FOM: determinate truth values, coherent pragmatism

[John Steel]

  I would like to add a few little comments about pragmatism vs. realism.

  First, I consider myself both a pragmatist and a realist. When I say
what it is I believe (e.g. there are sets, or there are measurable
cardinals) I speak as a realist. When I describe why I believe it (the
simplicity, scope, power, coherence with previously accepted principles,
and independently verified predictions of the theory these assumptions are
part of), I speak as a pragmatist. I see no inconsistency here. 

   Second, the danger in a pragmatic attitude is that it becomes too
facile. I always think of Quine, who emphasized his pragmatism concerning
choice of set theory, and at the same time came up with what seems so far
to be a truly useless set theory, NF. As an attitude toward research and
axiom acceptance, "long-run pragmatism" (which is, I hope, coherent) is
quite different from "whatever works for now". One of the last questions
a long-run pragmatist will ask is how palatable some principle is to
people who don't really understand it.

   It would be most useful to have a broadest point of view about sets
accepted by all. If different points of view arise, it will be of
immediate practical importance to put them together appropriately, so that
we can continue to use each other's work. I think set theorists are
engaged in uncovering such a broadest point of view, and deciding the CH
is the next fundamental problem along this (never-ending) road. (The
existence of a real valued measure, which is a statement of 4th order
arithmetic, is significantly further off.) 


John Steel
UC Berkeley