Deflationism About Logic
Logical consequence is typically construed as a metalinguistic relation between (sets of) sentences. Deflationism is an account of logic that challenges this orthodoxy. In Williamson’s recent presentation of deflationism, logic’s primary concern is with universal generalizations over absolutely everything. As well as an interesting account of logic in its own right, deflationism has also been recruited to decide between competing logics in resolving semantic paradoxes. This paper defends deflationism from its most important challenge to date, due to Ole Hjortland. It then presents two new problems for the view. Hjortland’s objection is that deflationism cannot discriminate between distinct logics. I show that his example of classical logic and supervaluationism depends on equivocating about whether the language includes a “definitely” operator. Moreover, I prove a result that blocks this line of objection no matter the choice of logics. I end by criticizing deflationism on two fronts. First, it cannot do the work it has been recruited to perform. That is, it cannot help adjudicate between competing logics. This is because a theory of logic cannot be as easily separated from a theory of truth as its proponents claim. Second, deflationism currently has no adequate answer to the following challenge: what does a sentence’s universal generalization have to do with its logical truth? I argue that the most promising, stipulative response on behalf of the deflationist amounts to an unwarranted change of subject.
KeywordsPhilosophy of logic Deflationism Deflationism about logic Williamson Hjortland Anti-exceptionalism Metavalidity Meta-argument Meta-argumentative equivalence Abduction Truth
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This paper has benefitted from discussion with Jared Henderson, Nathan Kellen, Gurpreet Rattan, and participants of the Society for Exact Philosophy annual conference at the University of Connecticut in 2018. I am also grateful to Joanna Lawson, Erik Stei, and Simon Varey for reading drafts. Special thanks are due to Gillian Russell. The idea for the paper came from participating in her Philosophy of Logic graduate class at UNC in the spring semester of 2017. She also provided extremely helpful feedback, and much-needed encouragement, at multiple stages of the writing and rewriting process. Finally, thank you to two anonymous reviewers, whose generous comments improved the paper greatly.
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