Forum Scientiarum

Metalogic and the Overgeneration Argument

Salvatore Florio (joint work with Luca Incurvati)

Dienstag 10. Mai, 18 Uhr c.t.

Forum Scientiarum, Doblerstr. 33, Seminarraum 1.3

The so-called overgeneration argument has figured prominently in the debate over the logicality of second-order logic. However, what the argument is supposed to establish is far from clear. 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 that makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic.