Generality and Existence I: Quantification and Free Logic

March 2019

“Generality and Existence I: Quantification and Free Logic,” Review of Symbolic Logic, 12 (2019) 1–29.


In this paper, I motivate a cut free sequent calculus for classical logic with first order quantification, allowing for singular terms free of existential import. Along the way, I motivate a criterion for rules designed to answer Prior’s question about what distinguishes rules for logical concepts, like ‘conjunction’ from apparently similar rules for putative concepts like ‘tonk’, and I show that the rules for the quantifiers—and the existence predicate—satisfy that condition.

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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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