Combining Texts

Ideas for 'fragments/reports', 'Could There Be Unicorns?' and 'fragments/reports'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

5 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
16951 It was realised that possible worlds covered all modal logics, if they had a structure [Dummett]
     Full Idea: The new discovery was that with a suitable structure imposed on the space of possible worlds, the Leibnizian idea would work for all modal logics.
     From: Michael Dummett (Could There Be Unicorns? [1983], 1)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
16952 If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett]
     Full Idea: If T is only possible if S obtains, and S is possible but doesn't obtain, then T is only possible in the world where S obtains, but T is not possible in the actual world. It follows that the relation of relative possibility is not transitive.
     From: Michael Dummett (Could There Be Unicorns? [1983], 1)
     A reaction: [compressed]
16953 Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett]
     Full Idea: If T is only possible if S obtains, T and S hold in the actual world, and S does not obtain in world v possible relative to the actual world, then the actual is not possible relative to v, since T holds in the actual. Accessibility can't be symmetrical.
     From: Michael Dummett (Could There Be Unicorns? [1983], 1)
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
16960 If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett]
     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.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     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.
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
16958 In S4 the actual world has a special place [Dummett]
     Full Idea: In S4 logic the actual world is, in itself, special, not just from our point of view.
     From: Michael Dummett (Could There Be Unicorns? [1983], 8)
     A reaction: S4 lacks symmetricality, so 'you can get there, but you can't get back', which makes the starting point special. So if you think the actual world has a special place in modal metaphysics, you must reject S5?