Talk:S5 (modal logic)

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Kripke Semantics section tough to read

The language under the Kripke semantics section is a bit cryptic and stilted. I would recommend that someone smooth it over for the sake of readability. Jordan 23:18, 31 July 2008 (UTC)

Sorry, I'm not an expert, and the article didn't help me understand: "if something is possibly necessary, then it is necessary". Is this to be interpreted as meaning "if it is true of some possible world that x is true in all possible worlds, then it is true of all possible worlds that x is true in all possible worlds". If so, that seems intuitive. If not, what does it mean? --Gargletheape (talk) 20:48, 11 November 2008 (UTC)[reply]

Yes, that expansion is exactly what it means. And yes, I agree that once expanded, it's easily seen to be axiomatically true; however, the unexpanded version "if P might be necessarily true, then it is necessarily true" doesn't sound nearly as intuitive. 91.107.151.20 (talk) 00:09, 24 December 2008 (UTC)[reply]

No, that expansion is not what it means. That would be the expansion of "if something is possibly necessary, then it is necessarily necessary". Instead, it should be interpreted as ""if it is true of some possible world that x is true in all possible worlds, then x is true in all possible worlds". --Freechickens (talk) 20:41, 18 November 2009 (UTC)[reply]

Invalid URL

At the bottom of the page, the link http://www.columbia.edu/~av72/modallogic/LectureNotes/ModalLogic06.pdf is no longer valid. Tarascon (talk) 23:06, 24 July 2011 (UTC)[reply]

Paul Almond

There was a mention that someone named Paul Almond refuted Plantinga. That article is no peer reviewed and, as far as I can tell, Paul Almond is just some random guy. Not only is *that* article not peer reviewed, he does not have a single peer reviewed article to his name. If he really did refute Plantinga's claim outright, then he should publish those results. Until then, it should not be on here. — Preceding unsigned comment added by 98.206.17.80 (talk) 00:29, 3 February 2012 (UTC)[reply]

Alvin Plantiga's really weird bit

To justify, he reasons that if X is possibly necessary, it is necessary in at least one possible world

Am I alone in finding this completely counterintuitive, and in fact, wrong? To me, "possibly necessary" collapses to "possible", not to "necessary". An unsolved conjecture, such as Goldbach's conjecture, may be true, and may be necessarily true due to some as-yet unknown mathematical proof. So it's possibly necessarily true. But that clearly doesn't make it necessarily true. What's my flaw in thinking? 146.90.239.121 (talk) 16:44, 13 October 2013 (UTC)[reply]

You're confusing two different kinds of modality. Goldbach's conjecture is possibly true and possibly false in an epistemic sense (i.e. it is possible that the conjecture is true as-far-as-we-know, and it is possible that the conjecture is false as-far-as-we-know.) But metaphysically speaking, Goldbach's conjecture is either necessarily true, or it is necessarily false. For analogy, consider a young child who cannot perform the calculation "6+9". Now as far as the child can tell, it might sum to 15 or it might not, and in that sense it is epistemically possible (for the child) that "6+9=15" is true and epistemically possible that it is false. However, if "6+9=15" is true at all, then it is true by metaphysical necessity - it is not the case that things might have been such that six and nine would not have made fifteen. OldCause (talk) 22:01, 27 December 2020 (UTC)[reply]