14 ideas
| 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) |
| 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) |
| 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. |
| 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? |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 16957 | Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett] |
| 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. |
| 16959 | If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett] |
| 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…. |
| 6649 | Chomsky now says concepts are basically innate, as well as syntax [Chomsky, by Lowe] |
| Full Idea: Chomsky now contends that not only the syntax of natural language but also the concepts expressible in it have an innate basis. | |
| From: report of Noam Chomsky (Chomsky on himself [1994]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.7 n25 | |
| A reaction: This seems to follow Fodor, who has been mocked for implying that we have an innate idea of a screwdriver etc. Note that Chomsky says concepts have an innate 'basis'. This fits well with modern (cautious) rationalism, with which I am happy. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
| 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. |
| 16954 | Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett] |
| 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. |