FOM: Re: Bishop-style constructive mathematics

[Roger Bishop Jones]

In response to: Peter Schuster Friday, December 29, 2000 11:53 AM
Subject: FOM: Bishop-style constructive mathematics


> This is what one could call the ambiguous character of Bishop-style
mathematics,
> which is of course hard to accept by people exclusively devoting their
professional life
> to one of the models, especially by any (leisure-time) platonist who
thinks that there
> is only one mathematics.

I wouldn't call myself a platonist, but I think others might.
However, I have no problem with "Bishop-style" mathematics.

I believe that the semantics of mathematical languages can
be made sufficiently clear that most of the statements of mathematics
have an objective truth value.

More generally, I believe that the notion of logical truth
can be made precise and objective, and encompasses mathematical
truth.

However, though I regard mathematical truth as (very close to) absolute,
I do not imagine that the truth of any sentence is independent of
the language in which it is expressed.
Different kinds of analysis are easily accomodated within
the one mathematics, provided only that one recognises
that mathematics can deal with any domain of discourse.
(or, as in Bishop loosely about multiple domains)

I'm curious to know whether there really are platonists out there
who have a problem with this.

Roger Jones
RBJones at RBJones dot com