FOM: Do realists really know?
marksa at vms.huji.ac.il
Tue Jun 13 13:52:28 EDT 2000
Re: FOM: Do realists really know?
Tue, 13 Jun 2000 20:49:52 +0300
Mark Steiner <marksa at vms.huji.ac.il>
Peter Schuster <pschust at rz.mathematik.uni-muenchen.de>
Peter Schuster wrote:
> Would anybody be so kind to explain why and how
> the law of bivalence, i.e., that any statement is
> either true or else false, does follow from what
> traditionally is called the realist philosophy
> of mathematics, i.e., that mathematical objects
> are existent disregarding whether they are known?
It doesn't follow. These are two different concepts of realism, as
a number of philosophers have pointed out. Bivalence is usually
regarded as a thesis about a particular class of mathematical (or other)
sentences. For example, even a mathematician who rejects intuitionism
and accepts the law of excluded middle in analysis, might balk at the
Continuum Hypothesis. For more discussion see Dummett, The Metaphysical
Basis of Logic.
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