Isomorphism invariance and overgeneration

Journal article

The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thought that logic is distinctively general or topic neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of 'logical constant' which respects the intuitively clear cases. Despite its attractions, the criterion has recently come under attack. Critics such as Feferman, MacFarlane and Bonnay argue that the criterion overgenerates by incorrectly judging mathematical notions as logical. We consider five possible precisifications of the overgeneration argument and find them all unconvincing.

Authors: Griffiths, O; Paseau, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Bulletin of Symbolic Logic
• Volume: 22
• Issue: 4
• Pages: 482-503
• Publication date: 2016-12-01
• Acceptance date: 2016-11-11
• DOI: 10.1017/bsl.2016.37
• EISSN: 1943-5894
• ISSN: 1079-8986
• Keywords: logical constants; logical consequence; overgeneration argument; isomorphism invariance; second-order logic; model theory