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

Jan Burse schrieb:

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

(*) The collected works of Gödel.

This is also taken from:

TYPES IN LOGIC AND MATHEMATICS BEFORE 1940
FAIROUZ KAMAREDDINE, TWAN LAAN, AND ROB NEDERPELT

About the Vicious Circle Principle:

Gödel [34] flls in this gap. He points out that whether
one accepts this second principle or not, depends
on the philosophical point of view that one has with
respect to logical and mathematical objects:

It seems that the vicious circle principle [: : : ]
applies only if the entities involved are constructed
by ourselves. In this case there must clearly exist a
definition (namely the description of the construction)
which does not refer to a totality to which the object
defined belongs, because the construction of a thing
can certainly not be based on a totality of things to
which the thing to be constructed itself belongs.

If, however, it is a question of objects that exist
independently of our constructions, there is nothing
in the least absurd in the existence of totalities
containing members, which can be described only by
reference to this totality.

I don't share this view in its fullest, his
argument about construction for the vicious
circle principle, is probably a little bit
to exagerated.

Bye

[34] Goedel , Russell's mathematical logic, The philosophy of
Bertrand Russell (P. A. Schlipp, editor), Northwestern University, Evanston & Chicago, 1944, also in [5], pp. 447Ð 469.
.

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