On The Significance Of Argumentation In Searching For Mathematical Proof

Abstract

In this paper, we argue that argumentation theory can be used to explore certain aspects of the development of discovery proof-events in time. Since argumentation is inseparable from the process of searching for a mathematical proof, a modified model of proof-events calculus, based on certain versions of argumentation theories primarily advanced by Toulmin and Pollock, can be used to this effect. We claim that the exchange of arguments and counterarguments set forward to clarify eventual gaps or implicit assumptions occurring in the course of a proof-event can be represented by appealing to argumentation theories. In this paper, a comparative analysis was carried out between the theory of proof-events and the theory of argumentation. The combination of these two theories enables us to represent controversial points in the process of searching for proof. By expanding the calculus of proof-events with the theory of argumentation we can take into consideration such moments as incomplete or even false purported proofs, intuitive ideas, correct or incorrect steps of reasoning, commentaries, etc. and represent them formally at the appropriate stages that take place during the evolution of a sequence of proof-events.