The Logic of Conditional Assertions

Dissertation, Indiana University (1983)

Authors
Daniel Cohen
Colby College
Abstract
It has been suggested that to say something of the form 'if P, then Q' is less an affirmation of a conditional than a conditional affirmation of the consequent, Q. If the condition of assertion, P, is true, then Q has been asserted. If the condition of assertion turns out to have been false, it is as if there had been no assertion. Such conditionals have come to be called "conditional assertions." This dissertation is a study of the logic conditionals, focusing on the logic of conditional assertions and the significance of that locution for accounts of language. ;Conditional assertions differ from assertions of conditionals in two important respects. First, a conditional assertion only succeeds in asserting when the condition of assertion is met. Second, what a conditional assertion asserts, when it does, is just its consequent. A logic of conditional assertions has to account for both the occasional contextual equivalence of a conditional and its consequent and the occasional nonassertiveness of some conditionals. ;It is pragmatic considerations that ground the proposed taxonomy of conditionals and so distinguish conditional assertions from other kinds of conditionals. Pragmatic concerns also provide desiderata for constructing a logic of conditional assertions. A logic is presented and proved sound and complete that meets these goals. The logic of conditional assertions is further developed along two main branches. The logic is first extended to a first-order theory, a theory with quantification. It is also combined with the Relevance Logic, R, so that an implication connective is incorporated. The result of the latter is a "multiconditional logic," a logic accommodating more than one kind of conditional. Soundness and completeness proofs are provided for these systems. Finally, the philosophical impact of a multiconditional logic with nonassertive elements on accounts of language is measured
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