Metalogic and the Overgeneration Argument

Mind:1-33 (2019)
Download Edit this record How to cite View on PhilPapers
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.
Keywords
No keywords specified (fix it)
PhilPapers/Archive ID
FLOMAT-4
Revision history
Archival date: 2019-01-17
View upload history
References found in this work BETA

View all 38 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index
2019-01-17

Total views
65 ( #26,386 of 38,007 )

Recent downloads (6 months)
65 ( #5,551 of 38,007 )

How can I increase my downloads?

Monthly downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.