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Symposium VI. Logical Consequence
Gillian Russell (Australian Catholic University) and Sara Uckelman (Durham)

2024 Joint Session of the Aristotelian Society and the Mind Association

University of Birmingham

12 - 14 July 2024

Symposium VI. Logical Consequence


Gillian RusselL

Australian Catholic University


Sara Uckelman

University of Durham


In this paper I ask what logical consequence is, and give an answer that is somewhat different from the usual ones. It’s natural to wonder why we need a new conception of logical consequence, and so I begin by explaining the work that I want the answer to do and why the standard conceptions aren’t well-suited to the task. Then I articulate a replacement view which is. This paper is a contribution to a conversation that has included Alfred Tarski, John Etchemendy, and Gila Sher, but the view that I articulate and argue for here differs substantially from each of theirs. First, it is a hybrid of the more common semantic and metaphysical approaches, and second (and perhaps this is initially more shocking) it rethinks the distinction between logical and non-logical expressions, and takes this to be an idealisation of a very different phenomenon in natural language. The result is a conception of logical consequence well-suited to capturing the entailment relation on both formal and natural languages, and on which there is no principled discontinuity between logical and analytic consequence.  
Logical Consequence (Slight Return),” Gillian Russell asks “what is logical consequence?”, a question which has vexed logicians since at least the 12th century, when people first began to wonder what does it mean for one sentence (or proposition) to follow from another sentence (or proposition; or set of sentences; or set of propositions), or whether it was possible to put down rules determining \emph{when} the relation of “follows from” (or “is antecedent to”) holds.  Her aim is threeofld: (1) to explain what an answer to the question “what is logical consequence?” would need to be able to do in order to be a satisfying answer, (2) to identify previous answers to the question, (3) to demonstrate why these previous answers are inadequate to do what the answer needs to be able to do, and to offer a new answer. In the present paper, we respond to these aims in two ways.  The first is to say something about where Russell’s central question even comes from, because this is not a topic that is often discussed by 20th- and 21st-century logicians, and even historians of logic tend to not have had much to say about when—and why—this question even comes about in the first place.  The second is to evaluate the accounts proposed and discussed by Russell, including her new proposal.  In the end, we will argue that she has reached the right account of the nature of logical consequence, but not necessarily for the right reasons.


Gillian K. Russell is Professor of Philosophy at the Australian National University.  She works in the philosophy of logic and language, including social and political applications.  Her newest monograph, Barriers to Entailment: Hume’s Law and other Limits on Logical Consequence came out with OUP in 2023.   She is also the author of Truth in Virtue of Meaning:  A defence of the analytic/synthetic distinction (OUP, 2008) and has edited two collections,  The Routledge Companion to the Philosophy of Language, with Delia Graff Fara,  New Waves in Philosophical Logic  with Greg Restall. 
Dr. Sara L. Uckelman is an associate professor of logic at Durham University. She received her PhD from the Institute for Logic, Language, and Computation at the University of Amsterdam in 2009, with a dissertation entitled Modalities in Medieval Logic. After completing her PhD, she held research positions in Amsterdam, Tilburg, and Heidelberg before coming to Durham in 2014. Dr. Uckelman is a specialist in modal logic and the history of logic, especially logic in the Middle Ages.

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