The Philosophical Fundamentals of Hilbert’s Program
In this chapter I shall attempt to set out Hilbert’s Program in a way that is more revealing than previous treatments. Specificially, I shall try to improve upon preceding accounts of Hilbert’s Porgram in each of the following respects: (1) in isolating and developing the distinctive form of mathematical instrumentalism which is basic to Hilbert’s Program, (2) in defining the central problems which must be overcome in order to successfully defend any form of mathematical instrumentalism, (3) in showing how Hilbert’s finitism can be related to his instrumentalism by natural and illuminating means, and (4) in identifying some important philosophical implications of the program which have hitherto not been brought to light.
KeywordsIdeal Method Justify Belief Epistemic Attitude Conservative Extension Ideal Mathematic
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