Grounding Concepts: An Empirical Basis for Arithmetical Knowledge

Grounding Concepts tackles the issue of arithmetical knowledge, developing a new position which respects three intuitions which have appeared impossible to satisfy simultaneously: a priorism, mind-independence realism, and empiricism.

Drawing on a wide range of philosophical influences, but avoiding unnecessary technicality, a view is developed whereby arithmetic can be known through the examination of empirically grounded concepts. These are concepts which, owing to their relationship to sensory input, are non-accidentally accurate representations of the mind-independent world. Examination of such concepts is an armchair activity, but enables us to recover information which has been encoded in the way our concepts represent. Emphasis on the key role of the senses in securing this coding relationship means that the view respects empiricism, but without undermining the mind-independence of arithmetic or the fact that it is knowable by means of a special armchair method called conceptual examination.

A wealth of related issues are covered during the course of the book, including definitions of realism, conditions on knowledge, the problems with extant empiricist approaches to the a priori, mathematical explanation, mathematical indispensability, pragmatism, conventionalism, empiricist criteria for meaningfulness, epistemic externalism and foundationalism. The discussion encompasses themes from the work of Locke, Kant, Ayer, Wittgenstein, Quine, McDowell, Field, Peacocke, Boghossian, and many others.