Denial Has Its Consequences: Peirce's Bilateral Semantics

In a few of his 1904–6 pragmaticist formulations of the pragmatic maxim, Peirce instructs us to look not only at the consequences of affirming some claim or concept, but also at the consequences of denying it. While Peirce isn't forthcoming about why he includes the consequences of denying claims, I argue that this inclusion is important, indeed prescient, and also under-appreciated. Specifically, after aligning these later formulations of the pragmatic maxim with bilateral tableau systems of logical proof, I show how they serve to defuse an objection that Brandom has raised against the semantic project of the classical pragmatists, namely, that it subscribes to an insufficiently one-sided view of meaning. I close by showing how Peirce's bilateral expressions of the pragmatic maxim also align with his existential graphs, suggesting that these expressions could well have been key to his attempt to provide a formal demonstration of pragmatism's correctness.