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# 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
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## This note was uploaded on 08/01/2008 for the course PHIL 290 taught by Professor Fitelson during the Fall '06 term at Berkeley.

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fabrizio - CONDITIONALS: WEEK 8, INTRO TO SUBJUNCTIVES...

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