Assertion, Conjunction, and Other Signs of Logic: A Contribution to the Philosophy of Notation

This paper is about Peirce’s understanding and notational realization of the relationship between the logical content of conjunction and the illocutionary force of assertion. The argument moves from an imaginary, subtextual dialogue between several authors in the history of logic and the philosophy of language (Aristotle, Ammonius, Boethius, Frege, Peirce, Geach, and Dummett) and shows that the problem of the relationship between conjunction and assertion is quite old and has received distinct and irreconcilable treatments. Peirce has an original take on the problem, which he addresses, as often happens in his mature writings, in notational terms: the anomaly of conjunction (i.e., the fact that, unlike the other connectives, conjunction is subject to assertion distribution) is not to be hidden behind a uniform notation, like standard sentential calculus, in which the conjunction connective is treated on a par with the other connectives. Rather, a sentential language is possible that embodies rather than conceals the anomaly, and this is Peirce’s system of Existential Graphs, which from 1896 onwards understandably becomes his preferred instrument of logical analysis.