Re: Amateur takes on Wiles's work

From: Tim Smith (reply_in_group_at_mouse-potato.com)
Date: 08/29/04 

Date: Sun, 29 Aug 2004 22:54:39 GMT

On 2004-08-29, James Harris <jstevh@msn.com> wrote:
> Taniyama and Shimura conjectured that there was a pattern here that held,
> as in fact modular forms and elliptic curves WERE related in some deep
> way, and that what mathematicians were noticing wasn't just one of those
> intriguing coincidences.
>
> But you have the setup for a logical fallacy called Cum Hoc, Ergo Propter
> Hoc, where people see what looks like a pattern, and leap to a conclusion,
> though at this point mathematicians were ok, as it was only a conjecture.

For those who don't know what Cum Hoc, Ergo Propter Hoc is, here are a
couple explanations:

    <URL:http://encyclopedia.thefreedictionary.com/correlation%20implies%20
causation%20%28logical%20fallacy%29>

    <URL:http://www.fallacyfiles.org/cumhocfa.html>

Basically, it is this kind of fallacious reasoning:

    Events C and E are observed to occur together. Therefore, C causes E.

For those who want to be clear, rather than pretentious, this is also known
as the "correlation implies causation" fallacy.

> It took Andrew Wiles coming in, with an attempt at proof by association
> for the logical fallacy to fully take hold.

Please explain what you think "proof by association" is.

...
> For instance, with my challenge to Wiles's work, someone should find a
> single logical step where the assumption of a non-modular elliptic curve
> will cause a contradiction, and be able to give the exact section in his
> work where it occurs!!!

Someone? Why not you?

...
> I'm asking for someone to produce the keystone in Wiles's work, which will
> ring out loud and clear if you assume the existence of a non-modular
> elliptic curve.

Do it yourself. Numerous mathematicians have gone through Wiles' work.
That's how the errors in the first version were found, after all. They have
found the final version correct. If you think they are wrong, then point
out where they are wrong, rather than making stupid accusations (such as
"correlation implies causation" even being applicable to a mathematical
proof) and then calling for others to do the hard work of showing that you
are simply wrong (for the Nth time for some large value of N). 

-- 
--Tim Smith

Relevant Pages

  • Re: JSH: Assocation does not prove
    ... Here the logical fallacy is looking at two things that appear related, ... some mathematician or mathematicians checked another elliptic ... curve and found IT TO connected to a modular form. ... elliptic curve and found it to connected to a modular form! ...
    (sci.math)
  • Re: Amateur takes on Wiless work
    ... >> Hoc, where people see what looks like a pattern, and leap to a conclusion, ... >> though at this point mathematicians were ok, as it was only a conjecture. ... the assumption that a non-modular elliptic curve exists. ... curve exists and pointing out where that would contradict with a step ...
    (sci.math)
  • Re: JSH: Assocation does not prove
    ... some mathematician or mathematicians checked another elliptic ... >curve and found IT TO connected to a modular form. ... >elliptic curve and found it to connected to a modular form! ... no. he actually proved the connection. ...
    (sci.math)
  • Re: Null test, Wiless work
    ... > But, James, it is your hypothesis that such an elliptic curve can exist. ... it's not my hypothesis that a non-modular elliptic curve exists. ... with his approach which fails by the logical fallacy Cum Hoc, ... different from the supposed would emerge if the Taniyama-Shimura ...
    (sci.math)