Mathieu Vidal

This paper examines how moods are used in declarative conditionals. Contrary to what is usually defended in the literature, the divide between indicative and subjunctive is unable to account for all the possible cases present in natural language. Therefore, the analysis goes down to the level of the antecedent and the consequent in order to examine their local and global interactions with moods. A formal semantics split into two layers is presented in order to model all the possible cases. The lower layer is the semantics of the conditional and the upper layer is the semantics for the indicative, subjunctive and conditional moods. Finally, it is shown that this proposal provides a unified solution to three puzzles: the Oswald-Kennedy example, the direct argument and the Gibbardian stand-offs. © 2018 Elsevier B.V., All rights reserved.

This article advances the first semantics that is neither for nor against a default implicational link between the progressive and perfective forms, when it comes to solving the imperfective paradox. Depending on the doxastic context of its use, we contend that the progressive form sometimes allows and sometimes does not allow the inference of the corresponding simple form. In other words, the preparatory phase of an event might or might not be believed to lead to its culmination. Indeed, the context can put constraints on beliefs about the time of the culmination and whether or not it allows this inference to be made. From a formal perspective, this new solution to the imperfective paradox combines a specific modal approach with an event-structure analysis originating in event semantics. Finally, this approach solves the associated difficulties that have plagued the most well-known theories in this field.

This paper presents the first possible world semantics for concessive conditionals (i.e., even if A, C conditionals) constructed in a compositional way. First, the meaning of if is formalized through a semantics that builds on the proposal given by Stalnaker (1968). A major difference from Stalnaker’s approach is that irrelevant conditionals (i.e., conditionals where the antecedent and the consequent have no connection) are false in this new setting. Second, the meaning of even is analyzed through a formal semantics based on the notion of scale. This analysis overcomes the problems arising in standard approaches, in which even is analyzed with the help of pragmatic presuppositions. Finally, the two particles are combined in order to provide a formal analysis of even if. This theory predicts the major phenomena concerning the behavior of concessive conditionals and without any call to pragmatic explanations. More generally, this approach creates the possibility of a compositional analysis of other conditionals such as if then or only if forms.

This paper presents the first compositional semantics for if then conditionals. The semantics of each element are first examined separately. The meaning of if is modeled according to a possible worlds semantics. The particle then is analyzed as an anaphoric word that places its focused element inside the context settled by a previous element. Their meanings are subsequently combined in order to provide a formal semantics of if A then C conditionals, which differs from the simple if A, C form. This semantics has the particularity of validating contraposition for the first type but invalidating it for the second type. Finally, a detailed examination of the sentences presented in the literature opposing this schema of reasoning shows that these counterexamples do not generally concern if then conditionals but, rather, even if conditionals and that contraposition is therefore a valid means of reasoning with regard to if then conditionals in natural language, as this system predicts.

This article focuses on defective conditionals ? namely indicative conditionals whose antecedents are false and whose truth-values therefore cannot be determined. The problem is to decide which formal connective can adequately represent this usage. Classical logic renders defective conditionals true whereas traditional mathematics dismisses them as irrelevant. This difference in treatment entails that, at the propositional level, classical logic validates some sentences that are intuitively false in plane geometry. With two proofs, I show that the same flaw is shared by a family of trivalent logics. I go on to examine the strict conditional and its derivatives. This family is the only one to avoid the faulty inference but it does so without addressing the status of the truth-value assigned to defective conditionals.