I amended my post to not reference the law of non-contradiction. Your response is great, but your links seem not to work. | |
| May 20, 2010 at 16:24 | comment | added | darij grinberg | Why can't I +2 a post... | |
| May 20, 2010 at 16:08 | history | answered | Andrej Bauer | CC BY-SA 2.5 |