Integrating fallibilism and formal logic: A Peircean approach to Lakatos’ methodology

Authentic learning of argumentation and proof in mathematics requires active conjecture development rather than passive reproduction of proofs. Lakatos' approach, widely used in mathematics education research, emphasizes this active process. Although Lakatos rejects formal logic as useless for knowledge development, investigating a potential logical framework for his approach could provide insights into its logical foundations and connect fallibilist and classical views on argumentation and proof in mathematics education research. This theoretical paper explores how an epistemic-logical model, mainly based on an intuitionistic version of the Peircean first-order existential graphs, can frame Lakatos' methodology, contributing to theoretical perspectives and offering a new analytic tool for researchers.