ARTICLE In Pursuit of the Non-Trivial Colin R. Caret* Yonsei University, Seoul, South Korea *Corresponding author. Email: colin.caret@gmail.com (Received 28 October 2018; revised 25 March 2019; accepted 1 April 2019; first published online 20 June 2019) Abstract This paper is about the underlying logical principles of scientific theories. In particular, it concerns ex contradictione quodlibet (ECQ) the principle that anything follows from a contradiction. ECQ is valid according to classical logic, but invalid according to paracon- sistent logics. Some advocates of paraconsistency claim that there are ‘real’ inconsistent theories that do not erupt with completely indiscriminate, absurd commitments. They take this as evidence in favor of paraconsistency. Michael (2016) calls this the non- triviality strategy (NTS). He argues that this strategy fails in its purpose. I will show that Michael’s criticism significantly over-reaches. The fundamental problem is that he places more of a burden on the advocate of paraconsistency than on the advocate of classical logic. The weaknesses in Michael’s argument are symptomatic of this preferential treatment of one viewpoint in the debate over another. He does, however, make important observations that allow us to clarify some of the complexities involved in giving a logical reconstruction of a theory. I will argue that there are abductive arguments deserving of further consideration for the claim that paraconsistent logic offers the best explanation of the practice of inconsistent science. In this sense, the debate is still very much open. Keywords: inconsistent science; logic; rationality; non-triviality; paraconsistency 1. The non-triviality strategy Broadly speaking, this paper is about the nature of scientific theories and the prospects for reasoned debate about their underlying logical principles. More narrowly, it is about ex contradictione quodlibet (ECQ), a form of argument that proceeds from contradic- tory premises to literally any conclusion you like. 1 P, ¬P[Q ECQ is valid according to classical logic, but invalid according to paraconsistent logics (this is the defining feature of paraconsistency), hence advocates of paraconsistent © Cambridge University Press 2019 1 I assume a standard Set-Fml framework in which arguments have a set of premises and a single con- clusion (Humberstone 2011: §1.2). In doing so, I ignore issues that might arise in the context of multiple- conclusion logics and substructural logics such as: How to describe an argument in a way that is neutral with respect to number of conclusions? How to characterize the mode of premise combination involved in an argument? I do this only for simplicity and not because I am opposed to multiple-conclusion or sub- structural logics (see e.g. Caret and Weber 2015). Episteme (2021), 18, 282–297 doi:10.1017/epi.2019.17 terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/epi.2019.17 Downloaded from https://www.cambridge.org/core. Universiteitsbibliotheek Utrecht, on 08 Jul 2021 at 08:01:15, subject to the Cambridge Core