Operational Iconicity As a Necessary Condition for Diagrammatic Reasoning
Charles S. Peirce formulated his ultimate conception of logic in the context of his theory of signs and his pragmaticist philosophy. For him, deduction was a process accomplished by means of diagrams, and diagrammatic reasoning was the accurate method for representing the “course of thinking”, and in fact he conceived eventually, from 1896 on, his diagrammatic system of the Existential Graphs. Peirce’s approach to logic followed directly from his conception of mathematics: mathematical thought was for him essentially diagrammatic. Algebraic equations were as diagrammatic as geometric figures.
Now, diagrams are icons. The notion of iconicity is not always a neat one. Peirce provided different characterization in his writings, originating a discussion among scholars. The idea of analogy and similarity (or resemblance) seems to play an important role. For example, in 1885 Peirce considered an icon as a “sign which stands for something because it resembles it (CP 5.163; CP 3.362)”, and around 1890 he wrote: “The first [kind of sign] is the diagrammatic sign or icon, which exhibits a similarity or analogy to the subject of discourse” (CP 1.369; CW 5.243).
However, it is important to stress that the “similarity” shared between a sign and an object is not enough for having a semiotic relation, because semiotic relations are asymmetric, whereas similarity is symmetric. Peirce introduces the asymmetry through the pragmatic notion of ‘use as a sign’. Hence, an icon a must signify through its similarity to its object (and not because of it).
The aim of this paper consists in showing that Frederik Stjernfelt’s idea of an operational iconicity provides a useful semiotic basis in order to understand the diagrammatic nature of deduction. According to this idea, “similarity as well as its utilization in sign reference are necessary prerequisites for the Icon, but only taken together do they become sufficient prerequisites.” (Stjernfelt 2007, p. 49)
Furthermore, it will be shown that this idea of operational iconicity paves the way for the analytic role played by the icons: An icon provides knowledge through its decomposition in basic elements. There is evidence that Peirce conceived his Existential Graphs not only as a diagrammatic proof procedure for deductive logic, but also (and mainly) as a tool for logical analysis. Finally, further comments on Peirce’s notion of analysis will be brought into the discussion.
References
Peirce, Charles Sanders (CP). Collected Papers. 8 volúmenes, vols. 1- 6 ed. by Charles Hartshorne & Paul Weiss, vols. 7-8 ed. by Arthur W. Burks. Cambridge (Mass.), Harvard University Press, 1931-1958.
Stjernfelt, Frederik (2007). Diagrammatology: An Investigation on the Borderlines of Phenomenology, Ontology, and Semiotics. Dordrecht: Springer.
Country:
Argentina
Theme And Axes:
Foundation and logical fundaments of semiotics
Semiotics and philosophy
Institution:
CONICET-UNIVERSIDAD DE BUENOS AIRES. INSTITUTO INTERDISCIPLINARIO DE ECONOMIA POLITICA DE BUENOS AIRES (IIEP-BAIRES)
Mail:
javier.legris@gmail.com
Estado del abstract
Estado del abstract:
Accepted