...
>
> There appears to be quite some interest in Mathematical Platonism.
> In the discussion I note some different ideas about this, quite far
> apart. Let me give them names.
>
> A-Platonism is the opinion that our mathematical objects have a
> real existence in some real world.
...
> I suppose that we all agree that A-platonism is irrelevant for
> QED. And I think that many people will admit that A-platonism is a
> bit dangerous as well. It makes believers believe that there is no
> need for an absolute level of accuracy.
I suspect that this is factually incorrect.
> Their idea may be that for
> the time being they can get away with sloppy definitions. They might
> believe that whenever any hard question comes up they can inspect the
> objects a bit closer and adjust the definitions a bit.
Are you thinking of any particular platonists who you claim to be sloppy
in this kind of way?
> The claim has been made that A-platonism agrees with the
> psychology of the mathematicians: during their work they imagine that
> the things they are talking about are real objects. Indeed, there are
> such emotions, but these are essentially the same feelings that a
> novelist has when writing imaginary stories about imaginary people
> and imaginary situations. An essential difference is that the
> mathematician may even be cheating: he starts with some assumptions
> that he wants to disprove, in the course of the argument he constructs
> objects, treats them psychologically as existing things, until at the
> end a contradiction is reached and the whole edifice falls into
> pieces. (This cheating is a point I miss in the Podnieks' chapter.)
This is more a litany of abuse than an argument against platonism.
Are you really intending to say that platonists are all deluded cheats?
Roger Jones
rbj@campion.demon.co.uk (at home)