Indicative Scorekeeping

Folklore has it that counterfactual Sobel sequences favor a variably strict analysis of conditionals over its plainly strict alternative. Recent discussions of the lore have focussed on the question whether data about reverse counterfactual Sobel sequences actually speak in favor of a dynamic revival of the strict analysis. This paper takes the discussion into a new direction by looking at straight indicative Sobel sequences. The observation is that a variably strict analysis fails to predict the felicity of these sequences given minimal semantic and pragmatic assumptions. A properly elaborated dynamic analysis of indicatives, in contrast, handles the data with grace. 1 Indicative Sobel Sequences Lewis [6] famously argues that the felicity of Sobel sequences speaks against a strict analysis of counterfactuals and instead supports a variably strict interpretation on which conditional consequents are evaluated at the closest possible worlds that verify the antecedent. Recent discussions of Lewis’s argument have focussed on Heim’s observation that reverse counterfactual Sobel sequences tend to be infelicitous: von Fintel [2] and Gillies [4] argue that this observation favors a dynamic strict interpretation of counterfactuals over a (static) variably strict analysis, but Moss [7] counters that the data can be handled by a pragmatic supplement to Lewis’s account. This paper takes the discussion into a new direction by arguing that straight indicative Sobel sequences favor a dynamic strict interpretation of conditionals. Indicative Sobel sequences are just as felicitous as their counterfactual cousins: (1) (a) If Alice comes to the party, it will be fun. (b) But if Alice and Bert come, it will not be fun. (c) But if Charles comes as well, it will be fun. . . A variably strict analysis of indicatives à la Stalnaker [8] predicts that (1) is consistent, the simple observation being that the closest possible worlds at which Alice comes to the party need not be worlds at which Bert comes too and that the closest possible worlds at which both show up may be such that Charles stays at home. Variably Strict Analysis. Take a connected and transitive relation ¤ that is provided by context and keeps track of relative similarity or closeness between worlds: 1. min¤,wpφq tw 1 : w P vφw and for all w : if w P vφw, then w ¤w w u 2. vpif φqpψqw 1 iff min¤,wpφq „ vψw This is fine as far as it goes, but it is not sufficient to predict that the sequence in (1) is felicitous since indicative conditionals also impose distinct constraints on the discourse context to be assertible. Compare: (2) (a) # Mary is not in New York. If she is in New York, she will meet Alex. (b) X Mary is not in New York. If she were in New York, she would meet Alex. The textbook explanation for the observation that (2a) is marked goes as follows. The first member of the sequence expresses the proposition that Mary is not in New York and eliminates from the context set—the set of possible worlds compatible with what is common Proceedings of the 19th Amsterdam Colloquium Maria Aloni, Michael Franke & Floris Roelofsen (eds.) 249 ground—all possible worlds at which that proposition is false (see [10]). But for the subsequent indicative to be felicitous there must be at least one such world in the context set because indicative conditionals—unlike their counterfactual cousins—presuppose that their antecedents are compatible with the common ground (see [9]). The textbook explanation just given relies on two pragmatic assumptions that are widely accepted in the literature. Given some context c, let sc be the context set of c: 1. If φ expresses a proposition vφw in context c, then the result of asserting φ in c, c φ, is such that sc φ sc X vφw. 2. An utterance of an indicative conditional of the form xpif φqpψqy in context c presupposes that sc φ H. The problem for the variably strict analysis is this: while it correctly predicts that indicative Sobel sequences are consistent, it wrongly predicts that such sequences are infelicitous given minimal constraints on the semantics of conditionals. I assume—as Lewis and Stalnaker do—that modus ponens is valid and thus that the members of (1) are bounded from below by the material conditional () in the following sense: 3. pif φqpψq ( φ  ψ Accordingly, on a variably strict analysis the similarity relation for the conditionals in (1) must be weakly centered : for all w and w, w ¤w w . (Linguists are less concerned with modus ponens than philosophers but there are no attested counterexamples to this rule for the kind of indicative conditionals that figure in simple Sobel sequences.) But then the result of uttering pif AqpF q and pif A ^ Bqp F q in any context cannot contain an pA ^ Bq-world since this would have to be an pF ^ F q-world, and so the antecedent of (1c) is incompatible with what is common ground once its predecessors have been asserted. So if a variably strict semantics were right, we would expect the utterance of (1c) in the Sobel sequence to be marked due to presupposition failure, which is simply not the case. One might suggest that the presupposition carried by (1c) is accommodated via expanding the context set but then we would expect this expansion to take place in (2a) as well since in both cases the conditional’s antecedent is incompatible with the context set. One might also suggest that the presupposition violation is real but overlooked/ignored in discourse, but then Sobel sequences would have no bite against a plain strict analysis in the first place since it is hard to see why its predictions should not be overlooked/ignored in discourse as well. A variably strict interpretation thus has no good explanation for why indicative Sobel sequences should be felicitous. The purpose of the next sections is to demonstrate that a proper dynamic strict analysis of indicative conditionals avoids the problem of its static variably strict alternative while preserving the pragmatic and semantic constraints articulated earlier. Assuming that conditionals are subject to a uniform semantic analysis, this result also suggests that a dynamic analysis of counterfactuals is on the right track.