• I present a puzzle for the standard, propositional semantic account of belief reports by considering novel inferences which it incorrectly predicts to be invalid under assumptions that are plausible by its advocates’ own lights. In response, I propose a conservative departure from the standard view on which certain ‘that’-clauses designate novel devices of semantic type that I call open propositions. After outlining some desiderata for a theory of open propositions, I provide some reasons for ad…Read more
  • In this paper, I argue that there are cases of explanatory induction in mathematics. To do so, I first introduce the notion of explanatory definition in the context of mathematical explanation. A large part of the paper is dedicated to introducing and analyzing this notion of explanatory definition and the role it plays in mathematics. After doing so, I discuss a particular inductive definition in advanced mathematics—CW\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \use…Read more