Phenomenology, Praxis, and the Question of Mathematical Objects

Luis Radford

Abstract: In this article, I discuss some aspects of the manner in which phenomenology
has dealt with the question of the nature of objects of knowledge and the knowability of
such objects. I focus on Kant’s phenomenology and consider in particular some ontological
presuppositions that make Kant’s phenomenology both Platonist and anti-Platonist.
Then, I make a brief incursion into Hegel’s phenomenological approach and Marx’s
critique of Hegel, Kant, and German idealism in general. In the last part of the article,
I comment on Marx’s idea of praxis as an entirely new path to tackle the question of
the nature and knowability of objects of knowledge. I discuss some of the implications
of such an idea for mathematics education. I end up sketching a Hegelian dialectic
materialist concept of knowledge that provides room for understanding knowledge as
something ineluctably embedded in cultural praxis.

Keywords: phenomenology, sense, sensation, mathematical objects, praxis, dialectical



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