Re: Some Simple Questions

From: Charlie-Boo (chvol_at_aol.com)
Date: 03/19/05 

Date: 19 Mar 2005 15:39:19 -0800

David C. Ullrich wrote:
> On 18 Mar 2005 12:24:32 -0800, "Charlie-Boo" <chvol@aol.com> wrote:
> >
> >> As I suggested: Why don't you re-read the question? It's
> >> _such_ a stupid question that it can't be what you actually
> >> meant to ask.
> >
> >It's stupid to not believe something that hasn't been proven?
>
> No. Why don't you re-read what your question actually asked???
>
> You didn't ask whether the lack of proof implies something
> hasn't been proven. You asked whether the lack of an explicit
> proof implies that something is _false_.

No. "implies" means logical certainty. I said "demonstrates",
"incresses the probability", gives "confirming evidence".

The paper that makes unsubstantiated claims about what the authors
accomplished is presumably expecting the reader to be persuaded that
the claims are true. My point was that to a logical person it is only
providing evidence that it is not true.

To add a little more detail: Suppose a paper describes a new system
that purportedly generates proofs of given theorems. It contains all
sorts of cryptic formalisms, and ends with the claim that the theorem
has been proven.

The naive reader will be impressed at the array of symbols, not
understand them, and conclude that it must be some new advanced theory
and that it is valid.

However, the logical reader knows that in the final analysis, any proof
is a convincing argument that the given proposition is true.
Formalisms do not constitute a proof. It is the logical argument that
they represent that is the proof. If an intuitive, semi-formal
convincing argument is not given, then there is no real proof.

Similarly with a system that purportedly generates computer programs.
The proof of the pudding is an actual, executable program that is
created by the system. Short of this, the truth of the claim has not
been supported.

Furthermore, the lack of such real examples suggests only that the
system does not work, and that the claims of success by the authors are
false.

C-B

> ************************
>
> David C. Ullrich

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