Logical Akrasia

Abstract The aim of this paper is threefold. Firstly, sections 1 and 2 introduce the novel concept logical akrasia by analogy to epistemic akrasia. If successful, the initial sections will draw attention to an interesting akratic phenomenon which has not received much attention in the literature on akrasia (although it has been discussed by logicians in different terms). Secondly, sections 3 and 4 present a dilemma related to logical akrasia. From a case involving the consistency of Peano Arithmetic and Gödel's Second Incompleteness Theorem, it's shown that either we must be agnostic about the consistency of Peano Arithmetic or akratic in our arithmetical theorizing. If successful, these sections will underscore the pertinence and persistence of akrasia in arithmetic (by appeal to Gödel's seminal work). Thirdly, section 5 concludes by suggesting a way of translating the Dilemma of Arithmetical Akrasia into a case of regular epistemic akrasia; and further how one might try to escape the dilemma when it's framed this way.