From: pralmo01@ulkyvx.louisville.edu
Newsgroups: alt.atheism
Subject: Re: The cause of existence. was: god before creationdir
Date: 6 Apr 92 18:17:06 GMT
Article-I.D.: ulkyvx.1992Apr6.141706.1
Organization: University of Louisville

In article <9!g+1+B@engin.umich.edu>, ingles@finch.engin.umich.edu (Ray Ingles) writes:
> 
> In article <1992Mar31.002010.1@ulkyvx.louisville.edu>, pralmo01@ulkyvx.louisville.edu writes:
>> In article <1992Mar27.031826.22794@jyusenkyou.cs.jhu.edu>, arromdee@jyusenkyou.cs.jhu.edu (Ken Arromdee) writes:
>> > In article <1992Mar26.215927.1@ulkyvx.louisville.edu> pralmo01@ulkyvx.louisville.edu writes:
>> >>A involves the intuitive idea that ...
>> >>B involves the very unintuitive idea that ...
>> > 
>> > That's like deciding that the world is flat because for it to be flat is
>> > very intuitive.  The cosmos has no obligation to live up to your intuition.
>> > 
>> > Kenneth Arromdee (UUCP: ....!jhunix!arromdee; BITNET: arromdee@jhuvm;
>> >      INTERNET: arromdee@jyusenkyou.cs.jhu.edu)
>>

Me: 
>> Apparently Kenneth is compaining because I have used my 'intuition' and
>> since some people have been terribly wrong before, using such 'intuitions',
>> my own comments are without merit.
>> 
>> I merely note that just because others have been wrong before using a method
>> which vaguely seems like my own does not bear on whether or not I am wrong.
>> Many, if not most, of the greatest mathematical discoveries were made by
>> employing 'intuition'.  In fact, there is a mathematical movement which will
>> only employ those axioms which are intuitively correct.
>> 
>> Joe Deasy 
> 


Ray Ingles:
>  As someone else has posted, you are somewhat misrepresenting the position
> of the 'intuitionists.'

Well, despite Graham Mathew's terse comment that I've misrepresented 
intuitionist mathematics, I still mantain that it is quite relevant
to the issue at hand.  THERE IS a modern mathematics movement which
rejects certain kinds of objects and certain kinds of reasoning because
they cannot be clearly understood intuitively.  The founders of that 
movement, such as Weyl and Brouwer, did in fact hold that some
objects, such as infinite sets, and some axioms, such as the law of
excluded middle applied to infinite sets, should not be invoked
because they are not clearly correct according to intuition.  You
can read more along this line in _The Loss of Certainty_ by Morris
Kline.

>  Anyway, you claim that something is intuitively obvious, ("common sense")

Good God I never said common sense!!!  Nor did I mean to imply that
it is intuitivly obvious for everyone!!  I said:  I intuit...

                                                       
> yet even after you've explicated for a while many of us still don't accept
> it. Hence, it should be obvious that it isn't intuitively obvious. :->
>  Finally, yes, mathematical discoveries are often by intuition. But this
> then needs to be checked by rigorous mathematical work.

I never said that intuition is always correct; that mathematical intuition
is often incorrect is of course true.  The question is:  is THIS intuitive
starting point a good one.  I still think so.  

>  So it's fine to discover a fruitful area of investigation by intuition,
> but intuition alone does not a proof make.

Let me note here that even modern mathematics has different traditions and
different answers for the question "What is a good proof?"  Sometimes, but
not always, the answers overlap.

Personally, I think statements for which there is strong intuitive support
and no counter evidence can sometimes be useful as beginning assumptions.
                               
Well, Ray, I thought you thought that it was a good question, what causes the
universe?, since you suggested some possible answers.


Sincerely,
Joe Deasy

"Proof is the idol before which the mathematician tortures himself"