Logical Types in Some Arguments about Knowability and Belief
Bernard Linsky · 2009
Abstract Over the years a number of arguments have been formulated in elementary modal logic purporting to show that there are limits to what can be known or believed. These include the ‘Fitch’ style arguments that will be the main interest of this chapter, versions of the paradoxes of the ‘Surprise examination’ and the ‘Preface’, and several arguments against analyses of truth in terms of verifiability under ideal conditions. A use of iteration of operators and even apparent self-reference seems to reappear in various of these arguments and so one might wonder what exactly is common to these arguments and if that common element reveals something about their validity. In recent years, it has also been claimed that verificationism is subject to logical difficulties revealed by these arguments. It would be a challenge to verificationism to have a proof that some true sentences simply cannot be known, or believed, even by an idealized agent. The understanding of these arguments is thus a pressing issue for the verificationist program. Proposals for analyses of truth in terms of verification in ideal conditions also confront difficulties when one worries about the truth conditions for statements asserting that such ideal conditions do or do not obtain. There appears to be at least self-application of the theory of truth to its own preconditions. This chapter identifies the elements of ‘self-reference’ in these various arguments, distinguish self-reference proper from the use of iteration of operators expressing epistemic conditions, and then provide a uniform account of them making use of the idea of logical types of propositions.