The Ideal in mathematics

A Spinozist Marxian Elaboration and Revision of the Theory of Knowledge Objectification


  • Wolff-Michael Roth University of Victoria


Spinoza; Marx; idealism; materialism; consciousness; society; praxis; mediation; individualism; abstraction; mathematics education


The theory of knowledge objectification, initially presented and developed by Luis Radford, has gained some traction in the field of mathematics education. As with any developing theory, its presentation contains statements that may contradict its stated intents; and these problems are exacerbated in its uptake into the work of other scholars. The purpose of this study is to articulate a Spinozist-Marxian approach, in which the objectification exists not in things—semiotic means that mediate interactions—but as real relation between people. As a consequence, the (problematic) concept of mediation is unnecessary and can be abandoned. A concrete classroom example from Radford’s own studies is used to exemplify and develop pertinent issues. In particular, the societal nature of the ideal—a synecdoche of relations between objects that reflect relations between people—should be added and the notion of (sign) mediation no longer is required.


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How to Cite

Roth, W.-M. (2020). The Ideal in mathematics: A Spinozist Marxian Elaboration and Revision of the Theory of Knowledge Objectification. Outlines. Critical Practice Studies, 21(02), 60–88. Retrieved from