Looking back from this moment, I think I see things a little differently. The critical question is whether our theoretical description of inquiry gives us a picture that is true to life, preserving the life of inquiry and serving to guide us on its way, or whether it “murders to dissect”, leaving us with nothing but a Humpty Dumpty hodge-podge of false idols and torn and twisted bits of maps that mislead the quest at every turn.
There is a natural semantics that informs mathematical inquiry. It permeates the actual practice even of those who declare for some variety of nominal faith in their idle off‑hours. Peirce is unique in his ability to articulate the full dimensionality of mathematical meaning but echoes of his soundings keep this core sense reverberating, however muted, throughout pragmatism.
If I sift the traditions of theoretical reflection on mathematics according to how well their theoretical images manage to preserve this natural stance on mathematical meaning, I would tend to sort Frege more in a class with Boole, De Morgan, Peirce, and Schröder, since I have the sense when I read them they are all talking like mathematicians, not like people who are alien to mathematics.