Re: Jan Burse gives support that godels use of impredicative statments invalidates his theorem

elsiemelsi schrieb:
� 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.)

What Godel understood by "propositions which make statements about
themselves"

is the sense Russell defined them to be

'Whatever involves all of a collection must not be one of the
collection.' Put otherwise, if to define a collection of objects one must use the total collection itself, then the definition is meaningless.
> This explanation given by Russell in 1905 was accepted by
> Poincare' in 1906, who coined the term impredicative definition,
> (Kline's "Mathematics: The Loss of Certainty"

Did you find a new concept of the enemy?
Impredicative definitions?
Are you sponsored by a pissed of decedant of Russel?

BTW(*): There is an interesting correspondence of Gödel and
Behmann, which shows that he was aware that untyped comprehension
leads easily to inconsistencies, such like the russel set.
So thats why his comprehension axiom is typed.

There is also an interesting correspondence of Gödel and Carnap,
which shows that he was aware that recursive definitions can
be replaced by second order definitions,
although impredicative.

Probably the decedant is pissed of by the success of Gödel...

(*) The collected works of Gödel.
.

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