ABSTRACT
Unlike Freudenthal in the introductory quote of this chapter, I am not concerned simply with mathematics (the quote is from a chapter on geometry) but with the epistemology of mathematics (geometry). The following should be understood in the spirit of the quote but with the extension that I am concerned with the epistemology of mathematics, or rather, with that of geometry. I begin the overview of epistemological approaches by sketching the position that presents mind in a metaphysical manner, consisting of representations that are grounded prior to all experience or that in some unspecifi ed way have been abstracted from experience. In fact, the intellectualist vision “is inseparable from the belief in the dualism of mind and body, spirit and matter” and “originates from an almost anatomical and therefore typically scholastic viewpoint on the body from outside” (Bourdieu, 1997, p. 160). Embodiment approaches have arisen from and are grounded in phenomenological studies of experience. These approaches are of interest because modern day neuroscientifi c studies that have appeared around the turn to the 21st century have essentially confi rmed the analyses of perception and social cognition that phenomenological philosophers have advanced in the fi rst half of the 20th century.1
