The Pragmatics of Verb-Initial Conditional Antecedents in English Edwin Howard (MIT) This paper concerns the distribution of antecedents of subjunctive conditionals in English which, unlike the if-clause in (1)a, are introduced by an inverted auxiliary, usually had, as in (1)b: (1) a. If the queen had been at home they would have hoisted the flag. b. Had the queen been at home they would have hoisted the flag. Although the pair in (1) might seem synonymous at first blush, the distribution of the verbinitial (V1) type in (1)b is more limited than that in (1)a, as observed by Iatridou & Embick 1994 (I&E), and more recently by Biezma 2011. This paper proposes a new pragmatic generalization governing the acceptable use of a V1 conditional antecedent (V1A) in terms of its discourse status with respect to the Question Under Discussion (QUD) of Roberts 1996/2012 among many others; the proposal is made here is broadly situated in the framework laid out in Beaver & Clark 2008 (B&C). The present proposal improves on previous accounts of the distribution of V1As by elegantly covering more data. QUD theories of discourse structure model the flow of discourse in terms of questions as issues raised, broken down into subquestions, and eventually resolved as proposed answers are accepted by conversational participants. Questions are sets of Hamblin alternative propositions, and the question that interlocutors mutually accept to be the most recent and immediate one to resolve is the Current Question (CQ). B&C stipulate the CQ Rule in (2), which determines whether a given question remains open: (2) Current Question Rule: The Current Question must contain at least one true alternative, and contain multiple alternatives which are not resolved as true or false in the common ground. (B&C: ex. 2.53) Assuming for concreteness that the denotation of a question ?p is the set of propositions {p, ¬p} (although see Biezma & Rawlins 2012 for arguments that in fact a polar question denotes a singleton), this paper’s proposal for the distribution of V1As can be stated thus: (3) The antecedent of a subjunctive conditional of the form if ϕ, ψ may undergo Conditional Inversion in a discourse where Q is the Current Question just in case Q = {⟦ϕ⟧, ¬⟦ϕ⟧}. The account predicts observed contrasts between a V1A and an if-clause attested in the previous literature, as these can all be characterized in terms of sensitivity to the CQ, and cases where the V1A is infelicitous are those where an appropriate CQ cannot be accommodated. Importantly the fact that only subjunctive conditionals can have V1As in English doesn’t imply that the antecedent question is settled, negatively; Biezma 2011 provides a version of Anderson’s 1951 famous arsenic example to show that speaker of a V1A conditional does not necessarily take the antecedent to be false. (4) Had Jones taken arsenic, he would have shown just exactly those symptoms which he does in fact show. (Biezma 2011: ex.11) In a construction that places its own requirements on the CQ, an if-clause is predicted to be acceptable, but a V1A will give rise to a clash of irreconcilable restrictions. This is what we observe question-answer pairs & with only: (5) A: Under what circumstances would Mary have come? B: If she had been offered many artichokes. B': *Had she been offered many artichokes. (I&E: ex.31)

In the dialogue in (5), the if-clause is an acceptable fragment answer to A’s question, while the V1A is unacceptable. The contrast is predicted since the discourse requires A’s utterance to be the CQ, but according to (3) the CQ has to be the polarity question “was Mary offered many artichokes?”; thus (5B’) results in a clash. The contrast in (6) can be explained similarly under a theory of only such as the one B&C argue for, according to which the interpretation of only refers to the CQ. (6) a. Only if I had thought that he was sick would I have called him. b. *Only had I thought that he was sick would I have called him. (I&E: ex.27) In the case of (6)a, the felicitous adjunction of only to the if-clause indicates that the CQ is of the form “Under what circumstances would I have called him?” whereas the V1A in (6)b requires the CQ to be the polar question “Did I think he was sick?” The current proposal can also account for I&E’s observation that there is a contrast where the claim that the conditional antecedent is true is made by the speaker in a parenthetical. We can make sense of the contrast in (7) given (3)’s requirement that the CQ in (6)b be ”did he break his leg in childhood?”, the question which the elliptical parenthetical “which in fact he did” purports to settle, yet material in a parenthetical cannot have a bearing on the CQ (or be atissue; Potts 2005). (7) a. If he had broken his leg in childhood, which, in fact, he did, b. #Had he broken his leg in childhood, which, in fact, he did, … he would have exactly this type of scar. (I&E: ex.46) Biezma’s 2011 proposal does not attempt to account for the contrasts observed in I&E, instead appealing to a syntactic stipulation to deal with these data. Rather Biezma focuses on dialogues where an “out of the blue” use of a V1A leads to infelicity in contrast to an ifclause, and accounts for such contrasts with an appeal to Schwarzschild’s (1999) notion of GIVENness. The essence of the proposal is that for a V1A to be licensed, it must find an antecedent constituent of the suitable form in the discourse context. However this proposal runs into some technical difficulties in its implementation, which I will discuss time permitting. In Error: Reference source not found, the subject of the V1A corefers with an element of the preceding utterance, the V1A is felicitous. (8) You should have called Anai.Had shei called [Pablo]F, he could have helped you. However Biezma’s account incorrectly predicts (8) to be unacceptable because the conditional antecedent is not GIVEN. The current accounts straightforwardly replicates the positive results of Biezma’s proposal while avoiding this pitfall.

References: Anderson, A. R. 1951. The Logic of Conditionals. Dordrecht; Beaver, D. & B. Clark. 2008. Sense and Sensitivity. Wiley-Blackwell; Biezma, M. 2011. Conditional inversion and GIVENNESS. Proceedings of SALT 21: 552-571; Biezma, M. & K. Rawlins. 2012. Responding to alternative polar questions. Linguistics & Philosophy 35: 361-406; Iatridou, S. & D. Embick. 1994. Conditional Inversion. Proceedings of NELS 24: 189–203; Potts, C. 2005. The Logic of Conventional Implicatures. Oxford Studies in Theoretical Linguistics, Oxford: OUP; Schwarzschild, R. 1999. GIVENness, AVOIDF and Other Constraints on the Placement of Accent. Natural Language Semantics 7: 141–177.