Abstract: This chapter focuses on the cognitive resources needed for basic geometry. It argues that the initial geometrical concepts of basic shapes depend on the way we perceive those shapes. In having geometrical concepts for shapes, we have certain general belief-forming dispositions. These dispositions can be triggered by experiences of seeing or visual imagining, and when that happens we acquire geometrical beliefs. The beliefs acquired in this way constitute knowledge, in fact synthetic a priori knowledge, provided that the belief-forming dispositions are reliable. Aspects of two-dimensional space perception are discussed.

Keywords: cognitive resources, geometrical concepts, space perception, belief-forming, two-dimensional space,