On 7/25/2012 4:18 PM, John Clark wrote:

`On Wed, Jul 25, 2012 Stephen P. King <stephe...@charter.net
``<mailto:stephe...@charter.net>> wrote:
`
> This lack of uniqueness [of Godel numbering] is a huge weakness!

`A huge weakness in regard to what? It certainly does not weaken
``Godel's proof! A Godel number is just a name given to a well formed
``symbol or sentence in a formal logical system, any statement in a
``logical system has a unique number. It turns out that there are an
``infinite number of ways to assign a unique number (name) to every such
``symbol or sentence, but Godel only needed one way to prove what he
``wanted to prove so he picked a method that he happened to like and was
``in his opinion easier to use than most. If you are uncomfortable with
``his way for some reason use your own method for assigning numbers to
``statements, the results will be the same. If there is more than one
``way to prove something it does not make it less certain.
`

`What Godel then did was find a way, in any logical system that is
``powerful enough to do arithmetic, to carefully construct a sentence
``that says in effect "the formula that has the Godel number G can not
``be proven in this system"; and then showed that the Godel number of
``that very sentence is G. Incredibly he found a way for a formula to
``talk about itself, in this case it is saying "I can not be proven", so
``if you prove it then your logical system is inconsistent, you can
``prove things that are not true, and if you can't prove it then it's
``incomplete. Incomplete is unfortunate but inconsistent would be
``catastrophic.
`
John K Clark

It is a weakness of the "1p plural" idea as Bruno defines it.
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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