Abstract

R L 210, Houghton Library. In this pivotal 1904 letter, Peirce critiques Huntington’s axiomatic approach to logic, rejecting the definitions of negation by consequence or by aggregation and composition alone. Defending his existential graphs, Peirce insists that logic must engage actual fact (assertions) and coexistence (colocation of assertions) rather than evaporate into pure form. He revisits his proof of the distributive principle (omitted from his 1880 American Journal of Mathematics paper due to grippe-clouded judgment; cf. LoF 3/1, p. 423), framing it as a corrective to Schröder’s skepticism. The letter underscores Peirce’s view that logic’s matter lies in its capacity to analyse real relations—a rebuke to the pure mathematical abstraction Huntington champions. Amid apologies for delayed vindication, Peirce’s tone reveals his lifelong struggle to anchor logic in lived reality: “But how it is possible to eviscerate logic of its meaning and leave it pure mathematical form, I don’t see. It appears to me that those very forms are the matter that logic studies”.