Peirce's semeiotic is not a branch of his philosophy but its circulatory system. Every other element of his architecture depends on it. Inference is a sign-process. Thought is a sign-process. The community of inquiry communicates through signs, fixes beliefs through signs, corrects errors through signs. The fundamental unit of the theory is the triadic sign-relation: the irreducible relationship among a sign (the vehicle of representation), an object (what the sign represents), and an interpretant (the cognitive effect produced by the encounter). The triad is irreducible — it cannot be decomposed into pairs without losing the essential character of signification. A sign without an interpretant is not a sign; an interpretant without a sign has no representational content. Meaning exists only in the full triadic relation.
The triadic structure distinguishes Peirce's semiotic from the dyadic semiology of Saussure that dominated twentieth-century continental theory. Saussure analyzed signs as pairs: signifier and signified. Peirce insisted on the third term — the interpretant, the cognitive effect — because without it, signs are merely marks, and representation has no content.
The theory classifies signs along multiple axes. The most important for the AI question is the classification by relation to object: icons, indices, and symbols. Icons represent through resemblance, indices through existential connection, symbols through convention. The classification identifies fundamentally different modes of representation, each with distinct cognitive implications.
The human-AI dialogue is a sign-process. Prompts are signs. Responses are signs. Each exchange produces interpretants that feed into subsequent exchanges, in a chain of unlimited semiosis. But the semiotic capacities of the participants are fundamentally asymmetric. The human produces interpretants in the full Peircean sense — cognitive events that integrate the sign with prior understanding, emotional engagement, and trained judgment. The machine's processing does not produce interpretants in this sense; it relates inputs to statistical patterns in training data.
The asymmetry has consequences. The machine's signs are systematically impoverished — pure symbolicity without iconic resemblance or indexical grounding. The human must supply the iconic intuitions (structural understanding built through experience) and indexical connections (direct experiential links to reality) that would anchor the machine's symbols to the world they purport to represent. Without this supplementation, the symbolic output floats free of reality, however polished its surface.
Peirce developed the semeiotic across his entire career, from early work in the 1860s through extensive correspondence with Lady Victoria Welby in his final years.
The theory is foundational to modern semiotics and has been applied across linguistics, anthropology, communication theory, cognitive science, and — increasingly — the analysis of AI systems.
Triadic structure. Sign, object, interpretant — irreducible to any dyadic relation.
Meaning is process. Not a static relation but a cascade of interpretants in unlimited semiosis.
Three classifications by object-relation. Icons (resemblance), indices (connection), symbols (convention).
Diagnostic for AI. LLMs are pure symbolicity; the absence of iconic and indexical grounding is structural, not incidental.