FOM: Friedman on Realism/Philosophy (reply)

[Torkel Franzen]

  Bill Tait says:

   >That anti-realists in math as opposed to realists in mathematics were
   >not included with the idealists (anti-realists about physical objects)
   >and solipsists (anti-realists about other minds) is explained by W's
   >ignorance of what was the normal form of expression in mathematics (by
   >the 1930s'-40's, when he was writing).

  Less charitably, the omission of anti-realists might be thought to
be connected with the fact that Wittgenstein had himself written in a
very anti-realist vein in other contexts.  Russell remarked of an
earlier manuscript of his (I think the Philosophical Remarks) that
they contained "a lot of stuff about infinity, which is always in
danger of becoming what Brouwer has said, and has to be pulled up
short whenever this danger becomes apparent". In these earlier
writings, Wittgenstein did not make the clear demarcation between
philosophical reflection and mathematical practice that he later
urged, and even suggested (perhaps influenced by Brouwer) that a
philosophically sound mathematics would differ from that currently
practiced.