Timeline for Metamathematics of buts
Current License: CC BY-SA 4.0
33 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 1, 2021 at 9:36 | comment | added | David Corfield | A clearer understand of 'and' would help as a starting point. Mere conjunction doesn't suffice. I propose that dependent type theory fares better in Sec 2.3 of my recent book, global.oup.com/academic/product/…. | |
| Jan 21, 2021 at 15:09 | comment | added | Tim Campion | It should be mentioned here that the word "but" is often used mathematically in a kind of strange way -- e.g. "$x = y$; but $y = z$; therefore $x = z$". This makes the most sense if one is arguing by contradiction, and arriving at the contradiction in the argument -- the "but" signals the strangeness of the arriving contradiction. But sometimes the usage creeps into arguments which are not by contradiction. It can give the writing a sense that the author is battling to prove to you something that you don't want to believe. | |
| Jan 21, 2021 at 9:40 | answer | added | mousetail 'he-him' | timeline score: 15 | |
| Jan 21, 2021 at 5:54 | comment | added | TheVillageIdiot | wow, there is so much in the world that I fortunately or unfortunately have no idea about. Thanks for posting the question, answers, and all the comments. | |
| Jan 21, 2021 at 3:59 | answer | added | Timothy Chow | timeline score: 34 | |
| Jan 21, 2021 at 0:04 | comment | added | Peter LeFanu Lumsdaine | @EmilJeřábek Reading the first paragraph of the question, I had the same reaction your comments show: it sounded like a question of linguistics, not mathematics. But the second paragraph makes clear that it is a mathematical question — it’s asking if there are mathematical logics that can express this linguistic distinction. | |
| Jan 20, 2021 at 20:56 | answer | added | Corbin | timeline score: 12 | |
| Jan 20, 2021 at 20:22 | comment | added | Todd Trimble | @MonroeEskew As Andres and Paul are suggesting, it's hard to rule out that mathematics might have some bearing on the matter, and much in logic that was once considered as "belonging to" philosophy has been mathematicized. The question is not a beginner question and merits consideration. | |
| Jan 20, 2021 at 17:48 | comment | added | Paul Taylor | "All", "some", "probably", "almost certainly", "necessarily", "possibly", "always" and "eventually" are natural language, but they have been given formal mathematical meanings. (I mean the plural for each of them.) Maybe "but" could have a formal mathematical meaning too. | |
| Jan 20, 2021 at 17:48 | comment | added | Andrés E. Caicedo | To those saying this is out of scope: the MSC (Mathematics Subject Classification) 03B65 is for logic of natural languages. We have had a class for it for 40 years. | |
| Jan 20, 2021 at 12:39 | history | became hot network question | |||
| Jan 20, 2021 at 12:13 | comment | added | Emil Jeřábek | Actually, philosophy.stackexchange.com is not the best fit. I didn’t realize we have a dedicated site for linguistics (linguistics.stackexchange.com), and indeed, there are various questions on formal semantics there. This is your best chance to get a sensible answer from an expert that actually knows what they are doing, rather than the feeble amateurish attempts we’ve seen here. | |
| Jan 20, 2021 at 11:08 | comment | added | arsmath | I'm asking if there is a mathematical concept with a natural language meaning, which is just the reverse question of what is the natural language meaning of a mathematical concept. | |
| Jan 20, 2021 at 11:07 | comment | added | Emil Jeřábek | You are not asking about the meaning of a mathematical concept. You are asking about the meaning of a non-mathematical construct in order to model it by a mathematical structure. | |
| Jan 20, 2021 at 11:02 | comment | added | arsmath | So you are saying that the meaning of mathematical concepts (which must be expressed in natural language) is off-topic for MathOverflow? I definitely don't agree with that. | |
| Jan 20, 2021 at 10:24 | comment | added | Emil Jeřábek | Whether there is a mathematical system that distinguishes “and” from “but” is (1) not a question of mathematics, but of semantics of natural language, and (2) subjective, so it’s certainly not “either there is or there isn’t”. If you think otherwise, here is a test case. I give you the system that only has constants 0 and 1 (no other connectives, propositions, or what not), where 0 represents “and”, and 1 represents “but”. Does it answer the question? If yes, how is it not trivial? If not, why not? Give me a purely mathematical reason that does not involve any semantics of natural language. | |
| Jan 20, 2021 at 9:07 | answer | added | Jii | timeline score: 16 | |
| Jan 20, 2021 at 8:56 | comment | added | arsmath | The arguments to close don't make any sense to me. Either there is a mathematical system that distinguishes "and" from "but", or there isn't. This a question about mathematics. I don't care about the philosophical question, and I wouldn't be equipped to understand the philosophical answer. | |
| Jan 20, 2021 at 7:38 | answer | added | user44143 | timeline score: 61 | |
| Jan 20, 2021 at 7:37 | comment | added | Emil Jeřábek | @PaulTaylor Whether or not it looks like an exam question is irrelevant. What is relevant that this is a question on the semantics of natural language and its philosophical interpretation, with hardly any mathematical content, and as such it is off topic for this site. It might be appropriate for philosophy.stackexchange.com . If and when someone figures out a formal system that describes such a logic, then questions about the mathematical properties of such a system may be on topic here. | |
| Jan 20, 2021 at 6:42 | comment | added | Noah Schweber | I think Aristotle wrote a bit about the logic of buts in his Posterior Analytic. (Sorry ...) | |
| S Jan 20, 2021 at 3:50 | history | edited | Will Sawin |
Added philosophy-related tag
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| S Jan 20, 2021 at 3:50 | history | suggested | gmvh |
Added philosophy-related tags
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| Jan 19, 2021 at 22:27 | comment | added | anemone | Isn't there a difference at the level of well-formed sentences, rather than truth values? - I supported him and his brother supported him. - *I supported him but his brother supported him. | |
| Jan 19, 2021 at 19:45 | comment | added | Paul Taylor | No, it shouldn't be closed just because it doesn't look like an exam question. Several settings have already been proposed and maybe in five year's time someone will stumble on this question and give a good formal answer. | |
| Jan 19, 2021 at 18:37 | review | Suggested edits | |||
| S Jan 20, 2021 at 3:50 | |||||
| Jan 19, 2021 at 15:15 | comment | added | Will Sawin | In some kind of probabilistic logic, one could do "$X$ and $Y$ and $P(X \textrm{ and }Y) < P(X) P(Y)$" where the probabilities are based on prior information... | |
| Jan 19, 2021 at 15:10 | review | Close votes | |||
| Jan 20, 2021 at 17:58 | |||||
| Jan 19, 2021 at 14:52 | comment | added | Monroe Eskew | I’m voting to close this question because it’s is too philosophical. | |
| Jan 19, 2021 at 14:51 | comment | added | Andreas Blass | There are modal logics that formalize notions of belief, and there are temporal logics that formalize the possibility of truth values changing over time. A suitable combination of these should be able to formalize "X but Y" as something like "X and Y and at some time in the past it was believed that at no time in the future (X and Y)." But (!) before attempting any formalization, we should try to agree on the intended meaning(s) of "but" in natural language. For example, is it a commutative operation on statements? | |
| Jan 19, 2021 at 14:43 | comment | added | LSpice | Maybe the place to look for a formalisation of surprise would be in the literature on the unexpected hanging paradox? | |
| Jan 19, 2021 at 14:14 | comment | added | Will Brian | It seems to me that the common usage of "but" is equivalent to "and" plus the expectation that the listener should be at least a little bit surprised. This expectation of surprise doesn't seem formalizable to me . . . but who knows? | |
| Jan 19, 2021 at 14:11 | history | asked | arsmath | CC BY-SA 4.0 |