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Full Idea
If some world is 'a way the world might be considered to be if things were different in a certain respect', that might show that the accessibility relation should not be taken to be transitive, and we should have to adopt modal logic T.
Gist of Idea
If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system
Source
Michael Dummett (Could There Be Unicorns? [1983], 8)
Book Ref
Dummett,Michael: 'The Seas of Language' [OUP 1993], p.348
A Reaction
He has already rejected symmetry from the relation, for reasons concerning relative identity. He is torn between T and S4, but rejects S5, and opts not to discuss it.
16952 | If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett] |
16953 | Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett] |
16951 | It was realised that possible worlds covered all modal logics, if they had a structure [Dummett] |
16954 | Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett] |
16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
16960 | If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett] |
16958 | In S4 the actual world has a special place [Dummett] |
16957 | Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett] |
16959 | If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett] |