Abstract: This book is a philosophical discussion of arithmetical knowledge. No extant account, it seems, is able to respect simultaneously these three strong pre-theoretic intuitions: (a) that arithmetic is an a priori discipline; (b) that arithmetical realism is correct, i.e.. that arithmetical claims are true independently of us; and (c) that empiricism is correct, i.e., that all knowledge of the independent world is obtained through the senses. This book investigates the possibility of a new kind of epistemology for arithmetic, one which will is specifically designed to respect all of (a)-(c). The book proposes that we could develop such an epistemology if we were prepared to accept three claims: (1) that arithmetical truths are known through an examination of our arithmetical concepts; (2) that (at least our basic) arithmetical concepts map the arithmetical structure of the independent world; and (3) that this mapping relationship obtains in virtue of the normal functioning of our sensory apparatus. Roughly speaking, the first of these claims protects a priorism, the second realism, and the third empiricism.

Keywords: empiricism, arithmetic, realism, a priori, concept grounding, epistemology, senses, concepts, independence