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Full Idea
If our space of possible worlds has no structure, as in the semantics for S5, then, from the standpoint of the semantics, all possible worlds are on the same footing; it then becomes difficult to resist the claim that all are equally real.
Gist of Idea
If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality
Source
Michael Dummett (Could There Be Unicorns? [1983], 8)
Book Ref
Dummett,Michael: 'The Seas of Language' [OUP 1993], p.348
A Reaction
This is a rather startling and interesting claim, given that modern philosophy seems full of thinkers who both espouse S5 for metaphysics, and also deny Lewisian realism about possible worlds. I'll ponder that one. Must read the new Williamson….
| 16953 | Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett] |
| 16952 | If something is only possible relative to another possibility, the possibility relation is not transitive [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] |