Bergen Logic Seminar: How Paradoxes Inform Logics

How Paradoxes Inform Logics

Abstract

While the logico-semantic paradoxes play a prominent role within contemporary philosophical logic, epistemologies of logic have so far failed to integrate them into our account of how we justify our theories of validity. This paper begins the project of providing an account of how paradoxes inform our logics of validity. By drawing on an analogy with the role of paradoxes in the sciences, we propose that the logico-semantic paradoxes serve to highlight putative incompatibilities between our established logic and other well-evidenced commitments (PIRM, for short). In order to assess PIRM we consider one of the most prominent discussions of a logico-semantic paradox in the modern literature, Williamson’s (1994) treatment of the sorites. By drawing on Williamson’s extensive arguments both against competing solutions and for his own, epistemicism, we find not only support for PIRM, but wider insights into the methodology of logic, that: (i) judgements about the acceptability of natural-language arguments inform our logics of validity, and (ii) contrary to philosophical tradition, logical knowledge is not unmediated.