Will the Real Higher-Order Logic Please Stand Up?

November 4, 2026 COMING SOON

Abstract: In this work-in-progress talk, I will attempt to clarify some of the issues surrounding second- and higher-order logics. How should we understand the relationship between the proof-theoretic inferentialist presentations of such logics and their model-theoretic truth conditional semantics? I will argue that in an important sense, the so-called full semantics for second- and higher-order logics is too strong, and that a wider class of models is not only necessary, but is mathematically and philosophically desirable. The good news: such a class of models already exists and is well understood. (And no, it’s just not the Henkin semantics.)

The slides for the talk can be downloaded here .
The talk is a presentation in the Arché Metaphysics and Logic Seminar, at the University of St Andrews.

about

I’m Greg Restall, and this is my personal website. ¶ I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology ¶ I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.

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contact

Social media: @consequently@scholar.social.
Personal email: greg@consequently.org.
St Andrews profile.
My office is in Edgecliffe, The Scores.