Re: Poll - are you a platonist?

What may be "truth" must be discovered. Invention is the (previously)
undiscovered expression of "truth" (i.e. accepted truth). Verily, one can
not discover truth, only express it, perhaps in the form of invention.
Thus, a proof of "truth" is an invention, a symbological expression of the
"truth" itself, and the discovery of the proof is a discovery of an
expression of the "truth", no more, no less.

<mikeh106@xxxxxxxxxxx> wrote in message
news:1139628889.165733.52740@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
The symbolism is invented. The truth it expresses is discovered.

peter@xxxxxxxxxxxxxxxxxx wrote:
Penrose' recent book discusses mathematics and is directed towards the
lay reader. Philosophers tend to consider platonism a delusion. Many
discussions have occured debating this.

This post is a request for you mathematicians, to add some evidence,
one way or another to this debate.

The poll is simple. Please answer the following question honestly (you
may not have thought about it much, so your first impression is what
I'm looking for) as a reply to this thread:

Do you believe that mathematical truths are invented or discovered?

There is, of course, no right, or wrong, answer. At the end of this
poll (arbitrarily the end of March), I'll add up the answers and see
what the ratio is. Hardly scientific. However, just as a straw poll, I
think it will add objective data to the debate. Are mathematicians
mainly plationist or not.

If any of you feel disinclinded to reveal your thoughts, please let me
know, and I'll set up an anonymous poll somewhere and post the URL
here. I don't think that there is any shame to admitting to either
answer to the above question - but only you can tell me if there is.

The background to this request is simple. I'm confused myself about
whether the answer ought to be 'yea' or 'nay'. Some people have claimed
that many mathematicians answer 'invented'. My personal experience is
that mathematicians that I know, if they can be bothered (which is
another question) say 'discovered'. That is my personal view, despite
my understanding the formidable philsophical objections to that view.

I'm not asking if you are a classical platonist who believes that there
is a universe or space of real mathematical objects waiting to be
discovered. That is an implication, but I think, an extreme implication
of the answer 'discovered' to the question.

This is more a question of how you feel, as a working mathematician,
about what you do.

If it comes to a poll in another place, or not, I'll post a result at
the end of March. The result might, of course, be that mathematicians
can't be bothered to answer this question. That's fine with me, I'm
just keen to posit the question and see the result.



.

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