PhilosophyIdeas.com Database     |     Current Total Ideas: 22,967     |     home     |     back

Ideas from 'Could There Be Unicorns?' by Michael Dummett [1983], by Theme Structure

[found in 'The Seas of Language' by Dummett,Michael [OUP 1993,0-19-823621-2]].

green numbers give full details    |     back to texts     |     unexpand these 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
                        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
16953 Relative possibility one way may be impossible coming back, so it isn't symmetrical
                        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)
16952 If something is only possible relative to another possibility, the possibility relation is not transitive
                        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]
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
                        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
                        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?
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
16957 Possible worlds aren't how the world might be, but how a world might be, given some possibility
                        Full Idea: The equation of a possible world with the way that the (actual) world might be is wrong: the way a distant world might be is not a way the world might be, but a way we might allow it to be given how some intervening world might be.
                        From: Michael Dummett (Could There Be Unicorns? [1983], 8)
                        A reaction: The point here is that a system of possible worlds must include relative possibilities as well as actual possibilities. Dummett argues against S5 modal logic, which makes them all equal. Things impossible here might become possible. Nice.
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
16959 If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality
                        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.
                        From: Michael Dummett (Could There Be Unicorns? [1983], 8)
                        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….
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
16956 To explain generosity in a person, you must understand a generous action
                        Full Idea: It cannot be explained what it is for a person to be generous without first explaining what it is for an action to be generous.
                        From: Michael Dummett (Could There Be Unicorns? [1983], 4)
                        A reaction: I presume a slot machine can't be 'generous', even if it favours the punter, so you can't specify a generous action without making reference to the person. A benign circle, as Aristotle says.
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
16954 Generalised talk of 'natural kinds' is unfortunate, as they vary too much
                        Full Idea: In my view, Kripke's promotion of 'natural kinds', coverning chemical substances and animal and plant species, is unfortunate, since these are rather different types of things, and words used for them behave differently.
                        From: Michael Dummett (Could There Be Unicorns? [1983], 2)
                        A reaction: My view is that the only significant difference among natural kinds is their degree of stability in character. Presumably particles, elements and particular molecules are fairly invariant, but living things evolve.