FOM: Objectivity of logical/mathematical truth?

Solomon Feferman sf at Csli.Stanford.EDU
Wed Dec 17 13:33:30 EST 1997

In his reply yesterday to Joe Shipman on conclusiveness, Moshe Machover
goes to the heart of the philosophical question: if one is not a platonic
realist, Kantian or empiricist, and if one believes (as I do) that
mathematics is "socially constructed", how can logical/mathematical truth
be objective in character?  What we have to accept is that more or less
objective communication is possible on a whole spectrum of socially
constructed concepts from nationality, marriage, money, English
grammar, the calendar, position in the university, to chess and
mathematics.  Perhaps this pushes the question back to a wider and more
puzzling question, but if one takes the possibility of such more or less
objective communication as a given, then the question rather becomes: what
is it about the conceptual and inferential structure of mathematics that
makes it such a distinctive and supremely objective part of human
objective communication?

Sol Feferman

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