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.
General
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