Grounding Concepts: An Empirical Basis for Arithmetical KnowledgeGrounding 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. |
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Grounding Concepts: An Empirical Basis for Arithmetical Knowledge C. S. Jenkins Limited preview - 2008 |
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accept analytic anti-realism anti-realist appeal aprioricity argue argument arithmetical concepts arithmetical knowledge arithmetical propositions arithmetical truths assume Boghossian BonJour brain C. I. Lewis causal Chapter concept grounding conceptual examination conceptual scheme conceptual truths condition confirmational holism conventions count counterfactual Daniel Nolan default reasonable dependence discussion empirically grounded empiricism empiricist epistemic epistemology experience explanans explanation of BAp explanatory express externalist foundationalism grounded concepts Hume's Principle implicit definition independent world indispensable instance intuition involved justification kind least linguistic logical mathematical McDowell meaning meaningful mental lives merely mind-independent modal independence neo-Fregean non-accidentally non-conceptual notion objection one’s outsider 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 semantic sense sort structure suggest supposed theory things true beliefs ultimate constituents unconceptualized sensory input understand worry