Re: A simple paradox in Godels incompleteness theorem that invalidat

On Oct 11, 7:50 am, Newberry <newberr...@xxxxxxxxx> wrote:
On Oct 11, 3:00 am, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:

Newberry <newberr...@xxxxxxxxx> writes:
On Oct 10, 8:55 am, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Newberry <newberr...@xxxxxxxxx> writes:
On Oct 9, 11:20 pm, Peter_Smith <ps...@xxxxxxxxx> wrote:
On 10 Oct, 03:25, Newberry <newberr...@xxxxxxxxx> wrote:

On Oct 9, 1:53 am, Peter_Smith <ps...@xxxxxxxxx> wrote:
On 9 Oct, 04:34, Newberry <newberr...@xxxxxxxxx> wrote:

On Oct 8, 8:53 am, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
The issue is whether the statement

"ANY (primitively) recursively axiomatized theory which can
represent all (primitive) recursive functions is
1) syntactically incomplete
3) omega-incomplete
is correct
Do you have an example proof theory where 1 applies but not 3?
Actually I do.

Really??

Really.

Oh, do tell then!

I'd like to see your example proof theory here also.

I already told it about 50 times and I seriously doubt that telling it
once more is going to make any difference.
http://xnewberry.tripod.com/Presuppositions_2007_05_19.html

You didn't make it clear that this was the logic you had in mind.

It might help clarify how widely the result can be generalised over
different logics ...

Peter Smith has already clarified that the generalisation supposes
that the proof system in question is effective, in that
there is a recursive procedure for deciding whether a formula is an axiom
(and whether a given inference rule applies).

Do you claim that this holds for the system linked to above?
That looks unlikely to me.

The system has not been axiomatized yet, but id does look likely to
me.

Not only has it not been axiomatized, you've not even given formation
rules for its well formed formulas. So your claim to have a
"primitively recursively axiomatized theory" is false no matter what
things look "likely" to you. You're yanking us.

MoeBlee


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