[FOM] Question on the relevance of pragmatism to mathematical abstraction

[Richard Haney]

As an undergraduate undertaking my (somewhat limited, formal) study of
introductory philosophy I was quite impressed with William James'
lecture "What Pragmatism Means", where is describes a semantic
question, but which he described as a "metaphysical" one, regarding a
woodsman and a squirrel chasing each other around a tree trunk.  I
thought that the lecture mostly likely described a very powerful
methodology for quickly getting to, clarifying, and properly disposing
of the essential issues in many a long-winded debate, especially
debates on "metaphysical" issues.  I also came to understand that
relevance to (usually publicly observable) empirical phenomena outside
the discourse at issue was one of the primary characteristics that
distinguished science from non-science.

But I have heard rumblings that have suggested that pragmatism and its
seemingly more dogmatic extension, operationalism, have lost favor in
the scientific community.  And although many of the discussions in this
forum seem to make a substantial, implicit use of pragmatism in
clarifying and qualifying issues, I am puzzled that pragmatism has not
played a more explicit role here in discussions of mathematical
abstraction.

As a result, I feel as if I may be woefully out of sync with modern
views on issues regarding pragmatism in regards to mathematical
abstractions.

Can anyone provide some modern references on the relation of pragmatism
to mathematical abstractions?

I would be particularly interested in any references and/or discussion
that might suggest or rebut the idea that "various mathematical ideas
are meaningless because they do not have a pragmatic relevance or
interpretation in terms of empirical phenomena".

Richard Haney



		
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