Metalogic and the Overgeneration Argument

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

External organisations

  • UNIVERSITY OF AMSTERDAM

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.

Details

Original languageEnglish
JournalMind
Early online date16 Jan 2019
Publication statusE-pub ahead of print - 16 Jan 2019