An imperative conditional is a conditional in the imperative mood (by analogy with “indicative conditional”, “subjunctive conditional”). What, in general, is the meaning and the illocutionary effect of an imperative conditional? I survey four answers: the answer that imperative conditionals are commands to the effect that an indicative conditional be true; two versions of the answer that imperative conditionals express irreducibly conditional commands; and finally, the answer that imperative conditionals express a kind of hybrid speech act between command and assertion.

I argues that quantificational adverbs are unselective binders over individuals. The Lewisian analysis, however, fails to recognize the ambiguity in some quantificationally modified conditionals. That the Lewisian approach cannot predict some attested reading is known as the “proportion problem.” I propose a solution based on the following ideas: (a) quantificational adverbs bind selectively; (b) a singular indefinite and its anaphoric pronoun may introduce a plural discourse referent, and (c) plural predication is elusive.

The material interpretation of conditionals is commonly recognized as involving some paradoxical results. I here argue that the truth functional approach to natural language is the reason for the inadequacy of this material interpretation, since the truth or falsity of some pair of statements ‘p’ and ‘q’ cannot per se be decisive for the truth or falsity of a conditional relation ‘if p then q’. This inadequacy also affects the ability of the overall formal system to establish whether or not (...) arguments involving conditionals are valid. I also demonstrate that the Paradox of Indicative Conditionals does not actually involve a paradox, but instead contains some paralogistic elements that make it appear to be a paradox. The discussion of the paradox in this paper further reveals that the material interpretation of conditionals adversely affects the treatment of disjunctions. -/- Much has been said about these matters in the literature that point in the same direction. However, there seems to be some reluctance against fully complying with the arguments against the truth functional account of conditionals, since many of the alternative accounts rely on the material conditional, or at least on an understanding of the conditional as a function of antecedent and consequent in a similar sense as the material conditional. My argument against truth functionality indicates that it may in general involve similar problems to treat conditionals as such functions, whether one deals with theories of truth, assertability or probability. (shrink)

In addition to full beliefs, agents have attitudes of varying confidence, or credences. For instance, I do not believe that the Boston Red Sox will win the American League East this year, but I am at least a little bit confident that they will – i.e. I have a positive credence that they will. It is also common to think that agents have conditional credences. For instance, I am very confident – i.e. have a conditional credence of very-likely strength – (...) that the Red Sox will win the AL East this year given that their pitching staff stays healthy. There are good reasons to think that conditional credences are neither credences nor some combination of credences. In this paper, I show that similar reasons support thinking that agents have what we can call quantificational credences – attitudes like, thinking that each AL East team with a healthy pitching staff is at least a little bit likely to win the division – which are neither credences, conditional credences, nor some combination thereof. I provide a framework for assessing the rationality of credal states which involve quantificational credences. And I give a general picture of credal states that explains the similarities and differences between ordinary, conditional, and quantificational credences. (shrink)

This paper outlines a formal recursive wager resolution calculus (WRC) that provides a novel conceptual framework for sentential logic via bridge rules that link wager resolution with truth values. When paired with a traditional truth-centric criterion of logical soundness WRC generates a sentential logic that is broadly truth-conditional but not truth-functional, supports the rules of proof employed in standard mathematics, and is immune to the most vexing features of their traditional implementation. WRC also supports a novel probabilistic criterion of logical (...) soundness, the fair betting probability criterion (FBP). It guarantees that the conclusion of an FBP-valid argument is at least as credible as a conjunction of premises, and also that the conclusion is true if the premises are. In addition, WRC provides a platform for a novel non-probabilistic, computationally simpler criterion of logical soundness – the criterion of Super-validity - that issues the same logical appraisals as FBP, and hence the same guarantees. (shrink)