Abstract: This chapter explains how the examination of arithmetical concepts can lead to knowledge. It argues that in order for an examination of our concepts to supply us with knowledge of an independent reality, it must be that those concepts are appropriately sensitive to the nature of that reality, or what is called here grounded. The core idea here — and indeed the core idea of this book — is that grounded concepts are like trustworthy on-board maps of the independent world. The chapter suggests that it is through the normal functioning of our senses that our arithmetical concepts come to be grounded, and argues that if this is so, then the ultimate source of our arithmetical knowledge is empirical, though that knowledge is still a priori by many standard definitions.

Keywords: concepts, concept grounding, a priori, empirical, maps, camera, filter, sensory input,