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

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6 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?
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
8859 The main modal logics disagree over three key formulae [Yablo]
     Full Idea: Lewis's different systems of modal logic differed about such formulae as □P implies □□P; ◊□P implies □P; and ◊S implies □◊S
     From: Stephen Yablo (Apriority and Existence [2000], §06)
     A reaction: Yablo's point is that the various version don't seem to make much difference to our practices in logic, mathematics and science. The problem, says Yablo, is deciding exactly what you mean by 'necessarily' and 'possibly'.