- These are iconic representations dealing with logical symbolic relations, and so of course are semiotic in Peirce’s sense, since logic is semiotic. But couldn’t a logician do all of this meticulous formalization and understand all of the discrete logical consequences of it without having any inkling of semiotics or of Peirce?
As I noted at the top of the article and blog series —
This article treats relations from the perspective of combinatorics, in other words, as a subject matter in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many of which arise quite naturally in applications. This approach to relation theory, or the theory of relations, is distinguished from, though closely related to, its study from the perspectives of abstract algebra on the one hand and formal logic on the other.
Of course one can always pull a logical formalism out of thin air, with no inkling of its historical sources, and proceed in a blithely syntactic and deductive fashion. But if we hew more closely to applications, original or potential, and even regard logic and math as springing from practice, we must take care for the semantic and pragmatic grounds of their use. From that perspective, models come first, well before the deductive theories whose consistency they establish.