The Challenge of Formal Logics and Metaphysical Systems to Semiotics

Formal diagrams and mathematical schemes have been an essential part of semiotic research since its beginning. It started with the algebraic formula adopted by Lévi-Strauss for his myth analyses; in structuralist research it was continued by A.J. Greimas and his Paris school. There was something like the air of magic formulas (Tzvetan Todorov) in the idea that the analysis was completed with such abstract models. Yet, in parallel, the formal logics were invented at the Vienna Circle as early as the 1920s by Carnap, Neurath, Wittgenstein, and others. Greimas assumed the use of deontic logic developed by Georg Henrik v. Wright. On the American scene, Charles S. Peirce had elaborated his ‘existential graphs’ to formalize syllogisms and other logical reasonings. Yet, the well-known ‘linguistic turn’ meant different things in the angloanalytic philosophy than in the Saussurean structural linguistics. The formal line was then followed by cybernetics until our time and its trend toward digitalization. However, one sign system has always existed in Western erudite music as a kind of ‘formalization’ by notations. Moreover, even a ‘metaphysical’ system such as existential semiotics can be formalized when it is applied to musical texts and discourse.