Assumptions, Hypotheses, and Antecedents
This paper is about the distinction between arguments and conditionals (premises and antecedents), and about a further distinction that I propose between two different kinds of arguments (two kinds of premises that I will call assumptions and hypotheses). The distinction between assumptions, hypotheses, and antecedents is easily made in artificial languages, and we are already familiar with it from our first logic courses (although not necessarily under those names, since there is no standard terminology for the distinction). After explaining their differences in artificial languages, I will argue that there are ordinary language counterparts of the three notions, meaning that some formal properties of the artificial notions nicely capture some features of the ordinary language counterparts and their behavior in contexts of reasoning. My next crucial claim is that these three notions often get confused in ordinary language, which leads to problems for translation into symbols. I will suggest a solution to the translation problem by pointing to some distinctive characteristics of the three notions that link them to their artificial language counterparts. Next I will argue that this confusion is behind some well known philosophical problems and puzzles. I will apply the distinctions in order to explain away some famous paradoxes: the direct argument (or-to-if inference), a standard argument for fatalism, and McGee's counterexample to modus ponens. As Stalnaker also solved the first two mentioned cases, using his theory of reasonable inference, I will explain the similarities of our solutions, and also explain why my distinctions apply more broadly, to some cases involving indicative conditionals and some cases with counterfactuals where reasonable inference does not apply.