Can Philosophic Methods without Metaphysical Foundations Contribute to the Teaching of Mathematics?

Abstract

Introduction: In the complex teaching paradigm constructed and celebrated in classical Greek philosophy, geometry was the gateway to knowledge. Historically, mathematics provided the generational basis of education in Western civilization. Its impact as a disciplining subject was philosophically served by Plato's most influential metaphysical involvement with the dialectical interplay of form and content, ideas and images, and the formal, hierarchic divisions of reality. Mathematics became a key--perhaps the key--for the establishment of natural, social and intellectual hierarchies in Plato's work, and mathematical capacities became synonymous with power--the power of abstraction needed to effect and control change (cf. Boisvert 153). It was the provenience of the academic demands, levels, and achievements celebrated as culturally Western. From ancient Athens to medieval Europe, it became the principle of interactional/hierarchic selection: Similia similibus cognoscuntur--that is, only those things alike (by nature) can interact cognitively; this launched the notion that mathematical ability is the best test for objectively determining who does and who does not qualify for a social, political, and intellectual meritocracy.