Re: mathematics

From: Eray Ozkural exa (examachine_at_gmail.com)
Date: 11/29/04 

Date: 29 Nov 2004 14:54:27 -0800

Patty was referring to the objectivity of mathematics over and above
other things in life:

patty <pattyNO@SPAMicyberspace.net> wrote in message news:<nVBqd.483095$D%.165874@attbi_s51>...
> Eray Ozkural exa wrote:
> >
> > What is this mysterious objectivity in a way that ordinary things
> > could not be?
>
> Because when people and\or computers correctly follow procedures using
> the signs of these things they always come up with exactly the same
> results. Try to do that with your cars, and tables, and other cudiments.

I don't see how that follows. When computers run the same program they
always come up with exactly the same results, regardless of whether
the program was was mathematical in any sense of the word.

If you mean that the facts about ordinary objects are fuzzy, then I
find that agreeable but it's still very mysterious how mathematics can
be more objective than everything else, in particular physics. Did
Neil mean only "commonsense concepts" when he said "ordinary things",
or did he mean "everything except mathematics" as I understood him?
Nothing transcends the objectivity of physics. It's no answer
comparing common sense reasoning to mathematics, either. Surely,
common sense reasoning is more general purpose, that's why it's
fault-tolerant, and it's because it deals with fuzzy concepts, unlike
the concepts in geometry or calculus. That doesn't mean common sense
is less objective, in my opinion, because mathematics is no more than
common sense and common language.

Also, I thought you had actually favored Quine, he could have said
that mathematics is continuous with common sense. What distinction is
there to draw? Are you now coming to defend an even stronger version
of the analytic-synthetic distinction that says mathematics is above
science? (A distinction that I never supported because I'm no logical
positivist.)

On the other hand, if you wanted to say that computation is a good
thing, don't you realize that common sense is computational? What is
common sense if it is not a computational model of everyday events?

Regards, 

--
Eray Ozkural

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