Suppose a theorem prover exists that mimics all of mathematics.

for every input to the TP, it outputs TRUE, FALSE, or NONSENSE.

when it inputs Godel's statement, the output is NONSENSE.

TP ( "x <-> ~Eproof(x)" ) = "NONSENSE"
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The theorem prover is trying to tell us that a statement that asserts its
own unprovability is not a valid formula. In godels proof it is 1st shown
that there is no proof of x. Then it is noticed that x asserts exactly that,
hence the dubious conclusion that x is true. But asserting x is TRUE
is itself an action that relies on a proof of x, so its really nonsense!

The conventional argument follows up on the paradox that x is proven
"in some other system". This is a consistent arrangement but is not necessary
as G is not strictly true.

Herc

Chris Degnen wrote:

In sci.logic, HW@..(Henri Wilson)

wrote
on Fri, 01 Dec 2006 10:21:47 GMT
4ax.com>:

"Phineas T Puddleduck" googlemail.com> wrote in message
news:phineaspuddleduck-5655BF.14320302122006@free.teranews.com...

"If the second law of thermodynamics were false, a ship would be able
to travel at the expense of the heat of the ocean." This argument is
typical of the era of Postscientism in which science is just money. The
argument is invalid: if the second law is false travelling would still
be impossible since the ocean and the ship would be at almost the same
temperature and in such almost isothermal conditions the heat exchange
would be extremely slow.

In another era (or in a different world) the question would be: Are
isothermal heat engines possible, although no money can be extracted
from them? In our world the silent but unanimous answer is: Who cares.
In the other world aliens would study isothermal heat engines
diligently and may even find a way to resolve the slow-heat-exchange
problem and ease the energy crisis.

Pentcho Valev