Notes on Peirce:
Peirce’s definition of a sign is usefully broad because it extends beyond words: “something which stands to somebody for something on some respect or capacity. It addresses somebody, that is, creates in the mind of that person an equivalent sign, or perhaps a more developed sign.” [note 1] More simply, a sign is something that evokes something for someone. A sign points to an object and, at the same time, it brings to the interpreter’s mind another sign (called the “interpretant”) that translates and mediates the original sign. This is the structure of semiosis, or the making of meaning, of which sign, object, and interpretant are three necessary parts. Without one of the parts, semiosis does not take place—the triad is not reducible to pairs of dyads.
This triadic structure recurs throughout Peirce’s analysis. He loves typologies, especially those that describe levels of mediation. The typology he returns to most is that of firstness, secondness, and thirdness, which describe degrees of mediation and reflexivity. Firstness is a condition of unmediated, unreflexive access. Firsts are experience without reaction, cause without effect. Secondness is a condition of mediated but not yet reflexive access. Seconds are experience and the reaction it evokes, cause and the effect it provokes, but not yet a reflection on the reaction or effect. Thirdness is a condition of mediated, reflexive access. Thirds are experience, reaction, and the reflection upon that reaction. They are cause, effect, and the extension of that effect to the form of habit or convention or law.
Peirce’s triads follow this structure, and they are nested. Consider the structure of semiosis: the sign is a first, the object it evokes is a second, and the interpretant is a third. Where signs are concerned, they are characterized by their presentative condition (the ground, or the quality that makes them a sign), a condition of firstness; by their representative condition (the relation in which they stand to their object), a condition of secondness; and finally by their interpretative power (their ability to direct attention to an object in such a way as to evoke an interpretant), a condition of thirdness.
Each of these conditions is also follows a triadic structure. Peirce identifies three types of signs as a function of their presentative condition: qualisigns, or qualities that act as signs (the color red), sinsigns, or actual instantiations of signs (a light that turns red), and legisigns, or signs that have a meaning deriving from convention, habit, or law (a red traffic light that signals to drivers to stop). [note 2] Qualisigns are firsts, sinsigns are seconds, and legisigns are thirds.
He also identifies three types of signs as a function of their representative condition: icons, or signs that resemble their object (an image of fire), indices, or signs that are contiguous with, are caused by, or somehow point to their objects (smoke coming from a fire), and symbols, or signs whose meanings are a function of convention, habit, or law (fire as knowledge in the story of Prometheus). Here again, icons are firsts, indices are seconds, and symbols are thirds.
The same is true of signs as a function of their interpretive condition: rhemes identify a sign but do not reveal whether it exists or can be judged true or false (“a dog”); dicents are propositions that can be judged true or false (“a dog is an animal”); and arguments are signs whose interpretation relates to convention, habit, or law (“a dog is a man’s best friend”). Rhemes are firsts, dicents are seconds, and arguments are thirds.
One implication of these typologies is that we can identify ten types of signs ranging from the barely elaborated (rhematic iconic qualisigns such as “a nebulous patch of color, seeing a blotch of red in an afterimage, hearing the wind blow through an old house, the musty smell while walking in a forest, the aftertaste from a deliciously exotic meal” [note 3]) to the complex (argumentative symbolic legisigns, where the “paradigm case is that of an inference of an argument, which shows the connection between one set of propositions [the premises] and another [the conclusion]” [note 4]).
Why only ten types, rather than twenty-seven, as three sets of triads would suggest? Peirce argues the interpretive condition of a sign cannot be of a higher order than its representative condition, which in turn cannot be of a higher order than its presentative condition. That is, a qualisign (a first) cannot be a dicent (a second) or an argument (a third), nor can it be an index (a second) or a symbol (a third). As a result, the only type of qualisign conceivable is a rhematic iconic qualisign, but many types of legisigns are conceivable. [note 5]
 Charles Peirce, The Philosphy of Peirce: Selected Writings, ed. Justus Buchler. London: Routledge and Kegan, 1940, p. 99.
 Examples adapted from James Jakób Liszka, A General Introduction to the Semeiotic of Charles Sanders Peirce. Bloomington: Indiana University Press, 1994, p. 35–36.
 Liszka, p. 48.
 Liszka, p. 52.
 Although these signs are conceivable, they are not in fact possible. By definition, any instantiation of a sign is a sinsign. Therefore, qualisigns and legisigns cannot be instantiated as such.