fabrizio - CONDITIONALS WEEK 8 INTRO TO SUBJUNCTIVES...

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CONDITIONALS: WEEK 8, INTRO TO SUBJUNCTIVES FABRIZIO CARIANI 1. Strict Conditionals and Variably Strict Conditionals Consider the following logical principles for an arbitrary conditional operator 99K : 1 (AS) p 99K r , ( p & q ) 99K r (T) p 99K q , q 99K r , p 99K r (AS) and (T) are short for ‘Antecedent Strengthening’, and ‘Transitivity’. (1) If 99K satisfies (T), then it satisfies (AS) Suppose (T) holds, and assume p 99K r . Since 99K is a conditional operator, we can plausibly assume that for all q , ( p & q ) 99K p is a valid schema of the logic of 99K . Therefore, we have ( p & q ) 99K p , and p 99K r , which by (T), legitimates ( p & q ) 99K r . Definition 99K is a strict conditional iff for some class W of possible worlds, and for every p , q , p 99K q is true iff p q is true at w , for every w W (2) If 99K is strict, then it satisfies (T) (and therefore (AS)) Just because satisfies both. Let p > q abbreviate ‘If it were the case that p , then it would be the case that q ’. (3) Intuitively, neither (AS) nor (T) holds for > Contrast: (a) If it had been sunny on Sunday, I’d have played soccer (on Sunday). (b) If it had been sunny on Sunday and I had had a car accident on Saturday, I’d have played soccer (on Sunday). Intuitively, the truth of (a) does not guarantee the truth of (b) because the antecedent is strengthened by a conjunct that pre-empts the consequent. Therefore > is not strict Definition 99K is a variably strict conditional iff for every p , q there is a class W of possible worlds s.t. p 99K q is true iff p q is true at w , for every w W . (4) In general, (i) not every variably strict conditional satisfies (AS), how- ever (ii) if 99K is variably strict each instance of p 99K q is strict. We need a conceptual analysis of the truth-conditions of subjunctive conditionals that explains the failure of (AS). An analysis of > as a variably strict conditional is 1 Notation: I use ‘ 99K ’ as a variable ranging over conditional operators (occasionally the range of this is just restricted to the subjunctive and the indicative conditional). 1
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2 FABRIZIO CARIANI particularly attractive because it preserves a connection with and accounts for the failure of (AS). 2. The Analysis of Subjunctives An important question in the theory of subjunctives is how do we gather empirical evidence about them, especially when we deal with counterfactuals. Supporters of the idea that p > q is variably strict have an answer: facts about the actual world, determine which worlds are relevant in the analysis of a given conditional. In particular the relevant worlds are the most similar to the actual world and in which the condition stated by the antecedent of p > q un obtains. Example: (c) If you had walked on the ice, it would have broken. Suppose that, in the actual world, no slab of ice in 1000 Km from where (c) was uttered is thinner than 6 feet: the relevant worlds, for the evaluation of (c),are ones in which that piece of ice is just about as thick, and presumably won’t break under the weight of a person.
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