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| 14626 | In S5 matters of possibility and necessity are non-contingent |
| Full Idea: In system S5 matters of possibility and necessity are always non-contingent. | |||
| From: Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 3) | |||
| A reaction: This will be because if something is possible in one world (because it can be seen to be true in some possible world) it will be possible for all worlds (since they can all see that world in S5). |
| 14625 | Necessity is counterfactually implied by its negation; possibility does not counterfactually imply its negation |
| Full Idea: Modal thinking is logically equivalent to a type of counterfactual thinking. ...The necessary is that which is counterfactually implied by its own negation; the possible is that which does not counterfactually imply its own negation. | |||
| From: Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 1) | |||
| A reaction: I really like this, because it builds modality on ordinary imaginative thinking. He says you just need to grasp counterfactuals, and also negation and absurdity, and you can then understand necessity and possibility. We can all do that. |
| 14623 | Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) |
| Full Idea: The strict conditional implies the counterfactual conditional: □(A⊃B) ⊃ (A□→B) - suppose that A would not have held without B holding too; then if A had held, B would also have held. | |||
| From: Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 1) | |||
| A reaction: [He then adds a reading of his formula in terms of possible worlds] This sounds rather close to modus ponens. If A implies B, and A is actually the case, what have you got? B! |
| 14624 | Counterfactual conditionals transmit possibility: (A□→B)⊃(◊A⊃◊B) |
| Full Idea: The counterfactual conditional transmits possibility: (A□→B) ⊃ (◊A⊃◊B). Suppose that if A had held, B would also have held; the if it is possible for A to hold, it is also possible for B to hold. | |||
| From: Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 1) |
| 14531 | Rather than define counterfactuals using necessity, maybe necessity is a special case of counterfactuals |
| Full Idea: Instead of regarding counterfactuals as conditionals restricted to a range of possible worlds, we can define the necessity operator by means of counterfactuals. Metaphysical necessity is a special case of ordinary counterfactual thinking. | |||
| From: report of Timothy Williamson (Modal Logic within Counterfactual Logic [2010]) by Bob Hale/ Aviv Hoffmann - Introduction to 'Modality' 2 | |||
| A reaction: [compressed] I very much like Williamson's approach, of basing these things on the ordinary way that ordinary people think. To me it is a welcome inclusion of psychology into metaphysics, which has been out in the cold since Frege. |
| 14628 | Imagination is important, in evaluating possibility and necessity, via counterfactuals |
| Full Idea: Imagination can be made to look cognitively worthless. Once we recall its fallible but vital role in evaluating counterfactual conditionals, we should be more open to the idea that it plays such a role in evaluating claims of possibility and necessity. | |||
| From: Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 6) | |||
| A reaction: I take this to be a really important idea, because it establishes the importance of imagination within the formal framework of modern analytic philosopher (rather than in the whimsy of poets and dreamers). |