SEMIOTIC RELATIONS AND PROOF METHODS

When a direct proof of a statement S seems hard or even impossible to obtain, there may exist another statement (or set of statements) S*, somehow related to S, on the basis of which S can be proved. In order to investigate what options can be used to move from S to S*, four kinds of semiotic relations inspired on the four master tropes of semiotic research are briefly reviewed. Specifically, our syntagmatic, paradigmatic, antithetic and meronymic relations correspond, respectively, to metonymy, metaphor, irony and synecdoche. It is suggested that these four semiotic relations determine the options to move from S to S*, leading to proof by inference, proof by analogy, proof by contradiction, and proof by case analysis.