A Counterexample to Modus Tollens

Abstract

This paper defends a counterexample to Modus Tollens, and uses it to draw some conclusions about the logic and semantics of indicative conditionals and probability operators in natural language. Along the way we investigate some of the interactions of these expressions with knows, and we call into question the thesis that all knowledge ascriptions have truth-conditions. A probabilistic dynamic semantics for probability operators, conditionals, and acceptance attitudes is developed around the idea of representing the common ground of a conversation as a set of probability spaces.