Timeline for Metamathematics of buts
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2021 at 12:17 | review | Suggested edits | |||
| Jan 21, 2021 at 13:53 | |||||
| Jan 21, 2021 at 7:05 | comment | added | მამუკა ჯიბლაძე | In fact "unexpectedness of $Y$ when $X$" can be, at least over S4, be expressed by something like $X\to\diamond(X\land\neg Y)$, which, again over S4, is implied by your "$X$ but $Y$". So maybe when not over S4, this has to be modified somehow? | |
| Jan 21, 2021 at 1:41 | comment | added | user44143 | @JasonC, to your last three comments: 2) I think "but also" is best analyzed as a unit within the "not only" / "but also" pair, so explaining "but also" would be separate from this explanation of "but". 3) On my proposal, "We'll serve you coffee or tea, but not both" is roughly "We'll serve you coffee or tea, and we won't serve you both, even though some other places might serve you both". 4) The "material conditional" that is common in math differs so much from the conditionals of ordinary English that I found it easier not to bring conditionals into this at all, but you could try that too. | |
| Jan 21, 2021 at 0:29 | comment | added | Jason C | In thinking, maybe it is more accurate to say $\diamond(X \nRightarrow Y)$ rather than $\diamond(X\wedge\neg Y)$ ? That is, "there is a possibility that X does not imply Y", which is different than the current form in that it does not force consideration of $X \wedge \neg Y$ as a valid logical state. | |
| Jan 21, 2021 at 0:12 | comment | added | Jason C | Another confusing example, to me, is: Exclusive-or means that one or the other is true, but not both. Can this fit the given logical pattern? | |
| Jan 21, 2021 at 0:03 | comment | added | Jason C | So, one example that confuses me involves the use of "not only" and "also". From an example at dictionary.cambridge.org/us/dictionary/english/but: She's not only a painter, but also a writer. Does this fit into the pattern still? I suspect it might but I can't quite cram it in there (although again, it could be the awkwardness of representing this in English throwing me off). | |
| Jan 20, 2021 at 15:26 | comment | added | user44143 | @AlexKruckman, that’s a good example. Maybe the conclusion is that $A\wedge B$ is the best interpretation of “A but B” in ordinary propositional logic; the above (or perhaps $A\wedge B \wedge \neg\square (A\to B)$) is the best interpretation in propositional modal logic; and there probably other logics that are even more faithful to the ordinary usage. | |
| Jan 20, 2021 at 15:05 | comment | added | Vincent | The addition of the third term is a great improvement over standard 'and' but for the reasons pointed out above the 'it would be possible' symbol is a bit too weak. In an ideal world I guess we would replace it by a symbol that says 'but conditioned on $X$, not $Y$ it is more probable than $Y$'. If only such a symbol existed... | |
| Jan 20, 2021 at 14:11 | comment | added | Alex Kruckman | "It's cloudy but it's raining" sounds wrong, while "it's cloudy but it's not raining" sounds right. Since it's possible for it to be either raining or not when it's cloudy, I don't think your suggested interpretation gets at the difference between these two examples. | |
| Jan 20, 2021 at 11:03 | comment | added | David Roberts♦ | @MonroeEskew "He was old but black-haired"? or "..young but grey" | |
| Jan 20, 2021 at 10:22 | comment | added | user44143 | $\diamond$ is the standard symbol for possibility in modal logic: en.wikipedia.org/wiki/Modal_logic#Axiomatic_systems | |
| Jan 20, 2021 at 9:51 | comment | added | Turbo | @MattF. What is the $\diamond$ meaning? | |
| Jan 20, 2021 at 8:14 | comment | added | Monroe Eskew | I'm saying that "young but blonde" sounds wrong. I would say it's because being blonde doesn't violate expectations after learning about being young. Yet it's possible to be young and not blonde. | |
| Jan 20, 2021 at 8:00 | comment | added | user44143 | @MonroeEskew, I think this analysis works well enough with that example. It would be unusual or awkward to say “the girl was young and blonde even though so many young girls have darker hair”, but if that’s what you’re saying then “young but blonde” is an appropriate summary. | |
| Jan 20, 2021 at 7:58 | comment | added | მამუკა ჯიბლაძე | Or how about simply "you would think it is true but it is not"? | |
| Jan 20, 2021 at 7:54 | comment | added | Monroe Eskew | How about, “the girl was young but blonde”? Counterexample? | |
| Jan 20, 2021 at 7:47 | history | edited | user44143 | CC BY-SA 4.0 |
simpler examples first; avoided critique
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| Jan 20, 2021 at 7:38 | history | answered | user44143 | CC BY-SA 4.0 |