Timeline for Metamathematics of buts
Current License: CC BY-SA 4.0
25 events
| when toggle format | what | by | license | comment | |
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| Jan 22, 2021 at 13:53 | comment | added | Timothy Chow | @მამუკაჯიბლაძე The relevant profession depends on what question one is asking. If one is asking for a taxonomy of different shades of meaning of a specific word in a specific language, then that is the job of a lexicographer. Such a study would be unlikely to be published in a linguistics journal unless the topic were broadened to multiple languages, or maybe multiple "contrastive words." But if the goal is to isolate a particular subset of meanings and capture them with reasonable fidelity using a mathematical model, then I'd look to either mathematics, logic, or the philosophy of language. | |
| Jan 22, 2021 at 6:19 | comment | added | მამუკა ჯიბლაძე | @NikWeaver Well, in a sense it does: raining in this context means a weather not suitable for going out. | |
| Jan 22, 2021 at 4:06 | comment | added | Will | In other words, constructions of the form "something could have happened, but it didn't!" do not indicate a probability, but rather juxtapose the narration of the speaker. I think there is an implicit expectation by the audience that any scenario described by the speaker relates to some reality (given the statistics of more usual contexts), so the subsequent "but" then "surprises" the audience (on some level) that this scenario did not happen. The probability here does not relate to the facts described, but rather to how they are described: a modality in a higher order of logic it seems. | |
| Jan 22, 2021 at 3:48 | comment | added | Will | Counterexample: "Coin flipping may result in tails ten times in a row, but that would be a rare occurrence". I'd say the probability of "coin flips resulting in tails ten times in a row" being a "rare occurrence" is not smaller than the probability of it *not being a rare occurrence". | |
| Jan 21, 2021 at 19:53 | comment | added | Nik Weaver | Oh, I see what you mean. But still ... it was raining, but I decided to go out anyway. This Y doesn't seem to "undermine" X. | |
| Jan 21, 2021 at 18:08 | comment | added | მამუკა ჯიბლაძე | @NikWeaver but I also tend more and more to agree with Emil that one needs professional linguist rather than a mathematician to argue about these things... | |
| Jan 21, 2021 at 17:59 | comment | added | მამუკა ჯიბლაძე | Yes it's definitely fun. Inevitability was unfortunate term I must admit. But I really meant something very close in meaning to inevitability. Like, the fact that I want strawberry sort of inevitably undermines (this time) my usual habit of getting chocolate. Or, the fact that [I still think ...] sort of inevitably spoils my [agree]ment. | |
| Jan 21, 2021 at 16:39 | comment | added | Nik Weaver | Anyway it is fun to debate these questions. | |
| Jan 21, 2021 at 16:38 | comment | added | Nik Weaver | Another example would be sentence in your comment: "I agree ... but I still think ..." --- this $Y$ also seems to me not to have any flavor of inevitability. | |
| Jan 21, 2021 at 16:36 | comment | added | Nik Weaver | What about "I usually get chocolate, but this time I want strawberry? I don't sense any "inevitability" in this $Y$ ... | |
| Jan 21, 2021 at 14:19 | comment | added | მამუკა ჯიბლაძე | I agree that the linguistic aspects interfere and probably confuse me as a non-native speaker, but I still think that one important feature of "but" is that $Y$ witnesses inevitability of something crucial that somehow diminishes $X$, no? | |
| Jan 21, 2021 at 13:56 | history | edited | Manfred Weis | CC BY-SA 4.0 |
fixed a typo
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| Jan 21, 2021 at 13:50 | comment | added | Nik Weaver | @TimothyChow thanks for pointing that out, it is indeed similar. I think I like "$P(Y|X)$ is small" better than "$P(X \wedge Y) < P(X)P(Y)$" because the latter condition is symmetric in $X$ and $Y$, while "but" usually implies that the second clause is the unexpected one, it seems to me. | |
| Jan 21, 2021 at 13:46 | comment | added | Nik Weaver | Well, ordinary English words are often used in multiple inconsistent ways. I guess the point is that "$P(Y|X)$ is small" captures the intuition that $Y$ is not expected once $X$ is known. | |
| Jan 21, 2021 at 13:44 | comment | added | Timothy Chow | Will Sawin made an earlier comment along similar lines. | |
| Jan 21, 2021 at 13:18 | comment | added | მამუკა ჯიბლაძე | Well, it could be also something like $Y\land\Box(Y\to X)$ but I am not sure... | |
| Jan 21, 2021 at 13:08 | history | edited | mousetail 'he-him' | CC BY-SA 4.0 |
added 663 characters in body
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| Jan 21, 2021 at 12:58 | comment | added | mousetail 'he-him' | @მამუკაჯიბლაძე Perhaps I could add a corollary that if X is subjunctive, X but Y could mean $\neg Y \rightarrow X$ | |
| Jan 21, 2021 at 12:54 | comment | added | მამუკა ჯიბლაძე | Or, even: "I wish I would not have done that, but you cannot alter the past". In this example, $P(Y|X)=1$ (in fact, $P(Y)=1$). | |
| Jan 21, 2021 at 12:47 | comment | added | მამუკა ჯიბლაძე | Or, say: "Ramanujan would be able to solve that, but he is dead". | |
| Jan 21, 2021 at 12:41 | comment | added | mousetail 'he-him' | @NikWeaver Yes, that is the same thing. I wanted to avoid using constants but it doesn't make a difference. | |
| Jan 21, 2021 at 12:39 | comment | added | მამუკა ჯიბლაძე | End of a proof: "We thus reduced our statement to $Y$. But the latter is obvious." | |
| Jan 21, 2021 at 11:34 | comment | added | Nik Weaver | I was going to suggest "$X$ and $Y$ and $P(Y|X)$ is small". (I think your version is equivalent to $P(Y|X) < .5$.) | |
| Jan 21, 2021 at 9:46 | review | First posts | |||
| Jan 21, 2021 at 10:33 | |||||
| Jan 21, 2021 at 9:40 | history | answered | mousetail 'he-him' | CC BY-SA 4.0 |