(2014). Capturing the relationship between conditionals and conditional probability with a trivalent semantics. Journal of Applied Non-Classical Logics: Vol. 24, Three-Valued Logics and their Applications, pp. 144-152. doi: 10.1080/11663081.2014.911535.

This paper clarifies the relationship between the Triviality Results for the conditional and the Restrictor Theory of the conditional. On the understanding of Triviality proposed here, it is implausible—pace many proponents of the Restrictor Theory—that Triviality rests on a syntactic error. As argued here, Triviality arises from simply mistaking the feature a claim has when that claim is logically unacceptable for the feature a claim has when that claim is unsatisfiable. Triviality rests on a semantic confusion—one which some semantic theories, (...) but not others, are prone to making. On the interpretation proposed here, Triviality Results thus play a theoretically constructive role in the project of natural language semantics. (shrink)

Indicative and subjunctive conditionals are in non-complimentary distribution: there are conversational contexts at which both are licensed (Stalnaker 1975; Karttunen and Peters 1979; von Fintel 1998). This means we can ask an important, but under-explored, question: in contexts which license both, what relations hold between the two? In this paper, I’ll argue for an initially surprising conclusion: when attention is restricted to the relevant contexts, indicatives and subjunctives are co-entailing. §1 introduces the indicative/subjunctive distinction, along with a discussion of the (...) relevant notion of entailment; §2 presents the main argument of the paper, and §3 considers some of the philosophical implications of the argument in §2. Finally, §4 argues that we can reconcile the equivalence of indicatives and subjunctives with apparently conflicting judgements. (shrink)

ABSTRACT A trivalent theory of indicative conditionals automatically enforces Stalnaker's thesis – the equation between probabilities of conditionals and conditional probabilities. This result holds because the trivalent semantics requires, for principled reasons, a modification of the ratio definition of conditional probability in order to accommodate the possibility of undefinedness. I explain how this modification is motivated and how it allows the trivalent semantics to avoid a number of well-known triviality results, in the process clarifying why these results hold for many (...) bivalent theories. In short, the slew of triviality results published in the last 40-odd years need not be viewed as an argument against Stalnaker's thesis: it can be construed instead as an argument for abandoning the bivalent requirement that indicative conditionals somehow be assigned a truth-value in worlds in which their antecedents are false. (shrink)

There is almost a consensus among conditional experts that indicative conditionals are not material. Their thought hinges on the idea that if indicative conditionals were material, A → B could be vacuously true when A is false, even if B would be false in a context where A is true. But since this consequence is implausible, the material account is usually regarded as false. It is argued that this point of view is motivated by the grammatical form of conditional sentences (...) and the symbols used to represent their logical form, which misleadingly suggest a one-way inferential direction from A to B. That conditional sentences mislead us into a directionality bias is a phenomenon that is well-documented in the literature about conditional reasoning. It is argued that this directional appearance is deceptive and does not reflect the underlying truth conditions of conditional sentences. This directional bias is responsible for both the unpopularity of the material account of conditionals and some of the main alternative principles and themes in conditional theory, including the Ramsey’s test, the Equation, Adams’ thesis, conditional-assertion and possible world theories. The directional mindset forgets a hard- earned lesson that made classical logic possible in the first place, namely, that grammatical form of sentences can mislead us about its truth conditions. There is a case to be made for a material account of indicative conditionals when we break the domination of words over the human mind. (shrink)

According to existing accounts of indicative conditionals, any argument of the following form is valid: ϕ → ψ, ( ϕ ∧ ψ ) → χ ∴ ϕ → χ. Here, I present a set of counterexamples to show that there exist invalid arguments of this form. I argue that this data poses serious problems to variably strict accounts of conditionals, as such accounts are structurally unable to accommodate it. Dynamic strict accounts, however, are a different story. While existing dynamic strict (...) accounts do not accommodate the data, they are in principle able to, and I propose a modified dynamic strict account, drawing from von Fintel, that does. The key modification is this: whereas existing dynamic strict accounts take into account only the effects of conditional antecedents in changing the semantic context, the data shows that we must also take into account the effects of conditional consequents in changing the semantic context. (shrink)

This book proposes a semantic theory of conditionals that can account for (i) the variability in usages that conditional sentences can be put; and (ii) both conditional sentences of the form ‘if p, q’ and those conditional thoughts that are expressed without using ‘if’. It presents theoretical arguments as well as empirical evidence from English and other languages in support of the thesis that an adequate study of conditionals has to go beyond an analysis of specific sentence forms or lexical (...) items. The resulting perspective on conditionals is one in which conditionality is located at a higher level than that of the sentence; namely, at the level of thought. The author argues that it is only through adopting such a perspective, and with it, a commitment to context-dependent semantics, that we can successfully represent conditional utterances as they are used and understood by ordinary language users. It will be of interest to students and scholars working on the semantics of conditionals in the fields of linguistics (especially semantics and pragmatics) and philosophy of language. (shrink)

ABSTRACTSeveral authors have claimed that indicative conditionals are sensitive to the epistemic perspective of agents. According to this sort of view, the truth of an indicative conditional depends on the background evidence of some relevant agent or group of agents. In this paper, I argue that the context-dependence of indicative conditionals goes beyond this. Indicative conditionals are not only sensitive to the evidence of agents, but also to contextual factors that determine what is inferable from such background evidence. More specifically, (...) my proposal is that when the inference associated with a conditional is defeasible, the truth of that conditional is sensitive to practical stakes. (shrink)

The view that if-clauses function semantically as restrictors is widely regarded as the only candidate for a fully general account of conditionals. The standard implementation of this view assumes that, where no operator to be restricted is in sight, if-clauses restrict covert epistemic modals. Stipulating such modals, however, lacks independent motivation and leads to wrong empirical predictions. In this paper I provide a theory of conditionals on which if-clauses are uniformly interpreted as restrictors, but no covert modals are postulated. Epistemic (...) if-clauses, like those in bare conditionals, restrict an information state parameter which is used to interpret an expressive layer of the language. I show that this theory yields an attractive account of bare and overtly modalized conditionals and solves various empirical problems for the standard view, while dispensing with its less plausible assumption. (shrink)