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

Authors
Luca Incurvati
University of Amsterdam
Salvatore Florio
University of Birmingham
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.
Keywords Overgeneration Argument  second-order logic  large cardinals  higher-order semantics
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