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Introduction: Diagrammatical reasoning and Peircean logic representations

Along with Gottlob Frege, Bertrand Russell, and David Hilbert, Charles S. Peirce is considered one of the founders of modern logic (Lukasiewicz 1970 [1961]: 111; Barwise and Etchemendy 1996: 211; Quine 1995: 23; Hintikka and Hilpinen 1997: ix). Independently of Frege, he developed the concepts of quantification and quantifying logic (Hintikka and Hilpinen 1997: ix; Quine 1995: 31; Putnam 1982: 297). He was author of the term and concept of “FirstOrder Logic” (Putnam 1988: 28), and “Trivalent Logic” (Fisch and Turquette 1966; Lane 2001), besides his anticipating Henry Sheffer’s “Stroke Function” by more than thirty years (W 4: 218–221; Houser 1997: 3), and he was working with the computational correspondence between truth functions and electrical circuitry that was later independently developed by Claude Shannon (W 5: 421– 422; Gardner 1982). He insisted on the relevance of logic in both metaphysics and epistemology and, thus, is a founding father of what Jaakko Hintikka has called the tradition of “logic as calculus” as a current competing with the major modern tradition of “logic as a universal language” (Frege, Russell, Wittgenstein, Quine, etc.). His algebraical logical notation developed in the 1880s was the first draft of a modern formal logic and developed, through Schröder and Peano, into the standard formalism used today. Later, he also developed an alternative logical notation using topological forms (existential graphs) that anticipated hybrid systems of notation — heterogeneous logic — based on graphs, diagrams, maps, networks, and frames (Roberts 1973; Shin 1994; Barwise and Etchemendy 1995; Allwein and Barwise 1996). Peirce’s system of existential graphs (EGs) is a geometric-topological logic notation. According to Gardner (1982 [1951]: 55–56), the existential graph (EG) is the most ambitious diagrammatical system ever built, and the most understandable and versatile system of geometrical logic ever constructed. Developed in different periods, starting in 1882 (Roberts 1973: 18) this revolutionary system (Shin 1994: 11) or group of systems (Alfa, Beta, and Gamma Graphs), not only overcomes several limitations of Euler and Venn diagrams (CP 4.356), but also allows for the beginning of the diagrammatization of modal logic (Houser 1997: 3). To Peirce, the merit of EGs is double: first, they 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42