11 ideas
8074 | There is a five shilling fine for each point of divergence from the thinking of Aristotle [Oxford Univ 1350] |
Full Idea: Bachelors and Masters of Arts who do not follow Aristotle's philosophy are subject to a fine of five shillings for each point of divergence, as well as for infractions of the rules of the Organon. | |
From: Oxford Univ 1350 (Oxford University Statutes [1350]), quoted by Keith Devlin - Goodbye Descartes Ch.2 | |
A reaction: Lovely quotation! We may defend the medieval period as a genuinely philosophical age, but this sort of statement suggests otherwise, and shows what intellectual heroes the few independent thinkers like William of Ockham really were. |
14626 | In S5 matters of possibility and necessity are non-contingent [Williamson] |
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). |
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. |
14625 | Necessity is counterfactually implied by its negation; possibility does not counterfactually imply its negation [Williamson] |
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) [Williamson] |
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) [Williamson] |
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 [Williamson, by Hale/Hoffmann,A] |
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 [Williamson] |
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). |
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). |