From Semiotic Categories to Categorical Semiotics

Semiotic Categories and Speculative Grammar

There is one diagram that runs throughout Peirce’s philosophy, but is explicitly drawn in … Peirce places this diagram as the foundation of his later philosophy and uses it as his basic system of classification. It is

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In a remarkable coincidence, this diagram was not only rediscovered by … and … in 19??, but was given the name ‘category theory’. The authors attributed the idea to multiple philosophers, but never mentioned Peirce, who had built his entire philosophical system on its development. This … attempts to remedy this unfortunate twist of fate.

Now one of the reasons that Mac Lane and Eilenberg did not mention Peirce in their litany of prior category theorists was that Peirce never developed a systematic explanation of the diagram, including what to call it. His 1867 paper “On a New List of Categories” contains the diagram in germ form, but this paper was never explicitly rewritten or updated, and there continues to be confusion For our purposes, we shall use the term “semiotic categories,” borrowed from …

Peirce never used the term “semiotic categories,” and probably would not have agreed with its application. In his 1903 Harvard Lectures, Peirce placed his categories in the branch of philosophy that the identified as “phenomenology” or “phaneroscopy”, which in turn were founded upon mathematics. So the reader may suspect us of revisionist history. Apel’s philosophical system is based upon placing semiotics itself, considered as the necessary presuppositions of argument, as the “grounding” of his system, rather than on mathematics and phenomenology. We find these arguments convincing. However, Peirce did carve out a place within his system for the semiotic categories as part of “speculative grammar.” This reference to what Peirce understood as the part of the philosophy of John Duns Scotus has a fascinating history itself, but development of this will have to wait as we would be getting well ahead of ourselves. We will content ourselves to placing the semiotic categories as part of speculative grammar, the latter as Peirce understood it, as a consideration of the “firstness” of the phenomenological categories within the “thirdness” of the normative sciences, with logic being the “thirdness” of the normative sciences (i.e. semiotic). But again, this is getting ahead of our development, which intends to make these dizzying Peircean stacks comprehensible with the help of mathematical category theory.

What does Peirce say about speculative grammar.

\begin{quote} This science is not aimed at studying the meaning, but is intended to analyze the conditions that must be satisfied so that the process of signification could be produced.\cite{Isnenghi08} \end{quote}

Now for Peirce, a philosopher should not seek novelty in fundamental concepts.

In his sketch for the uncompleted project “Guess at the Riddle”,

Diagram can be found in Aristotle. Category Theory and the Speculative Grammar of Mathematics The family resemblance between the semiotic categories and category theory is interesting, but can deeper connections be made between them?