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Grounding Concepts tackles the issue of arithmetical knowledge, setting forth a new theory satisfying three theses taken together: (1) Arithmetic is knowable without the need to conduct tests or otherwise gather empirical evidence. (2) Arithmetic is a body of mind-independent fact. (3) Arithmetical knowledge is based on sensory experience in some way.
Jenkins develops a theory whereby arithmetic can be known through the examination of empirically grounded concepts. These are concepts that, 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 theory respects empiricism, 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.
Grounding Concepts: An Empirical Basis for Arithmetical Knowledge
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Grounding Concepts: An Empirical Basis for Arithmetic Knowledge by C. S. Jenkins
