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Books > Humanities > Philosophy > Western philosophy > Ancient Western philosophy to c 500
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Plato Was Not a Mathematical Platonist (Paperback)
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Plato Was Not a Mathematical Platonist (Paperback)
Series: Elements in the Philosophy of Mathematics
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Loot Price R582
Discovery Miles 5 820
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This Element shows that Plato keeps a clear distinction between
mathematical and metaphysical realism and the knife he uses to
slice the difference is method. The philosopher's dialectical
method requires that we tether the truth of hypotheses to existing
metaphysical objects. The mathematician's hypothetical method, by
contrast, takes hypotheses as if they were first principles, so no
metaphysical account of their truth is needed. Thus, we come to
Plato's methodological as-if realism: in mathematics, we treat our
hypotheses as if they were first principles, and, consequently, our
objects as if they existed, and we do this for the purpose of
solving problems. Taking the road suggested by Plato's Republic,
this Element shows that methodological commitments to mathematical
objects are made in light of mathematical practice; foundational
considerations; and, mathematical applicability. This title is also
available as Open Access on Cambridge Core.
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