FOM: Objectivity of logical/mathematical truth?

[Reuben Hersh]

  On Wed, 17 Dec 1997, Solomon Feferman wrote:

> 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
> 
> 	You ask, "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?"

	I suggest holding this puzzle by the other end.  We observe, 
	experience, recognize, that a certain part of human objective 
	communication is "distinctive and 
	supremely objective."  We should give a name to this interesting 
	and important part of human communication.  In fact, such a name has 
	already been given, and retained over the centuries.  It's called 
	"mathematics."   "Mathematics" is what we call the supremely
	objective part of human communication.

	That still leaves Kant's question, "How is 
	mathematics possible?"  If that question is
	ever answered, it will be answered by neurophysiologists and
	sociologists, not by logicians or philosophers.  However, even if 
	we don't know how mathematics is possible, we do know it is
	possible--which is the principal thing to know.  

	Compare with Heidgger's question, "Why does anything exist?"
	Physicists don't try to figure out why anything exists.  The main 
	thing, the starting point for everything else, is this:  there is a 
	world, there is existence.

	Reuben Hersh