Mind 128 (511):761-793 (2019)

Authors
Luca Incurvati
University of Amsterdam
Salvatore Florio
University of Birmingham
Abstract
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.
Keywords Second-Order Logic  Overgeneration Argument  Continuum Hypothesis  Higher-Order Semantics  Logicality
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DOI 10.1093/mind/fzy059
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References found in this work BETA

Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford University Press.
Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
Plural Predication.Thomas McKay - 2006 - Oxford University Press.
Plural Logic.Alex Oliver & Timothy Smiley - 2013 - Oxford University Press UK.

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