the australian philospher colin dean points out that godel makes 2
deceitful moves in his imcompleteness theorem proof
http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf
godels incompleteness theorem reads- note it says to every ω-consistent
recursive class c of formulae
Godel's first Incompleteness Proof at MROB at MROB
Quote:Proposition VI: To every ω-consistent recursive class c of formulae there correspond recursive class-signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg(c) (where v is the free variable of r).
now
1) he derives his incompleteness theorem from system P which is made up of
peano and PM but decietfully says it applyies to other system
quote
Quote:In the proof of Proposition VI the only properties of the system P
employed were the following:
1. The class of axioms and the rules of inference (i.e. the relation
"immediate consequence of") are recursively definable (as soon as the
basic signs are replaced in any fashion by natural numbers).
2. Every recursive relation is definable in the system P (in the sense of
Proposition V).
Hence in every formal system that satisfies assumptions 1 and 2 and is
ω-consistent, undecidable propositions exist of the form (x) F(x), where
F is a recursively defined property of natural numbers, and so too in
every extension of such
[191]a system made by adding a recursively definable ω-consistent class
of axioms. As can be easily confirmed, the systems which satisfy
assumptions 1 and 2 include the Zermelo-Fraenkel and the v. Neumann axiom systems of set theory,
note his theorem says
to every ω-consistent recursive class c of formulae
but he has only proved his theorem for system P ie PM
so he cant extend that to to every ω-consistent recursive class c of
formulae
he thus trys to decieve us by saying a proof only relevant to system PM is
relevant to every ω-consistent recursive class c of formulae
2 after useing peano and PM in his proof he says
WITHOUT PROOF that footnote 16
Quote:16 The addition of the Peano axioms, like all the other changes made in the system PM, serves only to simplify the proof and can in principle be dispensed with.
he has only said that peano and PM can be dropped in any proof after
making his deceitfull extention of his theorem and then
this is deceitfull circular reasoning
in other words
he reasons incorrectly and deceitfully
example
i have used system P to make my proof but my proof is general to other
systems which are not P[WITHOUT PROOF]thus we can drop system P in other
incompleteness proofs [WITHOUT PROOF]
from these decietfull acts people have argued that the system P proof is
only an object proof
but
it is the main proof -as godel tell us
quote
Quote:In the proof of Proposition VI the only properties of the system P
employed were the following
and from that proof he gets his incompleteness theorem AND FROM NO WHERE ELSE
THUS GODELS PROOF IS A HOTCHPOTCH OF TRYING TO DECIEVE
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