In a recent paper of this journal, del Valle-Inclán (Journal of Philosophical Logic, 53(5), 1321–1346, 2024) criticized the proposed solution of Bonnay and Westerståhl (Erkenntnis, 81(4), 721–739, 2016) to Carnap’s (categoricity) problem. They there claim that Bonnay and Westerståhl avail themselves of second-order notions in order to resolve the underdetermination discovered by Carnap (Formalization of Logic, 1943) at the first-order level, and that the proposed solution therefore does not really address the first-order case appropriately. The purpose of this brief note is to point out the highly local conception of (logical) quantification underlying del Valle-Inclán’s argument against Bonnay and Westerståhl, which severely limits the force of the counterexamples proposed and undermines the criticism. del Valle-Inclán’s paper has two main critical parts, one addressing the sufficiency of the constraint of permutation-invariance on quantifiers and the other the nature of the constraint of compositionality as used by Bonnay and Westerståhl. I here only address the former aspect of their paper, though the points made have consequences for their subsequent argument as well.
