Cognitive semiotic processes in mathematical reasoning: Raymond Duval's thought in light of Charles Sanders Peirce's semiotic theories

Abstract

The comparison between the theories of Raymond Duval and Charles Sanders Peirce offers a way to investigate the role of representations in mathematical reasoning. Peirce’s perspective, centered on the cognitive function of signs and the inferential power of diagrams, provides an interpretative key to overcoming the object–representation dualism, which lies at the heart of Duval’s cognitive paradox.