Title: Generic Validity
By Jack Woods (University of Leeds, Philosophy)
Date: Thursday, April 25, 2024
Time: 1530-1700
Room: H232
Abstract: Until 20 years ago, it would have been very difficult to deny that there was a most basic, foundational, or fundamental relation of logical consequence. These days, though, logical pluralism is on the rise (Beall and Restall 2005, Field 2009, Russell 2008) and some have even made the stronger claim that no notion of logical consequence holds across all contexts (Shapiro 2014, Russell 2018). Yet many of us still hold onto the thought that there really is one most basic, foundational, fundamental notion of logical consequence which underlies all the rest. I’ll refer to this notion of logical consequence as generic in what follows, for reasons that will become clear below.
Why think that there really is a notion of generic validity? There are a number of sophisticated considerations and one pugnacious one. The sophisticated ones range from the idea that there’s a fixed domain of existing propositions which are logically related to each other, to the necessary use of logic in areas like abduction, the theory of credences, and belief revision, to the thought that no pluralist picture could do explain the uniformity of our judgments of what we’re committed to by means of the beliefs and theories we adopt. Put these to the side, though I think they’re individually compelling and jointly conclusive. The pugnacious reason is equally damning and far more fun. It’s best thought of in the form of an obnoxious question to the pluralist. Which logic is your book written in?
Of course, that’s facile. The serious version goes like so: the books and papers defending logical pluralism contains arguments and those arguments are presumably meant to be taken seriously. That is, they’re taken to be at least valid. We can thus fairly ask which notion of validity is employed in arguing for logical pluralism. As well as asking which logic is used in evaluating which logic is best for which purpose, which logic outlines connections between results in one domain and another, and which logic is used for the metatheory in which pluralism is usually defined. This is especially important since whether or not we can justify various claims made in defending particular pluralisms depends on which logic we use when evaluating those claims.
The most natural and unified answer to these questions is that there’s a single notion of validity that provides the standard of argument for pluralist claims. Moreover, the most charitable interpretation of their systematic lack of discussion of the pugnacious question is that they intend their interlocutors to use, when evaluating their arguments, a relation of logical consequence which is uniquely appropriate to the context of deciding about philosophical views like logical pluralism. My contention in this paper that this relation simply is the most basic, foundational, fundamental relation of logical consequence.
About the speaker: Jack Woods is University Academic Fellow in Mathematical Philosophy at the University of Leeds. His research focuses on issues in the philosophy of language, philosophical logic, and metaethics. His work has appeared in such journals as Ethics, Nous, the Philosophical Review, the Journal of Philosophical Logic, Oxford Studies in Metaethics, and Oxford Studies in Normative Ethics. In 2021 he co-edited (with Gil Sagi) “The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning”, published by Cambridge University Press.
