Volume 115, Issue 7, July 2018
A BULLET for Invariance: Another Argument against the Invariance Criterion for Logical Terms
According to the classical invariance criterion, a term is logical if and only if its extension is isomorphism-invariant. However, a number of authors have devised examples that challenge the sufficiency of this condition: accepting these examples as logical constants would introduce objectionable contingent elements into logic. Recently, Gil Sagi has responded that these objections are based on a fallacious inference from the modal status of a sentence to the modal status of the proposition expressed by that sentence. The present paper demonstrates that Sagi’s response, though successful, is futile. There is another objection, based on the same type of example, that is not susceptible to Sagi’s criticism: accepting the examples as logical terms would have the fatal consequence that any contingent metalanguage sentence is entailed by the truth of some logically true object-language sentence. I conclude with a sketch of an alternative to the classical invariance criterion.