Possible worlds truth table task

In this paper, a novel experimental task is developed for testing the highly influential, but experimentally underexplored, possible worlds account of conditionals (Lewis, 1973; Stalnaker, 1968). In Experiment 1, this new task is used to test both indicative and subjunctive conditionals. For indicative conditionals, five competing truth tables are compared, including the previously untested, multi-dimensional possible worlds semantics of Bradley (2012). In Experiment 2, these results are replicated and it is shown that they cannot be accounted for by an alternative hypothesis proposed by our reviewers. In Experiment 3, individual variation in truth assignments of indicative conditionals is investigated via Bayesian mixture models that classify participants as following one of several competing truth tables. As a novelty of this study, it is found that a possible worlds semantics of Lewis and Stalnaker is capable of accounting for participants' aggregate truth value assignments in this task. Applied to indicative conditionals, we show across three experiments, that the theory both captures participants' truth values at the aggregate level (Experiments 1 and 2) and that it makes up the largest subgroup in the analysis of individual variation in our experimental paradigm (Experiment 3).

Williamson on conditionals and testimony

In Suppose and Tell, Williamson makes a new case for the material conditional account. He tries to explain away apparently countervailing data by arguing that these have been misinterpreted because researchers have overlooked the role of heuristics in the processing of conditionals. Cases involving the receipt of apparently conflicting conditionals play an important dialectical role in Williamson's book: they are supposed to provide evidence for the material conditional account as well as for the defeasibility of a key procedure underlying our everyday assessments of conditionals. We argue that they can serve neither of these purposes and that Williamson overestimates the reach of heuristics. We specifically challenge Williamson's assumption that, in the kind of cases centrally at issue in his book, the recipient of conflicting conditionals will typically accept those at face value, even granting Williamson that conditionals can be freely passed among speakers under normal conditions of testimony.

Williamson on indicatives and suppositional heuristics

Timothy Williamson has defended the claim that the semantics of the indicative 'if' is given by the material conditional. Putative counterexamples can be handled by better understanding the role played in our assessment of indicatives by a fallible cognitive heuristic, called the Suppositional Procedure. Williamson's Suppositional Conjecture has it that the Suppositional Procedure is humans' primary way of prospectively assessing conditionals. This paper raises some doubts on the Suppositional Procedure and Conjecture.

Indicatives, Subjunctives, and the Falsity of the Antecedent

It is widely held that there are important differences between indicative conditionals (e.g., "If the authors are linguists, they have written a linguistics paper") and subjunctive conditionals (e.g., "If the authors had been linguists, they would have written a linguistics paper"). A central difference is that indicatives and subjunctives convey different stances toward the truth of their antecedents. Indicatives (often) convey neutrality: for example, about whether the authors in question are linguists. Subjunctives (often) convey the falsity of the antecedent: for example, that the authors in question are not linguists. This paper tests prominent accounts of how these different stances are conveyed: whether by presupposition or conversational implicature. Experiment 1 tests the presupposition account by investigating whether the stances project-remain constant-when embedded under operators like negations, possibility modals, and interrogatives, a key characteristic of presuppositions. Experiment 2 tests the conversational-implicature account by investigating whether the stances can be cancelled without producing a contradiction, a key characteristic of implicatures. The results provide evidence that both stances-neutrality about the antecedent in indicatives and the falsity of the antecedent in subjunctives-are conveyed by conversational implicatures.

Cancellation, negation, and rejection

In this paper, new evidence is presented for the assumption that the reason-relation reading of indicative conditionals ('if A, then C') reflects a conventional implicature. In four experiments, it is investigated whether relevance effects found for the probability assessment of indicative conditionals (Skovgaard-Olsen, Singmann, & Klauer, 2016a) can be classified as being produced by (a) a conversational implicature, (b) a (probabilistic) presupposition failure, or (c) a conventional implicature. After considering several alternative hypotheses, and the accumulating evidence from other studies as well, we conclude that the evidence is most consistent with the Relevance Effect being the outcome of a conventional implicature. This finding indicates that the reason-relation reading is part of the semantic content of indicative conditionals, albeit not part of their primary truth-conditional content.