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Books > Science & Mathematics > Mathematics > Philosophy of mathematics
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Explanation in Ethics and Mathematics - Debunking and Dispensability (Hardcover)
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Explanation in Ethics and Mathematics - Debunking and Dispensability (Hardcover)
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How far should our realism extend? For many years philosophers of
mathematics and philosophers of ethics have worked independently to
address the question of how best to understand the entities
apparently referred to by mathematical and ethical talk. But the
similarities between their endeavours are not often emphasised.
This book provides that emphasis. In particular, it focuses on two
types of argumentative strategies that have been deployed in both
areas. The first-debunking arguments-aims to put pressure on
realism by emphasising the seeming redundancy of mathematical or
moral entities when it comes to explaining our judgements. In the
moral realm this challenge has been made by Gilbert Harman and
Sharon Street; in the mathematical realm it is known as the
'Benacerraf-Field' problem. The second strategy-indispensability
arguments-aims to provide support for realism by emphasising the
seeming intellectual indispensability of mathematical or moral
entities, for example when constructing good explanatory theories.
This strategy is associated with Quine and Putnam in mathematics
and with Nicholas Sturgeon and David Enoch in ethics. Explanation
in Ethics and Mathematics addresses these issues through an
explicitly comparative methodology which we call the 'companions in
illumination' approach. By considering how argumentative strategies
in the philosophy of mathematics might apply to the philosophy of
ethics, and vice versa, the papers collected here break new ground
in both areas. For good measure, two further companions for
illumination are also broached: the philosophy of chance and the
philosophy of religion. Collectively, these comparisons light up
new questions, arguments, and problems of interest to scholars
interested in realism in any area.
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