Paradox and argumentation: From rhetoric to the refinement of mathematics

Abstract

Paradoxes –?and the problem they present for logic?– can be traced as a subject for reflection from the Sophists to contemporary language philosophers and mathematicians, visiting Aristotle, Abel and Russell along the way, during which time rhetorical algebra transitioned into syncopated algebra and then to symbolic algebra. The paradox can be seen as an obstacle to aseptic reasoning, but it can also act as a compelling stimulus for imagination and the practice of argumentation or persuasion, a rhetorical tool that has encouraged rigorous thinking throughout history, in an attempt to avoid «concealed» lies in all kinds of discourses. It is, therefore, a challenge that inspires creativity within a culture indebted to the rhetorical tradition.