Exploratory diagramming and diagram theory: Greimas, Peirce and Châtelet

ABSTRACT

Exploratory diagrams can be distinguished from statistical and explanatory diagrams in that they do not merely communicate what already exists, but provide a method of discovery, experiment and creative invention. As such, they are recommended as productive modes which can be utilized for art, education and philosophy. This paper seeks to draw out a number of key concepts and approaches to exploratory diagramming by examining three powerful diagram theories. First, A.J. Greimas’ invention of the ‘semiotic square’; second, C.S. Peirce’s semiotic account of the diagram as icon; and third, Gilles Châtelet’s retelling of scientific and mathematical discovery through diagrammatic devices. Respectively, these theories can each be identified according to a primary operative principle: opposition, relation and gesture.

KEYWORDS:

• Diagrams
• semiotic square
• Greimas
• Peirce
• existential graph
• Châtelet

Acknowledgements

I would like to thank David Burrows, John Cussans and Mary Yacoob co-members of the Diagram Research Group for conversations throughout the period of research for this paper. I’d also like to thank the editor Claire Scanlon for giving me the opportunity to finally examine a number of diagram theories in some depth.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 The point here is to indicate a direction of travel rather than lay down strict borders. Many statistical and explanatory diagrams are exploratory in various ways (traces of discovery and invention remain) whilst more strongly exploratory diagrams do not necessarily dispense with information or explanation.

2 For a reading of my Metallurgy of the Subject diagrams, see Weeks (2019).

3 Greimas and Rastier's semiotic square appears to be based on Aristotle's logical ‘square of opposition’ system of ‘contraries’ and ‘contradictories’ as presented in ‘On Interpretation’ (2001, 49–52), although this is not cited. Aristotle's rectangular plotting of the four qualities (hot, cold, moist and dry) as a set of two contraries standing opposite each other, ‘gives rise to’ the four elements (Fire, Air, Water and Earth) as points located in between: ‘For Fire is hot and dry, whereas Air is hot and moist’ etc. (Aristotle 2001, 511). Notwithstanding its utilization as a fixed model of the elements, it is the creative capacity of Aristotle's logic machine which the semiotic square develops and which seems to mark the former as ‘exploratory’ compared with Plato's (1974) ‘explanatory’ descriptions of tabulated hierarchies (e.g. Forms – physical things – images and shadows).

4 See for example Clifford James’ (1988) wonderful ‘Art-Culture System’ diagram, subtitled ‘A Machine for Making Authenticity’. See also the ‘posthuman’ squares of N. Katherine Hayles (1999).

5 As Peirce is a realist, ‘real things’ extend much beyond empirical objects.

6 If one would devote several hours a day for a week or two to practicing with the graphs, Peirce wrote, he would soon be able to solve problems with a facility ‘about equal’ to that of any algebraic method yet devised, including one such system of his own (Gardner 1958, 56).

7 Peirce was himself a trained chemist and experimental physicist and his logic graphs were inspired by chemistry diagrams showing, in a notation of spots and lines, how elements combined to form compounds (see Roberts 1973, 17).

8 Peirce termed such second-order indices ‘degenerate’ (1998, 274).

9 The many diagrams in Châtelet's book are drawn in a generic style, which has the function of equalizing the diagrams whether they exist in the world as actual sketches or geometrical drawings, or as technical devices, thought experiments, written description, etc. This equalization also guards against the intrusion of biography (historical documents) and thus maintains the intense immanence of the diagrammatic unfolding.

10 This gives us a nice example of Peirce's icon-index-symbol triad in combinatory action.

11 See however Williams (2007) for an account of how Maxwell misinterpreted Faraday's conception of ‘force’, aligning it with Newtonian action at a distance. Williams reproduces Maxwell's diagram, although unfortunately at low resolution.

12 ‘Organized material is knowledge and knowledge is organized material’. Denis Diderot, Encyclopedia (1751) quoted in Welcome Collection (2016, 8).

Additional information

Notes on contributors

Dean Kenning

Dean Kenning is an artist, writer and educator. His artworks range from kinetic sculptures to videos and diagrams, and employ DIY, allegorical and autodidactic methods and modes of representation to generate visceral, uncanny and humorous encounters and to explore political and philosophical material. Solo exhibitions include Where IT Was (Piper Keys, 2018), The Origin of Life (Beaconsfield, 2019) and Psychobotanical (Matt’s Gallery, 2019). He has often worked collaboratively, recently as part of the Capital Drawing Group (Bergen Assembly, 2019) and the Diagram Research Group (Flat Time House, 2020). He has written for journals such as Third Text, Mute and Art Monthly, including on the politics of art and art education. Kenning is Research Fellow at Kingston School of Art and an Associate Lecturer in Fine Art at Central St Martins. He is the winner of the Mark Tanner Sculpture Award 2020–21.