FOM: Friedman on Realism/Philosophy

[Torkel Franzen]

  John Steel says:

   >First, I agree that the philosophy of mathematics which leads to
   >mathematical progress is by far the most interesting kind. Without this
   >connection, philosophy of math tends to fall into an endless and fruitless
   >war of metaphors.

  I suspect that what you have in mind here is only foundationally
oriented philosophy of mathematics. Lakatos and Wittgenstein, to take
two philosophers who have been mentioned on the list, didn't think
their philosophizing about mathematics should lead to mathematical
progress; but nor was their philosophizing a contribution to
the conflict over "discovered" vs "invented", "real" vs "imaginary",
"constructed" vs "postulated", and so on.

  >To my mind, Realism in set theory is simply the doctrine that there are
  >sets, and that these sets do not depend causally on us (or anything else,
  >for that matter).

  Such a Realism should be acceptable to one and all, as long as it is
compatible with the view that there are not necessarily any questions
of truth or falsity where set theory is concerned, but only questions
of what can or cannot be proved from certain formal principles. It is
not apparent from your formulation whether Realism is compatible with
such a view or not.

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Torkel Franzen
http://www.sm.luth.se/~torkel/