Re: OT: The film Expelled: No Intelligence Allowed

On Fri, 25 Apr 2008 21:24:23 -0400, "ian@xxxxxxxxxx" <iann@xxxxxxxxxx>
wrote:

Sorry Howard, you can't prove a negative. The assertion that there is a
god is the one that needs proving. In saying that there is no god, all
we are saying is that the existence of god has not been proven - just as
a man cannot be found innocent by a jury at trial, only not guilty.

Two celebrated cases of proving a negative:

http://en.wikipedia.org/wiki/Abel-Ruffini_theorem
The Abel?Ruffini theorem (also known as Abel's impossibility theorem)
states that there is no general solution in radicals to polynomial
equations of degree five or higher.

Niels Henrik Abel (August 5, 1802?April 6, 1829), was a noted
Norwegian mathematician.


http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems
Gödel's incompleteness theorems, proved by Kurt Gödel in 1931, are two
theorems stating inherent limitations of all but the most trivial
formal systems for arithmetic of mathematical interest.

The theorems are also of considerable importance to the philosophy of
mathematics. They are widely regarded as showing that Hilbert's
program to find a complete and consistent set of axioms for all of
mathematics is impossible, thus giving a negative answer to Hilbert's
second problem. Authors such as J.R. Lucas have argued that the
theorems have implications in wider areas of philosophy and even
cognitive science as well as preventing any complete theory of
everything from being found in physics, but these claims are less
generally accepted.

Gödel's first incompleteness theorem, perhaps the single most
celebrated result in mathematical logic, states that:

For any consistent formal, recursively enumerable theory that
proves basic arithmetical truths, an arithmetical statement that is
true, but not provable in the theory, can be constructed. That is, any
effectively generated theory capable of expressing elementary
arithmetic cannot be both consistent and complete.

(In other words, an infinite set of elements like the set of natural
numbers, which is generated by a finite number of axioms, can never be
proven to be self-consistent. That is, there will always be true
statements that cannot be proven true, and false statements that
cannot be proven false. And it can never be shown that there are not
provable statements within the system that are self-contradictory. -
HD)

Kurt Gödel (April 28, 1906 Brno (Brünn), Austria-Hungary (now Czech
Republic) - January 14, 1978 Princeton, New Jersey) was an Austrian
American mathematician and philosopher.
--
Howard
.

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