What Counts as Evidence for a Logical Theory?

Abstract

Anti-exceptionalism about logic is the Quinean view that logical theories have no special epistemological status, in particular, they are not self-evident or justified a priori. Instead, logical theories are continuous with scientific theories, and knowledge about logic is as hard-earned as knowledge of physics, economics, and chemistry. Once we reject apriorism about logic, however, we need an alternative account of how logical theories are justified and revised. A number of authors have recently argued that logical theories are justified by abductive argument (e.g. Gillian Russell, Graham Priest, Timothy Williamson). This paper explores one crucial question about the abductive strategy: what counts as evidence for a logical theory? I develop three accounts of evidential confirmation that an anti-exceptionalist can accept: (1) intuitions about validity, (2) the Quine-Williamson account, and (3) indispensability arguments. I argue, against the received view, that none of the evidential sources support classical logic.

Limits of Abductivism About Logic

“…Truths, e.g., that can be expressed in sentences of the form α&β occur only together with the truths of the corresponding α and β. This view is opposed, e.g., to the idea behind relevance logic that necessary truth-preservation (in virtue of logical form) is necessary but not sufficient for consequence (Hjortland, 2019). 10 Field attributes such a view to Harman and writes: "One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form)" (Field, 2009b, 251).…”

“…First, there is the question of whether deductive strength is a theoretical virtue in logical theories, holding fixed adequacy to the data. 11 Williamson thinks it is; others disagree (Russell, 2019;Hjortland, 2019 (2017) holds that classical logic is preferable on abductive grounds. He thinks that restricting classical logic, e.g.…”

“…Anti-exceptionalism about logic, i.e. the view that logic does not have any special status but is continuous with science, is currently popular in the philosophy of logic (Hjortland, 2019;Russell, 2019;Read, 2019;Finn, 2019;Costa and Arenhart, 2018;Wyatt and Payette, 2018;Williamson, 2017;Priest, 2014;Quine, 1964). One central tenet of anti-exceptionalism is abductivism about logic.…”

The Problem with ‘the Background Logic Problem’

“…Obviously, here there is infiltration of the theoretical apparatus of the classical logician in judging the further stated desiderata of a logical theory, just as Priest had his own desiderata in light of his own apparatus. That is, in the measure that such desiderata involve logical concepts, they are also judged from 7 Which ones, is a matter for discussion elsewhere, but see Hjortland (2019) for the difficulties of using non-evidential factors in logical theory selection. 8 See, for instance Scharp -Shapiro (2017) for a discussion on conceptual revision involving truth in the light of paradoxes.…”

“…Now, it could well be that one may provide for separate answers to each question, forming a coherent version of anti-exceptionalism. As we have mentioned, anti-exceptionalism still requires further articulation, and people have been developing it on a step by step basis, leaving the background problem without an answer (Hjortland 2019) (Martin 2020). However, as we shall argue here, this piecemeal treatment of the problems only postpones the major difficulties that the background logic problem generates, and ignores the fact that the background problem somehow impacts on the other two problems as well.…”