FOM: NATURE of maths

[Charles Silver]

On Sat, 14 Mar 1998, Julio Gonzalez Cabillon wrote:

> Dear Professor Charles Silver,
> At 07:50 AM 14/03/1998 -0500, you wrote:
> | ... I think another way our discussion could be made more profitable
> | would be for you [referring to Hersh, JGC] to acknowledge that the
> | sociology of mathematical agreement is insufficient to determine what
> | mathematics is, really.
> 
> So as to make the discussion profitable, and personally to fully grasp
> your objections and viewpoints, I would be very pleased and most grateful
> to listen to (read) in a few words your own opinions/thoughts about the
> NATURE of mathematics -- necessary and sufficient conditions of mathematics.

	I do not have a fully developed philosophy of mathematics.  My
primary objection to Hersh's view has been stated over and over in this
list.  Other people have also stated objections to Hersh's view, and you
can find some lively discussions between them and him in the archive. 
Besides responding to criticisms, Hersh has also posted a favorable review
of his book that he approves of.  There is another recent favorable review
of his book in the NY Times by Rothstein that Hersh does not entirely
approve of.  If you wish to see some positive viewpoints on the philosophy
of mathematics, I recommend Solomon Feferman's posts, particularly the one
including ten theses.  Also, read people's reactions to Feferman's theses. 

Charlie Silver
Smith College