From owner-qed Wed Nov  9 14:48:01 1994
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Date: Wed, 09 Nov 1994 20:24:51 GMT
From: rbj@campion.demon.co.uk (Roger Bishop Jones)
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To: qed@mcs.anl.gov
Subject: Re: Platonism
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In message <QEC0FA83@pc8012> "N.G. de Bruijn" writes:
> 

...

> 
>    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)