This paper is concerned with Sir Peter Strawson’s critical discussion of Paul Grice’s defence of the material implication analysis of conditionals. It argues that although Strawson’s own ‘consequentialist’ suggestion concerning the meaning of conditionals cannot be correct, a related and radically contextualist account is able to both account for the phenomena that motivated Strawson’s consequentialism, and to undermine the material implication analysis by providing a simpler account of the processes that we go through when interpreting conditionals.

Bradley has argued that a truth-conditional semantics for conditionals is incompatible with an allegedly very weak and intuitively compelling constraint on the interpretation of conditionals. I argue that the example Bradley offers to motivate this constraint can be explained along pragmatic lines that are compatible with the correctness of at least one popular truth-conditional semantics for conditionals.

What we want to be true about ordinary indicative conditionals seems to be more than we can possibly get: there just seems to be no good way to assign truth-conditions to ordinary indicative conditionals. Some take this argument as reason to make our wantings more modest. Others take it to show that indicative conditionals don't have truth-conditions in the first place. But we have overlooked two possibilities for assigning truth-conditions to indicatives. What's more, those possibilities deliver what we want and (...) turn out to be equivalent. CiteULike Connotea Del.icio.us Digg Reddit Technorati What's this? (shrink)

Robert Stalnaker’s formal semantics for his indicative conditional (which his 1975 paper takes over from his 1968 paper and Stalnaker and Thomason 1968) validate modus ponens, as one might expect. But they do so at the cost of a tension between his philosophical remarks in his 1975 paper and his formal constraints. Stalnaker commits himself to the following: he defines a “context set” as “the possible worlds not ruled out by the presupposed background information” (Stalnaker 1975 p 142). He later (...) states a “pragmatic principle” that “normally a speaker is concerned only with possible worlds within the context set, since this set is defined as the set of possible worlds among which the speaker wishes to distinguish. So it is at least a normal expectation that the selection function should turn first to these worlds before considering counterfactual worlds—those presupposed to be non-actual” (p 144). Then two paragraphs later, in apparent reference to this principle he says “I would expect that the pragmatic principle stated above should hold without exception for indicative conditionals”. Yet when the actual world is not one in which the presuppositions all hold, from his definition of the “context set” it is not among the worlds of the context set, and elsewhere in his 1975 as well as his 1968 he stipulates that the selection function given the actual world and an antecedent true at the actual world yields the actual world (p 144 of Stalnaker 1975, condition 3 on p 104 of Stalnaker 1968). These remarks on the face of it lead to inconsistency if it is possible to presuppose falsehoods: for then the presuppositions create a context set which does not include the actual world (but may perfectly well nevertheless contain some possible worlds in which the antecedent of a given conditional holds when that antecedent is also actually true). In evaluating a conditional with a true antecedent which also holds in some world in the context set, Stalnaker enjoins us to employ a selection function which selects the actual world, and to (“without exception”) employ a selection function which selects some world in the context set in preference to any world outside it.. (shrink)

One very popular kind of semantics for subjunctive conditionals is aclosest-worlds account along the lines of theories given by David Lewisand Robert Stalnaker. If we could give the same sort of semantics forindicative conditionals, we would have a more unified account of themeaning of ``if ... then ...'' statements, one with manyadvantages for explaining the behaviour of conditional sentences. Such atreatment of indicative conditionals, however, has faced a battery ofobjections. This paper outlines a closest-worlds account of indicativeconditionals that does better (...) than some of its cousins in explaining thebehaviour of such conditionals. The paper then discusses objectionsoffered by Dorothy Edgington and Frank Jackson to closest-worldsaccounts of indicative conditionals, and shows that these objections canbe met by the account outlined. (shrink)

I outline and motivate a way of implementing a closest world theory of indicatives, appealing to Stalnaker’s framework of open conversational possibilities. Stalnakerian conversational dynamics helps us resolve two outstanding puzzles for a such a theory of indicative conditionals. The first puzzle—concerning so-called ‘reverse Sobel sequences’—can be resolved by conversation dynamics in a theory-neutral way: the explanation works as much for Lewisian counterfactuals as for the account of indicatives developed here. Resolving the second puzzle, by contrast, relies on the interplay (...) between the particular theory of indicative conditionals developed here and Stalnakerian dynamics. The upshot is an attractive resolution of the so-called “Gibbard phenomenon” for indicative conditionals. (shrink)

It is known that indicative and subjunctive conditionals interact differently with a rigidifying “actually” operator. The paper studies this difference in an abstract setting. It does not assume the framework of possible world semantics, characterizing “actually” instead by the type of logically valid formulas to which it gives rise. It is proved that in a language with such features all sentential contexts that are congruential (in the sense that they preserve logical equivalence) are extensional (in the sense that they preserve (...) material equivalence). For a subjunctive conditional, the natural conclusion to draw is that it is non-congruential. It is much harder to defend the claim that an indicative conditional is non-congruential. The pressure to treat the indicative conditional as truth-functional is correspondingly greater. The implications of these results for attempts to interpret the indicative conditional as an epistemic or doxastic operator are assessed. (shrink)

§0. A familiar if obscure idea: an indicative conditional presents its consequent as holding in the actual world on the supposition that its antecedent so holds, whereas a subjunctive conditional merely presents its consequent as holding in a world, typically counterfactual, in which its antecedent holds. Consider this pair.