FOM: Do realists really know?

Mark Steiner marksa at
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>
              Hebrew University
              Peter Schuster <pschust at>

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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