Logic of Relatives and Semiotics in Peirce. From the “Subject-Predicate” Inferential Structure to the Synechistic Topology of Interpretation

Charles Sanders Peirce is known to be the inventor of many concepts and theoretical objects that have shaken the foundations of the disciplines in which they were developed: the theory of existential graphs and the triadic system in logic; the set theory founded on a Leibnizian conception of infinitesimals in mathematics; the synechistic theory of continuum in metaphysics, etc. Peirce is also well known to have invented ex-novo whole disciplines, semiotics for example. Peirce is also renowned for having formulated very original theories of interpretation, action, perception, and so on. What is known less – and what I would like to show here – is that Peirce had also something to do with that epistemological movement that in the 20th century would be called “structuralism”, grounded in the study of language. In this paper I would like to show: (i) that Peirce used to call “Logic of Relatives” this “structuralist” analysis of language; (ii) that this Logic of Relatives is exactly what – approximately 80 years later – would be called “actantial syntax” by two renowned French structuralists, Lucien Tesnière and A.J. Greimas; (iii) how this structuralist foundation of language and propositions radically changed Peirce’s conception of semiotics, previously founded on the theory of inference of his anti-Cartesian essays and on the “subject-predicate” structure of the proposition found in “On a New List of Categories”; (iv) how this Logic of Relatives represents the condition of possibility of Peircean synechism and of his new phenomenological theory of categories.