Logic and Metaphysical Presuppositions

Colloquium Mathematical Philosophy, Otávio Bueno (Miami) gives a talk at the MCMP Colloquium (22 January, 2015) titled "Logic and Metaphysical Presuppositions". Abstract: Does logic (in particular, classical logic) have metaphysical presuppositions? It may be thought that it doesn’t: logical principles and logical inferences are often taken as not requiring the existence of any objects for them to hold. Logical principles are supposedly true in any domain (so there is no reliance on the subject matter at hand), and logical inferences are traditionally understood as being similarly independent of the subject matter under consideration. As Rudolf Carnap famously pointed out: “If logic is to be independent of empirical knowledge, then it must assume nothing concerning the existence of objects (Carnap [1937], p. 140).” In this paper I examine a number of arguments to the contrary, according to which, despite appearances, logical principles and logical inferences do have metaphysical presuppositions. I consider critically these arguments and indicate how they can be resisted, and motivate an alternative that, I argue, recognizes the nature and limitations of such presuppositions. In the end, as will become clear, it does require a suitable understanding of logic and some strategies to avoid commitment to abstract objects to block such presuppositions. Left unassisted, logic may not be presupposition free after all.