Is Stalnaker Inconsistent about the Indicative Conditional? Daniel Nolan, University of St Andrews [email protected] ©Daniel Nolan 6 March 2004

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. The actual world is not in the context set in such cases, so Stalnaker has given us inconsistent conditions for the selection function in these cases. What are we to make of this? I think there are four ways of constructing a consistent theory for Stalnaker out of what he says in Stalnaker 1975, though I do not

2 know which is to be definitely preferred. The first way to avoid the inconsistent result is that Stalnaker would rule out anything but truths from being presupposed: while this would make his position most like mine, I think it is the least plausible (why couldn’t speakers presuppose falsehoods?) and is discouraged by other parts of the text: for instance, when he says “The most important element of a context, I suggest, is the common knowledge, or presumed common knowledge and common assumption of the participants of the discourse” he strongly suggests that these common assumptions need not necessarily be true. I therefore think that Stalnaker would want to reject this first way. The second way to avoid the inconsistency would be to drop the condition that the selection function relative to a world w, given a proposition that is true at w, yields w (i.e. the “closest world” for a given antecedent which is true at the world of evaluation may be other than the world of evaluation). The most salient problem with this option is that, given the other things Stalnaker says, modus ponens would not be valid in his system. Consider an indicative conditional “If A then B” with a true antecedent A, a false consequent B, but, for example, B is one of the things presupposed in the context (and nothing is presupposed about A either way). The Aworlds in the context set C are all A-and-B worlds (since B is true at all worlds in C, and there are some A worlds in C). So the selection function will select an A-and-B world. So “If A then B” comes out true, as does A, but B is false. We have a counter-model for modus ponens. Some writers on indicative conditionals, even those working with a closest worlds framework, have wanted to deny the validity of modus ponens: Lycan 2001 is one prominent recent example, and McGee 1985 famously offered objections to modus ponens for the indicative conditional. But I suspect Stalnaker would not be tempted by this radical solution. Stalnaker’s formal system certainly rules out this option, as it stands. The final two construals are plausible, internally consistent, and are suggested by the text. Unfortunately, since they are inconsistent with each other, we cannot reconstruct a consistent Stalnaker as holding both, and Stalnaker 1975 does not seem to me to provide enough evidence as to which one he would prefer. The third construal would be to always include the actual world in the context set, even if what was presupposed did not always hold there. The definition of context sets from p 142 quoted above would thus need amending, though this would have the advantage that it would become more plausible that it could follow from the definition of context set that “this set is defined as the set of possible worlds among which the speaker wishes to distinguish”, something which he says about the definition of the context set on p. 144 but which is not mentioned in what appears to be the explicit definition on p 142.

3 The fourth construal is that when the actual world is “presupposed to be counterfactual” in the sense of not being in fact consistent with what is presupposed, and the antecedent of an indicative conditional is in fact true, this is a case in which an exception is made to the rule that the selection function “turns first” to worlds in the context set. This is suggested by the fact that his remarks about what the selection function should “turn first” to are in the context of motivating a more restricted principle: that the selection function relative to a world i selects a world in the context set C provided that iεC. This suggests that when we are evaluating at a world outside C, even when it is unknown to the speaker that that world is outside C (because the speaker is labouring under a false presupposition), the rule about selecting a world within C, if available, need not be enforced. In addition, the tentativeness of the “I would expect…” construction of his claim about indicative conditionals may indicate that he it is one he would happily modify should it prove troublesome (e.g. by being inconsistent with other things he wishes to say). It may even be that what he intends by “the pragmatic principle stated above” is the restricted one that “if iεC, then f(A, i)εC”, though the text itself reads as if this amounts to the same thing as the “normal expectation” of the next paragraph. The limitation of this interpretation is that it has trouble making sense of his remark that “the normal expectation that the selection function should turn first to these worlds [i.e. the worlds in C] before considering counterfactual worlds—those presupposed to be non-actual”, especially since the cases he discusses for overturning this expectation are ones where context suggests movement to a world which is “counterfactual” in this (unusual) sense. It also can do less justice to his previously mentioned claim that “this set [the context set] is defined as the set of possible worlds among which the speaker wishes to distinguish”: the speaker inter alia surely wants to assert something evaluated as true at the actual world, and so presumably the actual world has some claim to be among the worlds the speaker wishes to distinguish (as with most assertions!) and if so the speaker may be concerned with more than just the contents of C. Since the claim that this is true by definition is uncomfortable on any reasonable construal of the definition offered on p 142, however, perhaps this last claim should not bear too much weight. Either reconstruction would produce a view in the spirit of Stalnaker’s paper: and the positions produced seem to me to be on a par. That they are incompatible positions, though, and that they both involve some compromise of the generality of at least some of Stalnaker’s motivations, is something which is not widely recognised. Both involve a “oh, except for the actual world sometimes” kind of rider to more general conditions, and my (partisan) judgment would be that either construal yields a theory which provides truth conditions in an ad hoc fashion given his remarks about

4 assertability conditions. Not that this would be worse than giving up modus ponens or accepting an inconsistent theory, of course: but it is one reason to search for possibleworlds accounts of indicative conditionals that lack this sort of one-off modifications for the actual world. (I recommend the kind of view defended in Nolan 2003.) References Jackson, F. (ed). 1991. Conditionals. Oxford Uni Press, Oxford. Lycan, W. G. 2001. Real Conditionals. Oxford Uni. Press, Oxford. McGee, Vann. 1985. “A Counterexample to Modus Ponens”. Journal of Philosophy. 82: 462-471 Nolan, D. 2003. “Defending a Possible Worlds Account of Indicative Conditionals”. Philosophical Studies 116.3: 215-69 Stalnaker R., and Thomason, R. 1968. “A semantic analysis of conditional logic”. Theoria 36: 23-42 Stalnaker, R. 1968. "A Theory of Conditionals" in Rescher, N (ed). 1968. Studies in Logical Theory, American Philosophical Quarterly Monograph Series, no.2. Basil Blackwell, Oxford. pp 98-112 Stalnaker, R. 1975. “Indicative Conditionals”. Philosophia 5: 269-286. Reprinted in Jackson 1991, pp 136-154. Page numbers given are for the Jackson collection.