Abbreviations

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Introduction to the Logic of Conditionals

The purpose of this course is to give an introduction to the logic and semantics of conditional sentences (sentences of the form "if P then Q") in natural language. We will start by a review of the limitations of the truth-functional analysis of conditionals in classical logic, and will give a detailed exposition and comparison of the conditional logics of Stalnaker, Lewis, and Adams, with emphasis on the Lewis-Kratzer account of if-clauses as restrictors of quantifiers (day 1-2). We will then focus on three aspects of the logic of conditionals: (i) the probability of conditionals (Adam's Thesis) and the significance of Lewis's triviality results (do conditionals have truth conditions?) (day 2-3); (ii) the problem of giving a unified semantics for indicative conditionals and counterfactual conditionals (interaction between tense and modality) (day 4); (iii) the pragmatic treatment of special classes of conditionals (relevance conditionals and anankastic conditionals) (day 5). The course is open to linguists, philosophers and logicians, and presupposes only knowledge of propositional logic.