Logician, mathematician, philosopher, and scientist Charles Sanders Peirce (1839–1914) began writing on semeiotic, semiotics, or the theory of sign relations in the 1860s, around the time that he devised his system of three categories. He eventually defined semiosis as an "action, or influence, which is, or involves, a cooperation of three subjects, such as a sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs" (Houser 1998, 411). This specific type of triadic relation is fundamental to Peirce's understanding of "logic as formal semiotic". By "logic" he meant philosophical logic. He eventually divided (philosophical) logic, or formal semiotic, into (1) speculative grammar, or stechiology, on the elements of semiosis (sign, object, interpretant), how signs can signify and, in relation to that, what kinds of signs, objects, and interpretants there are, how signs combine, and how some signs embody or incorporate others; (2) logical critic, or logic proper, on the modes of inference; and (3) speculative rhetoric, or methodeutic, the philosophical theory of inquiry, including his form of pragmatism. His speculative grammar, or stechiology, is this article's subject.

In semiotics, a sign is something that can be interpreted as having a meaning, which is something other than itself, and which is therefore able to communicate information to the one interpreting or decoding the sign. Signs can work through any of the senses, visual, auditory, tactile, olfactory or taste, and their meaning can be intentional such as a word uttered with a specific meaning, or unintentional such as a symptom being a sign of a particular medical condition.

There are two major theories about the way in which signs acquire the ability to transfer information; both theories understand the defining property of the sign as being a relation between a number of elements. In the tradition of semiotics developed by Ferdinand de Saussure the sign relation is dyadic, consisting only of a form of the sign (the signifier) and its meaning (the signified). Saussure saw this relation as being essentially arbitrary motivated only by social convention. Saussure's theory has been particularly influential in the study of linguistic signs. The other major semiotic theory developed by C. S. Peirce defines the sign as a triadic relation as "something that stands for something, to someone in some capacity"[1] This means that a sign is a relation between the sign vehicle (the specific physical form of the sign), a sign object (the aspect of the world that the sign carries meaning about) and an interpretant (the meaning of the sign as understood by an interpreter). According to Peirce signs can be divided by the type of relation that holds the sign relation together as either icons, indices or symbols. Icons are those signs that signify by means of similarity between sign vehicle and sign object (e.g. a portrait, or a map), indices are those that signify by means of a direct relation of contiguity or causality between sign vehicle and sign object (e.g. a symptom), and symbols are those that signify through a law or arbitrary social convention.

Charles Sanders Peirce (/ˈpɜrs/,[9] like "purse", September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician, and scientist, sometimes known as "the father of pragmatism". He was educated as a chemist and employed as a scientist for 30 years. Today he is appreciated largely for his contributions to logic, mathematics, philosophy, scientific methodology, and semiotics, and for his founding of pragmatism.

Algirdas Julien Greimas (1917-1992) (born Algirdas Julius Greimas), known among other things for the Greimas Square (le carré sémiotique), is considered, along with Roland Barthes, the most prominent of the French semioticians. With his training in structural linguistics, he added to the theory of signification and laid the foundations for the Paris School of Semiotics. Among Greimas's major contributions to semiotics are the concepts of isotopy, the actantial model, the narrative program, and the semiotics of the natural world. He also researched Lithuanian mythology and Proto-Indo-European religion, and was influential in semiotic literary criticism.

The semiotic square, also known as the Greimas square, is a tool used in the structural analysis of the relationships between semiotic signs. The semiotic square was developed by Algirdas J. Greimas, a Lithuanian linguist and semiotician, and first presented in Semantique Structurale (1966). The book was later published as Structural Semantics: An Attempt at a Method (1983). Greimas further developed the semiotic square with Francois Rastier in "The Interaction of Semiotic Constraints" (1968). Greimas considered the semiotic square to be the elementary structure of meaning.

Peirce's Sign Theory, or Semiotic, is an account of signification, representation, reference and meaning. Although sign theories have a long history, Peirce's accounts are distinctive and innovative for their breadth and complexity, and for capturing the importance of interpretation to signification. For Peirce, developing a thoroughgoing theory of signs was a central philosophical and intellectual preoccupation. The importance of semiotic for Peirce is wide ranging. As he himself said, “[…] it has never been in my power to study anything,—mathematics, ethics, metaphysics, gravitation, thermodynamics, optics, chemistry, comparative anatomy, astronomy, psychology, phonetics, economics, the history of science, whist, men and women, wine, metrology, except as a study of semiotic” (SS 1977, 85–6). Peirce also treated sign theory as central to his work on logic, as the medium for inquiry and the process of scientific discovery, and even as one possible means for 'proving' his pragmatism. Its importance in Peirce's philosophy, then, cannot be overestimated.

If Peirce saw a trichotomy in anything he thought about, Greimas saw a
semiotic square. Thus I was faced with a choice. Was I to remain a
trichomaniac like Peirce or become a Cartesian quadramaniac? I ended up being both, as I will explain later.