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.
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
accept analytic anti-realism anti-realist appeal aprioricity argue argument arithmetical concepts arithmetical knowledge arithmetical propositions arithmetical truths assume Boghossian BonJour C. I. Lewis causal Chapter concept grounding conceptual examination conceptual scheme conceptual truths condition confirmational holism conventions count counterfactual Daniel Nolan dependence discussion empirical grounding empiricism empiricist epistemic epistemology experience explanans explanation explanatory express externalist fact foundationalism grounded concepts Hume’s Principle implicit definition inaccurate concepts independent world indispensable instance intuition justification kind linguistic logical mathematical McDowell meaning meaningful mental lives merely mind-independent modal independence neo-Fregean Newton non-accidentally non-conceptual notion objection ofthe one’s Patricia Blanchette Peacocke philosophical philosophy of mathematics possession possible posteriori priori knowledge problem proposal quasi-realist question Quine rational realism reject relevant reliabilism representations response Section seems sense seriously inaccurate sort structure subject’s suggest supposed theory things true beliefs ultimate constituents unconceptualized sensory input worry