The Peirce line — triad, relay, and the three credentials

1 · The triad is a relay, not a triangle

Sign (representamen) — object — interpretant. The load-bearing definition: the interpretant is NOT the mental event of understanding; it is the next sign that the sign produces in the interpreter. Meaning is not cargo stored inside a sign; it is what the sign triggers. Since every interpretant is itself a sign, interpretation chains — unlimited semiosis:

The brake Peirce built into the "unlimited": the chain's terminus — the final interpretant — is not a thought but a habit: a settled disposition to act. This is where his semiotics welds onto his pragmatism: meaning's ultimate cash value is habit change. Translation to the marketing register: brand equity is a final interpretant installed in a population — an automatic disposition (see logo, trust, buy) that no longer runs any inference. Marketing's whole job restated: lay interpretant chains until they collapse into habit.

2 · Icon / index / symbol — three credentials for representing

By what right does a sign stand for its object?

• Icon: by RESEMBLANCE — portrait, map, trash-can UI glyph. Subtypes: image (looks like), diagram (structure-alike: a metro map shares no appearance with the city, only connectivity; mathematical formulas are diagrams — Peirce held that math reasoning is observation and experiment performed on iconic signs), metaphor (parallel-alike).
• Index: by REAL CONNECTION — smoke, footprint, weathervane, a knock, a pointing finger. Needs no convention, but needs the object to have actually been there. The only one of the three that has touched the world.
• Symbol: by PURE CONVENTION — words, flags, logos. Maximal freedom, maximal lying capacity (the whole of the-lying-criterion mostly lives here), and the only credential that can express generality ("all dogs" is available to no icon and no index).

3 · The practical rule: dimensions, not boxes

Nearly every real sign is a blend; analysis = decomposing the mixture:

• photograph = icon + index (photons really flew from object to film — the entire evidential force of photography is its index component);
• traffic light = symbol (red means stop by code) + index (THIS lamp, THIS crossing, now);
• logo = born pure symbol, absorbs index-ness over years (its presence becomes a trace of the genuine article) — anti-counterfeiting is the defense of a logo's index component;
• deictics ("I", "this", "now") — indexical nails hammered through the middle of a conventional system.

Two working consequences: the persuasive force of a real screen recording is its index component (a trace the world left); the disaster of an AI-generated still with melted letterforms is a symbol wearing an index's face — an audience catches precisely the forged credential. The era-scale version: photography is losing its indexicality while the public's reading habit still assumes "photo = trace"; that mismatch is deepfake's entire leverage.

4 · Shelved for depth later

The full grid: three trichotomies (sign-in-itself / sign-to-object / sign-to-interpretant) crossing into ten sign classes — icon/index/symbol is the middle trichotomy; the everyday analytical workhorse. Open hooks: final-interpretant-as-habit vs predictive processing (habit = a prior hardened past needing correction); the diagram subtype and mathematical reasoning.

Kin: abduction (same author, same engine: the interpretant is abduced) · the-lying-criterion · cut-discipline (the viewer's between-shots inference is interpretant production).