Re: mathematics

From: patty (pattyNO_at_SPAMicyberspace.net)
Date: 11/30/04 

Date: Tue, 30 Nov 2004 02:16:22 GMT

Eray Ozkural exa wrote:
> 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.
>

I was providing a definition of objectivity which i though addressed the
particular question you asked. That abstract computations also meet the
requirements of objectivity, does not cast our criteria in the trash.

> 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.

I find it amazing, perhaps that is what you are calling "mysterious".

> 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.

When *same results* is the criteria, physics cannot hold a candle to
mathematics. I remember trying to calculate G in my physics lab ...
very messy ... measurements are messy ... the real is messy.

> 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.

Sorry i can't get your drift here. "More general" does not equate to
"same results".

> 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.)

Well i don't buy Quine and logical positivism as a package deal. I do
buy that there is no hard fast distinction between analytic statements
and synthetic statements from a god's eye view. However within any
particular view of some world, one can easily draw the distinction
between what is sensed at the periphery from that world, and what is
only internal to that world view. A scientific web of belief will
contain mathematics close to the center of its web, whereas noumenal
reality is sensed on the periphery of the web. I got that from Quine's
two dogmas. But i think Quine was coming from a
science-is-king-god's-eye-perspective and was not concerned that the
same arguments apply to each of our personal world views.

>
> 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 with this good thing, bad thing, stuff ?

> What is
> common sense if it is not a computational model of everyday events?
>

Well the computational model of common sense does not seem to work very
well ... else Doug would have already had his IPO.

patty

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