Though the introduction of visual devices in logic is old, such diagrams received relatively little attention from past logicians. Recent works, both in mathematics and philosophy, brought a new interest in visual logic. The aim of this tutorial is to familiarise the participants with the most widely used graphical methods in logic, and to understand their historical evolution and philosophical status. We will introduce essentially the spatial diagrams of Euler, Venn and Peirce. However, we will provide an initiation to some other methods, such as the linear methods (Lambert, Keynes) and the tabular methods (Marquand, Carroll). We will see not only how to conceive these diagrams, and what are their topological and semiotic features, but also how to use them to solve logical problems in the calculus of classes and propositions. More recent methods, essentially intended for the simplification of propositions and logic circuits, such as the Karnaugh map widely used in computer science, will also be explained. We will conclude with a general discussion of the status of these diagrams and the place they deserve in logic, compared to other linguistic representations.

References

Edwards, A. W. F., Cogwheels of the mind: The story of Venn diagrams, Baltimore , Maryland : Johns Hopkins University Press, 2004.

Euler, Léonhard, Lettres à une princesse d’Allemagne, Lausanne: Presses polytechniques et universitaires romandes, 2003 (Various other reprints and translations).

Gardner, Martin, Logic machines and diagrams, 2^nd edition, Brighton , Sussex : The Harvester press, 1983.

Karnaugh, Maurice, « The map method for synthesis of combinational logic circuits », Transactions of the American institute of electrical engineers, Part1, vol. 72, November 1953, pp. 593-599.

Shin, Sun-Joo, The logical status of diagrams, New York : Cambridge University Press, 1994.

Venn, John, « On the diagrammatic and mechanical representation of propositions and reasonings », The philosophical magazine, vol. 10, n° 59, July 1880, pp. 1-18.