Timeline for Are buttons really enough to bound validities by S4.2?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 10, 2019 at 20:31 | comment | added | Joel David Hamkins | Yes! That seems to refute all these variations of the question. Basically, it is saying, "there are no switches". | |
| Sep 10, 2019 at 20:16 | comment | added | Robert Passmann | Let me try once more: I claim that the principle $\Diamond\Box\phi\vee\Diamond\Box\neg\phi$ is valid in the model of finite subsets of $\omega$ with the valuation from above: Given any formula $\phi$ at a node $v$ move to a successor node where all propositional letters appearing in $\phi$ are evaluated true. Then $\phi$ is either true or false, and will stay so for ever because the valuation of the affected letters cannot change anymore (they always stay true from now on by definition). However, this principle is not contained in S4.2. Does this work? | |
| Sep 10, 2019 at 20:02 | comment | added | Robert Passmann | @JoelDavidHamkins Oh yes, you're right. Of course it's not part of the logic of the model. I managed to confuse myself... | |
| Sep 10, 2019 at 19:58 | comment | added | Joel David Hamkins | @WillSawin I am so glad that you are able to present my regrettable situation in a positive light! | |
| Sep 10, 2019 at 19:56 | comment | added | Joel David Hamkins | @RobertPassmann That assertion is not valid in the model, in the sense of "valid principle" that we use for potentialism (meaning that one considers all substitution instances), since there are true statements that are not necessary at some worlds. So I don't agree with the argument of your comment. | |
| Sep 10, 2019 at 19:46 | comment | added | Will Sawin | It would be great if we could get everyone who makes claims on Twitter to reconsider them and potentially change their mind by asking questions about it on the appropriate Stack Exchange website... | |
| Sep 10, 2019 at 18:44 | comment | added | Robert Passmann | Consider the restriction of my counterexample to the finite subsets of $\omega$ with the valuation defined as above. Every node in this model has independent buttons, but the frame satisfies the principle $p \rightarrow \Box p$ which is not a theorem of S4.2. So it seems that we need an even stronger assumption? | |
| Sep 4, 2019 at 17:28 | vote | accept | Robert Passmann | ||
| Sep 4, 2019 at 16:10 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
Retract the claim.
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| Sep 4, 2019 at 15:05 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
I am editing the answer.
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| Sep 4, 2019 at 14:44 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 55 characters in body
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| Sep 4, 2019 at 14:25 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |