In this ambitious study, David Corfield attacks the widely held
view that it is the nature of mathematical knowledge which has
shaped the way in which mathematics is treated philosophically and
claims that contingent factors have brought us to the present
thematically limited discipline. Illustrating his discussion with a
wealth of examples, he sets out a variety of approaches to new
thinking about the philosophy of mathematics, ranging from an
exploration of whether computers producing mathematical proofs or
conjectures are doing real mathematics, to the use of analogy, the
prospects for a Bayesian confirmation theory, the notion of a
mathematical research programme and the ways in which new concepts
are justified. His inspiring book challenges both philosophers and
mathematicians to develop the broadest and richest philosophical
resources for work in their disciplines and points clearly to the
ways in which this can be done.
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