Re: Godel proves his own incompleteness theorems invalid

On 30 Sep, 16:28, "elsiemelsi" <cyprin...@xxxxxxxxxxxxxxx> wrote:
peter smith says
So the reasoning Gödel uses in
proving his theorem is also certainly not impredicative (whether he is
proving the theorem about an impredicative theory or not).

but godel tells us he is using impredicative statements in his reasoning
quote
" The solution suggested by Whitehead and Russell, that a proposition
cannot say something about itself , is to drastic... We saw that we can
construct propositions which make statements about themselves,... ((K Godel
, On undecidable propositions of formal mathematical systems in The
undecidable , M, Davis, Raven Press, 1965, p.63 of this work Dvis notes,
"it covers ground quite similar to that covered in Godels orgiinal 1931
paper on undecidability," p.39.)


That quotation has absolutely nothing to do with impredicativity. It
has to do with the arithmetization of syntax (coding up propositions
about what is provable-in-T into the arithmetical subsystem of T),
which is an entirely finitistic procedure.


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