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.
| Original language | English |
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| Title of host publication | The Semantic Conception of Logic |
| Editors | Gil Sagi, Jack Woods |
| Publisher | Cambridge University Press |
| Publication status | Accepted/In press - 6 May 2019 |