Re: A simple paradox in Godels incompleteness theorem that invalidat

On 4 Oct, 04:29, Newberry <newberr...@xxxxxxxxx> wrote:
On Oct 3, 8:21 am, Peter_Smith <ps...@xxxxxxxxx> wrote:

Sigh. More idiocy.

Gödel's "holds for a very wide class of formal systems" is entirely
different from your "independent of the nature of the formal system".
The theorem holds for those those formal systems whose nature is such
that they can encode enough arithmetic. In other words, the
applicability of the theorem depends crucially on the nature of the
formal system under consideration.

I have a problem with this vagueness. Goedel proved a number of things
about one particular system:

1) It is syntatctically incomplete
2) It is semantically incomplete
3) It is omega incomplete
4) It cannot prove its own consistency

Specifically which of these holds for ANY system that can encode
enough arithmetic??

Prescinding from standard worries about exactly what we mean by
"cannot prove its own consistency", then being a primitively
recursively axiomatized theory that contains Q (Robinson arithmetic)
gives us all of (1) to (4). [Errrr .... is that the sort of answer you
wanted??]

.

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