Overgeneration in the higher infinite

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In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic : Essays on Consequence, Invariance, and Meaning. New York, NY: Cambridge University Press (2021)
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Abstract

The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to one which uses higher-order resources.

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Author Profiles

Salvatore Florio
University of Oslo
Luca Incurvati
University of Amsterdam

Citations of this work

Unrestricted Quantification and the Structure of Type Theory.Salvatore Florio & Nicholas K. Jones - 2021 - Philosophy and Phenomenological Research 102 (1):44-64.

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