Comments and criticism: The modal and epistemic arguments against the invariance criterion for logical terms

There is a criticism of the isomorphism-invariance criterion for logical terms that is expressed in several variations in the literature on logical terms. The criticism in most cases was aimed against the criterion of invariance under isomorphism,1 but it can be seen as applying to criteria of invariance under other transformations2 just as well. The gist of the objection is that invariance criteria pertain only to the extension of logical terms, and neglect the meaning, or the way the extension is fixed. A term, so claim the critics, can be invariant under isomorphisms and yet involve a contingent or a posteriori component in its meaning, thus compromising the necessity or apriority of logical truth and logical consequence.