Semiotic square

The semiotic square, also known as the Greimas square, is a tool used in structural analysis of the relationships between semiotic signs through the opposition of concepts, such as feminine-masculine or beautiful-ugly, and of extending the relevant ontology.

The semiotic square, derived from Aristotle's logical square of opposition, was developed by Algirdas J. Greimas, a Lithuanian-French linguist and semiotician, who considered the semiotic square to be the elementary structure of meaning.

Greimas first presented the square in Semantique Structurale (1966), a book which was later published as Structural Semantics: An Attempt at a Method (1983). He further developed the semiotic square with Francois Rastier in "The Interaction of Semiotic Constraints" (1968).

The Greimas square is a model based on relationships:

• S₁ = positive seme
• S₂ = negative seme
• S = complex axis (S₁ + S₂)
• ~S = neutral axis (neither S₁ nor S₂)

1. The semiotic square is formed by an initial binary relationship between two contrary signs. S₁ is considered to be the assertion/positive element and S₂ is the negation/negative element in the binary pair:
2. The second binary relationship is now created on the ~S axis. ~S₁ is considered to be the complex term, and ~S₂ is the neutral term. This is where the principle of difference is brought into play: every element in a system is defined by its differences from the other elements.
3. In most modes of interpretation, the S-axis is a hyponym of the ~S-axis. The ~S₁ element combines aspects of S₁ and S₂ and is also contradictory to S₁ . The ~S₂ element contains aspects of neither S₁ nor S₂ .
4. Finally, the ~S₂ element can be identified. Considered to be "always the most critical position and the one that remains open or empty the longest time, for its identification completes the process and in that sense constitutes the most creative act of the construction.".^[1]

Starting from a given opposition of concepts S1 and S2, the semiotic square entails first the existence of two other concepts, namely ~S1 and ~S2, which are in the following relationships:

• S1 and S2: opposition
• S1 and ~S1, S2 and ~S2: contradiction
• S1 and ~S2, S2 and ~S1: complementarity

The semiotic square also produces, second, so-called meta-concepts, which are compound ones, the most important of which are:

• both S1 and S2
• neither S1 nor S2

For example, from the pair of opposite concepts masculine-feminine, we get:

• S1: masculine
• S2: feminine
• ~S1: not-masculine
• ~S2: not-feminine
• both S1 and S2: masculine and feminine
• neither S1 nor S2: neither masculine nor feminine

The Greimas square is a tool used within the system of semiotics.

• As such, one form of interpretation is to look at each of the elements: S1, S2, ~S1, and ~S2 as either developed by Ferdinand de Saussure (bi-modal) or Charles Sanders Peirce (tripartite) sign.
• In the Peircean system of semiotics, the interpretant becomes the representamen for another, interrelated sign. In this same way, each of the elements of the semiotic square (S1, S2, ~S1, and ~S2) can become an element in a new, interrelated square.
• Finally, Greimas suggests placing semiotic squares of associated meaning on top of one another to create a layered effect and another form of analysis and interpretation.

The semiotic square has been used to analyze and interpret a variety of topics, including corporate language,^[2] the discourse of science studies as cultural studies,^[3] the fable of Little Red Riding Hood,^[4] narration,^[5] and print advertising.^[6]

• Bonfiglioli, Stefania. 2008. "Aristotle's Non-Logical Works and the Square of Oppositions in Semiotics," Logica Universalis. 2(1): 107-126.
• Chandler, Daniel. 2007. Semiotics: The Basics. London: Routledge.
• Luca Cian, "A comparative analysis of print advertising applying the two main plastic semiotics schools: Barthes' and Greimas'", Semiotica 190: 57–79, 2012.
• Greimas, A.J. and Francis Rastier. 1968. "The Interaction of Semiotic Constraints," Yale French Studies. 41: 86-105.
• Greimas, A.J. 1988. Maupassant: The Semiotics of Text. John Benjamins Publishing Co.
• Greimas, A.J., Paul Perron, Frank Collins. 1989. "On Meaning," New Literary History. 20(3): 539-550.
• Hébert, Louis (2006), "The Semiotic Square", in Louis Hébert (dir.), Signo (online), Rimouski (Quebec)
• Lenoir, Timothy. 1994. "Was That Last Turn a Right Turn? The Semiotic Turn and A.J. Greimas," Configurations. 2: 119-136.
• Levi-Strauss, Claude. 1955. "The Structural Study of Myth," The Journal of American Folklore. 68(270): 428-444.
• Perron, Paul and Frank Collins. 1989. Paris School Semiotics I. John Benjamins Publishing Co.
• Robinson, Kim Stanley. 1994. Red Mars. New York: Bantam Books.
• Schleifer, Ronald. 1987. A.J. Greimas and the nature of meaning: linguistics, semiotics and discourse theory. Kent: Croom Helm Ltd.
• Schleifer, Ronald. 1997. "Disciplinarity and Collaboration in the Sciences and Humanities," College English. 59(4): 438-452.
• Schleiner, Louise. 1995. Cultural semiotics, Spenser, and the captive woman. Cranbury: Associated University Press, Inc.
• Sebeok, Thomas A. and Jean Umiker-Sebeok (Eds). 1987. The Semiotic Web 1986. Berlin: Walter de Gruyter & Co.

• Modules on Greimas: On the semiotic square
• Timothy Lenoir, Was That Last Turn A Right Turn? The Semiotic Turn and A.J. Greimas, Configurations, Vol.2 (1994): 119-136