FOM: Do realists really know?

[Mark Steiner]

Subject:
              Re: FOM: Do realists really know?
         Date:
              Tue, 13 Jun 2000 20:49:52 +0300
        From:
              Mark Steiner <marksa at vms.huji.ac.il>
 Organization:
              Hebrew University
           To:
              Peter Schuster <pschust at rz.mathematik.uni-muenchen.de>
  References:
              1





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.