Topics in Logic and Semantics: Conditionals

The truth condition for material conditionals states that a material conditional is true whenever its antecedent is false or its consequent true. Suppose you didn't raise an eyebrow when you first learned this. On the material implication analysis, it's true that if you DID raise an eyebrow, the sun will explode! This surely is an odd result. Can we do better? In this course, we will examine ways to better theorize about conditionals in natural language. We will cover both indicative conditionals (e.g., "If Oswald didn't kill Kennedy, someone else did"), and counterfactuals (e.g., "If Oswald hadn’t killed Kennedy, someone else would have"). We shall survey a wide range of analyses: from the Gricean pragmatic defense of material implication to the Lewis-Stalnaker similarity semantics, to premise semantics, and to the more recent dynamic approach to conditionals. Along the way, you will be introduced to basic modal logics and conditional logics. In the second half of this course, we will explore the connection between conditional probability and the probability of conditionals. In particular, we will examine Lewis's famous triviality results which show why we can't simply identify the probability we ascribe to a conditional statement with the conditional probability of its consequent given its antecedent. We will then look at several ways to tackle the triviality results. Additional topics may include but not limited to: biscuit conditionals (e.g., “There are biscuits on the sideboard if you want them”) and conditional speech acts, counterfactuals and causal dependence, case studies of certain conditional inferences (e.g., Modus Ponens, Simplification of Disjunctive Antecedents).