Re: Platonism

From: Eray Ozkural exa (examachine_at_gmail.com)
Date: 11/26/04 

Date: 26 Nov 2004 12:40:10 -0800

Mitch Harris <harrisq@tcs.inf.tu-dresden.de> wrote in message news:<30ope0F33hklmU1@uni-berlin.de>...
> Eray Ozkural exa wrote:
> > Mitch Harris <harrisq@tcs.inf.tu-dresden.de> wrote in message news:<30lna1F30mb3bU1@uni-berlin.de>...
> >
> >>I was under the impression that
>
> (in general)
>
> >> mathematicians are naively platonistic, in that,
> >>without giving too much thought to it, they consider all the things
> >>they work with as real as anything a mechanical engineer works with.
> >>
> >>But for those mathematician who care about philosophy, they are split
> >>between those who think that platonism is totally discredited, and
> >>those who accept a weak form of it ("realism" or "naturalism").
> >
> > I agree. However, as evidenced by this newsgroup most mathematicians
> > are naive platonists.
>
> How does the anecdote go? "On weekdays I'm a platonist, but on the
> weekend I'm a formalist" ?

Yes, I think I've heard this quote often. Maybe it serves to
illustrate that most mathematicians don't even care about these
incompatible positions.

> > They don't understand the distinction between
> > the reality of a table and mathematical ideas.
>
> That is a bit strong. "understand"? maybe they don't -care-. or maybe
> it is more important to them the similarities.

Most mathematicians don't care, and many of which do not care probably
do not have enough motivation to know either. The ones who care
probably understand much better than the rest. :) Maybe, they wouldn't
subscribe to any position, but they would know what each prominent
position actually means philosophically.

> > Godel claimed that there was no distinction. Godel was not naive.
> > Actually, some of his arguments are quite strong. But he was wrong
> > about that, in my opinion, and I also think you can't argue for
> > mathematical platonism without also arguing against a mechanical mind,
> > or arguing for the existence of a mathematical god.
>
> I don't see the "against a mechanical mind" connection.

This is an almost direct paraphrasing of Godel's disjunctive
proposition! I have added nearly nothing to it, except for the word
"god". We can talk about it further. I think Godel was the only
philosophically rigorous mathematical Platonist. Except him, it's just
a lot of handwaving and make-belief. He was intelligent enough to
present a detailed and quite strong argument that mathematical objects
have an independent existence, just like your keyboard.

> As to a god, maybe Einstein's Spinoza's God.

Maybe. I don't know if Einstein was a Platonist. Was Spinoza's
pantheism a kind of Platonism? I don't know, I'll have to read Spinoza
directly to answer that.

Regards, 

--
Eray Ozkural

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