Logical Partisanhood

Jack Woods

doi:10.1007/s11098-018-1054-2

Abstract

A natural suggestion and increasingly popular account of how to revise our logical beliefs treats revision of logic analogously to the revision of scientific theories (Hjortland, Priest, Russell, Williamson, etc.). I investigate this approach and argue that simple applications of abductive methodology to logic result in revision-cycles, developing a detailed case study of an actual dispute with this property. This is problematic if we take abductive methodology to provide justification for revising our logical framework. I then generalize the case study, pointing to similarities with more recent and popular heterodox logics such as naïve logics of truth. I use this discussion to motivate a constraint—logical partisanhood—on the uses of such methodology: roughly: both the proposed alternative and our actual background logic must be able to agree that moving to the alternative logic is no worse than staying put.

Highlights

An increasingly popular account of logic, Anti-Exceptionalism, views logic as similar to, and continuous with, other scientific theories
I argue that there’s a class of recent theories situated with respect to classical logic. The trouble with these examples is that applying abductive methodology in order to evaluate them with respect to an alternative results in a rational agent oscillating between the alternative and the starting logic
Especially recent attempts to defend naıve theories of truth,27 use theorems like CLASSICAL RECAPTURE FOR T (CRT) to compensate for logical weakness

Summary

Introduction

An increasingly popular account of logic, Anti-Exceptionalism, views logic as similar to, and continuous with, other scientific theories. I’ll highlight this by posing a challenge for this method and, in response, proposing a principled constraint on abductive approaches to logical revision Adopting this constraint rules out many putative logical options as reasonable alternatives to classical logic, at least given their current state of development, but there remain interesting challengers to classical orthodoxy. I argue that there’s a class of recent theories situated with respect to classical logic The trouble with these examples is that applying abductive methodology in order to evaluate them with respect to an alternative results in a rational agent oscillating between the alternative and the starting logic. I turn to developing the problem case that leads to adopting this constraint

Theoretical virtues for logics

Assessment and a precis of the problem

Case study

Generalizing: recapture theorems

Some responses

Wrapping up: a plea for neutrality