In the end of 1890s, C.S. Peirce introduced the system of diagrammatic logic, which he called “Existential Graphs.” Peirce conceived the Graphs as pictorial expressions of relations inherent in thought and believed that by means of a predefined array of graphic conventions and transformational rules, the Graphs are capable of visually demonstrating the immediate logical continuity of thinking. Two decades earlier, in May 1879, Peirce published a short paper in the American Journal of Mathematics describing his new “quincuncial” map. The map was a variation of conformal stereographic projection and one of the first diagrams created with the application of complex analysis.
These two examples, together with some other Peirce’s writings and diary notes, show that Peirce deeply believed in the logical and mathematical advantage of diagrammatic representation over ordinary writing and considered visual experience as the core of linguistic competence. Moreover, according to Peirce, the role of visual experience and diagrammatic thinking in mathematics and logic was closely related to left-handedness, difficulty with written language, and unconventional behaviour.
By presenting Peirce’s quincuncial projection and the Graphs as two illustrations of Peirce’s theory of signs, this paper aims to provide an example of the intersection of scientific practice and philosophical speculation by showing some correlations between Peirce’s personal intellectual habits as a logician and mathematician, his semiotic theory, and his ideas about the nature of visual experience.