The semiotic approach to mathematical evidence and generalization

Abstract

The fundamentals of Peircean semiotics have been applied by Peirce himself to the main philosophical questions relating mathematics. Following Michael Otte's suggestion of resorting to a semiotic approach to mathematical epistemology in order to understand mathematical cognition, it is possible to account for the chief problem of generalization, going beyond the traditional explanations exemplified by Locke's use of abstract general ideas and Berkeley's criticism to it. Against the background of Peirce's main lines of departure from Kantian transcendentalism, the problem of the evidence obtained from proofs performed upon individual diagrams and laying claim to universality can be faced within a semiotic frame that focuses on the interplay of iconic, indexical and symbolic elements of signs. © 2005 Springer Science+Business Media, Inc.