The Beauty of Graphs Ahti-Veikko Pietarinen 1,2(B ) 1 Tallinn University of Technology, Tallinn, Estonia ahti-veikko.pietarinen@ttu.ee 2 Nazarbayev University, Astana, Kazakhstan Abstract. The beauty of logical graphs consists in many facets, includ- ing notational simplicity, multi-modality and normativity. This paper aims at understanding the nature of Peirce’s graphical method and its implications to philosophy of logic. Keywords: Logical graphs · Existential graphs · Beauty · Logicality 1 Introduction Adapting Russell’s words on the beauty of mathematics, a study of Peirce’s method leaves little doubt that “a logical graph, rightly viewed, possesses not only truth, but supreme beauty”. This beauty has not merely or even predomi- nantly an aesthetic but an exact logical and intellectual quality. The continuity of the sheet on which logical graphs are scribed makes the sheet in Peirce’s terms a “perfect sign” (R 283(s)). Being perfect, it has got to be the “quasi- mind” that unifies symbol, index and icon. Graphs are propositional symbols (“phemes”), and thus picture one or more of the three categories: intellectual concepts, thoughts, or generalities. Our exploration on the beauty of graphs comes in three parts. First, the- ories of logical graphs can exploit notational simplicity. Graphical representa- tions of logical constants perform well when they unify the notational apparatus of the theory. With such notational simplicity, other things then follow. Nota- tional advances contribute to the development of science. Changes—sometimes radical—in notations facilitate discovery and innovation. Advances in science are invariably preceded by representational advances in systems of signs as much as they are in methods of communication. Obviously notations and communication methods co-evolve. The concept of notational parsimony is itself not a simple one. The movement of a double pendulum is described by unassuming formulas whose predictions are tedious to compute. A three-body system is simple but has no formalization that we could solve out without infinities. The two are very different cases. Peirce’s A. -V. Pietarinen—Supported by the Estonian Research Council’s Personal Research Grant PUT 1305 and Nazarbayev University’s Social Policy Grant 2018–2019. My thanks to Francesco Bellucci for comments. c  Springer International Publishing AG, part of Springer Nature 2018 P. Chapman et al. (Eds.): Diagrams 2018, LNAI 10871, pp. 1–4, 2018. https://doi.org/10.1007/978-3-319-91376-6_2 Author Proof