Geometry from the Materialist and Idealist Perspectives

In this chapter, I consider – from the two perspectives (Idealist and Materialist) – our geometric beliefs: their acquisition, truth and warrant. I present a difficulty attending the attempt to explain our acquisition of geometric beliefs, and consider two suggestions for contending with it. My conclusions will be that the difficulty notwithstanding, Hume’s Idealist can account for our having the geometric beliefs we do, although he can’t adequately explain why we do not have some non-Euclidean ones. Furthermore, many of them are justified, even count as knowledge, albeit “imprecise” (in a sense to be explained). I then consider the questions from the Materialist perspective. I argue that Hume the Materialist can only account for the acquisition of our geometric belief if he thinks they are acquired empirically, and that they are then unjustified, indeed, unjustifiable.