A paper published in Mind by Birmingham Senior Lecturer Dr Salvatore Florio (co-written with Luca Incurvati) has been selected for Oxford University Press’s prestigious Best of Philosophy 2019 article collection - a roundup of some of the most popular articles published in OUP's Philosophy journals in 2019.
A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely, the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic.
Mind, Volume 128, Issue 511, July 2019, Pages 761–793, https://doi.org/10.1093/mind/fzy059
Published: 16 January 2019
Salvatore Florio is a Senior Lecturer in Philosophy at the University of Birmingham and an editor of The Review of Symbolic Logic. He specializes in philosophy of language, philosophical and mathematical logic, and philosophy of mathematics. His monograph The Many and The One: A Philosophical Study (co-written with Øystein Linnebo) is forthcoming with OUP.