# Godels incompleteness theorems are a complete failure and invalid

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### elsiemelsi

Oct 2, 2007, 2:11:10 AM10/2/07
to
The Australian philosopher colin leslie dean argues what Gödel proved he
proved this with flawed and invalid axioms- axioms that either lead to
paradox or ended in paradox –thus showing that Godel’s proof is based upon
a misguided system of axioms and that it is invalid as its axioms are
invalid."

GÖDEL’S INCOMPLETENESS THEOREM. ENDS IN ABSURDITY OR MEANINGLESSNESS
GÖDEL IS A COMPLETE FAILURE AS HE ENDS IN UTTER MEANINGLESSNESS CASE STUDY
IN THE MEANINGLESSNESS OF ALL VIEWS
http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf

For those who say godel did not use the axiom of reducibility, axiom of
choice, theory of types -or impredicative definitions
Godel states that he is going to use the system of PM -which uses the
axiom of reducibility, axiom of choice, theory of types

quote
“ before we go into details lets us first sketch the main ideas of the
proof … the formulas of a formal system (we limit ourselves here to the
system PM) …” ((K Godel , On formally undecidable propositions of principia
mathematica and related systems in The undecidable , M, Davis, Raven Press,
1965,pp.-6)

Godel uses the axiom of reducibility and axiom of choice from the PM

Quote
http://www.mrob.com/pub/math/goedel.htm
“A. Whitehead and B. Russell, Principia Mathematica, 2nd edition,
Cambridge 1925. In particular, we also reckon among the axioms of PM the
axiom of infinity (in the form: there exist denumerably many individuals),
and the axioms of reducibility and of choice (for all types)” ((K Godel ,
On formally undecidable propositions of principia mathematica and related
systems in The undecidable , M, Davis, Raven Press, 1965, p.5)

AXIOM OF REDUCIBILITY
(1) Godel uses the axiom of reducibility axiom 1V of his system is the
axiom of reducibility “As Godel says “this axiom represents the axiom of
reducibility (comprehension axiom of set theory)” (K Godel , On formally
undecidable propositions of principia mathematica and related systems in
The undecidable , M, Davis, Raven Press, 1965,p.12-13. Godel uses axiom 1V
the axiom of reducibility in his formula 40 where he states “x is a
formula arising from the axiom schema 1V.1 ((K Godel , On formally
undecidable propositions of principia mathematica and related systems in
The undecidable , M, Davis, Raven Press, 1965,p.21
( 2) “As a corollary, the axiom of reducibility was banished as irrelevant
to mathematics ... The axiom has been regarded as re-instating the semantic
2)“does this mean the paradoxes are reinstated. The answer seems to be
yes and no” - http://fds.oup.com/www.oup.co.uk/pdf/0-19-825075-4.pdf )

3) It has been repeatedly pointed out this Axiom obliterates the
distinction according to levels and compromises the vicious-circle
principle in the very specific form stated by Russell. But The philosopher
and logician FrankRamsey (1903-1930) was the first to notice that the
axiom of reducibility in effect collapses the hierarchy of levels, so that
the hierarchy is entirely superfluous in presence of the axiom.

AXIOM OF CHOICE
Godel states he uses the axiom of choice “this allows us to deduce that
even with the aid of the axiom of choice (for all types) … not all
sentences are decidable…” (K Godel , On formally undecidable propositions
of principia mathematica and related systems in The undecidable , M,
Davis, Raven Press, 1965. p.28.)
(“The Axiom of Choice (AC) was formulated about a century ago, and it was
controversial for a few of decades after that; it may be considered the
last great controversy of mathematics…. A few pure mathematicians and many
applied mathematicians (including, e.g., some mathematical physicists) are
uncomfortable with the Axiom of Choice. Although AC simplifies some parts
of mathematics, it also yields some results that are unrelated to, or
perhaps even contrary to, everyday "ordinary" experience; it implies the
existence of some rather bizarre, counterintuitive objects. Perhaps the
most bizarre is the Banach-Tarski Paradox “–
http://www.math.vanderbilt.edu/~schectex/ccc/choice.html)

Godel used impredicative definitions - but these are regarded as an evil
in mathematics

Quote from Godel
“ 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.)

yet Godels has argued that impredicative definitions destroy mathematics
and
make it false

http://www.friesian.com/goedel/chap-1.htm

Godel uses the theory of types

In Godels second incompleteness theorem he uses the theory of types- but
with out the very axiom of reducibility that was required to make the
theory of types work.
As he states “ we shall depend on the theory of types as our means for
avoiding paradox” (K Godel , On undecidable propositions of formal
mathematical systems in The undecidable , M, Davis, Raven Press, 1965,
p.63 of this work Davis notes, “it covers ground quite similar to that
covered in Godels orgiinal 1931 paper on undecidability,” p. 46.) Russell
propsed the system of types to eliminate the paradoxes from mathematics.
But the theory of types has many problems and complications .One of the
devices Russell used to avoid the paradoxes in his theory of types was to
produce a hierarchy of levels. A big problems with this device , is
that the natural numbers have to be defined for each level and that
creates insuperable difficulties for proofs by inductions on the natural
numbers where it would more convenient to be able to refer to all natural
numbers and not only to all natural numbers of a certain level. This
device makes virtually all mathematics break down.
(http://planetmath.org/encyclopedia/AxiomOfReducibility.html) For example,
when speaking of real numbers system and its completeness, one wishes to
quantify over all predicates of real numbers…, not only of those of a
given level. In order to overcome this, Russell and Whitehead introduced
in PM the so-called axiom of reducibility – but as we have seen this Axiom
obliterates the distinction according to levels and compromises the
vicious-circle principle in the very specific form stated by Russell. But
The philosopher and logician Frank Ramsey (1903-1930) was the first to
notice that the axiom of reducibility in effect collapses the hierarchy of
levels, so that the hierarchy is entirely superfluous in presence of the
axiom. But in the second incompleteness theorem Godel does not use the
very axiom of reducibility Russell had to introduce to avoid the serious
problems with the theory of types.
(http://www.helsinki.fi/filosofia/gts/ramsay.pdf)
(http://planetmath.org/encyclopedia/AxiomOfReducibility.html)

thus we see that as promised godel uses the system of PM but this systems
axioms are invalid thus making godels incompleteness theorems a complete
falure and invalid

### Peter_Smith

Oct 2, 2007, 3:04:16 AM10/2/07
to

elsiemelsi wrote:
> The Australian philosopher colin leslie dean argues what Gödel proved he
> proved this with flawed and invalid axioms

And "philosopher" (ho! ho! ho!) Dean is plain wrong, for the reasons
that have been repeatedly explained here. Repeating elementary
mistakes doesn't make them any less silly mistakes.

All together now .....

Whatever you think about the cut-down-version of PM that Gödel proves
the incompleteness of, Gödel's reasoning applies equally to other
theories that don't involves types, choice or the like. As Gödel says,
loud and clear.

Whatever you think about the cut-down-version of PM that Gödel proves
the incompleteness of, Gödel's reasoning *about* this theory doesn't
draw on type structure or choice or any other fancy feature *in* the
theory. As Gödel says, loud and clear.

Elsiemelsi might like to heed the excellent advice "when in a hole,
stop digging". But why do I think that won't happen!

### elsiemelsi

Oct 2, 2007, 3:34:15 AM10/2/07
to
sorry godel tell us all that he is going to use the axioms of PM -in his
proof

### elsiemelsi

Oct 2, 2007, 3:51:31 AM10/2/07
to
Peter smith you once said godel did not use the axiom of reducibility i
proved you wrong by pointing out he used it in formula 40
YOU WHERE WRONG HERE

Godel uses the axiom of reducibility axiom 1V of his system is the axiom
of reducibility “As Godel says “this axiom represents the axiom of
reducibility (comprehension axiom of set theory)” (K Godel , On formally
undecidable propositions of principia mathematica and related systems in
The undecidable , M, Davis, Raven Press, 1965,p.12-13. Godel uses axiom 1V
the axiom of reducibility in his formula 40 where he states “x is a
formula arising from the axiom schema 1V.1 ((K Godel , On formally
undecidable propositions of principia mathematica and related systems in
The undecidable , M, Davis, Raven Press, 1965,p.21

godel says he uses impredicative statements

“ 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.)

when i asked you to show us the propositions that make statments about
themselves you did not
thus showing us you dont know which one they are-if you dont know which
ones they are you cant say he does not use them in his proof

Even though you have written a book on godel on two point your
incompetenace has been pointed out
now you are telling us that even though godel tells us he is going to use
the system of PM he in fact does not

ie so what is this axiom used in formula 40 he tells us is the axiom of
reducibility

### zencycle

Oct 2, 2007, 4:07:30 PM10/2/07
to
Geeze dude, you got an axe to grind over Godel....What, did he steal

On Oct 2, 2:11 am, "elsiemelsi" <cyprin...@nosam.yahoo.com> wrote:
> The Australian philosopher colin leslie dean argues what Gödel proved he
> proved this with flawed and invalid axioms- axioms that either lead to

> paradox or ended in paradox -thus showing that Godel's proof is based upon

> a misguided system of axioms and that it is invalid as its axioms are
> invalid."
>
> GÖDEL'S INCOMPLETENESS THEOREM. ENDS IN ABSURDITY OR MEANINGLESSNESS
> GÖDEL IS A COMPLETE FAILURE AS HE ENDS IN UTTER MEANINGLESSNESS CASE STUDY

> IN THE MEANINGLESSNESS OF ALL VIEWShttp://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf

>
> For those who say godel did not use the axiom of reducibility, axiom of
> choice, theory of types -or impredicative definitions
> Godel states that he is going to use the system of PM -which uses the
> axiom of reducibility, axiom of choice, theory of types
>
> quote
> " before we go into details lets us first sketch the main ideas of the

> proof ... the formulas of a formal system (we limit ourselves here to the
> system PM) ..." ((K Godel , On formally undecidable propositions of principia

> mathematica and related systems in The undecidable , M, Davis, Raven Press,
> 1965,pp.-6)
>
> Godel uses the axiom of reducibility and axiom of choice from the PM
>

> Quotehttp://www.mrob.com/pub/math/goedel.htm

> "A. Whitehead and B. Russell, Principia Mathematica, 2nd edition,
> Cambridge 1925. In particular, we also reckon among the axioms of PM the
> axiom of infinity (in the form: there exist denumerably many individuals),
> and the axioms of reducibility and of choice (for all types)" ((K Godel ,
> On formally undecidable propositions of principia mathematica and related
> systems in The undecidable , M, Davis, Raven Press, 1965, p.5)
>
> AXIOM OF REDUCIBILITY
> (1) Godel uses the axiom of reducibility axiom 1V of his system is the
> axiom of reducibility "As Godel says "this axiom represents the axiom of
> reducibility (comprehension axiom of set theory)" (K Godel , On formally
> undecidable propositions of principia mathematica and related systems in
> The undecidable , M, Davis, Raven Press, 1965,p.12-13. Godel uses axiom 1V
> the axiom of reducibility in his formula 40 where he states "x is a
> formula arising from the axiom schema 1V.1 ((K Godel , On formally
> undecidable propositions of principia mathematica and related systems in
> The undecidable , M, Davis, Raven Press, 1965,p.21
> ( 2) "As a corollary, the axiom of reducibility was banished as irrelevant
> to mathematics ... The axiom has been regarded as re-instating the semantic

> 2)"does this mean the paradoxes are reinstated. The answer seems to be

> yes and no" -http://fds.oup.com/www.oup.co.uk/pdf/0-19-825075-4.pdf )

>
> 3) It has been repeatedly pointed out this Axiom obliterates the
> distinction according to levels and compromises the vicious-circle
> principle in the very specific form stated by Russell. But The philosopher
> and logician FrankRamsey (1903-1930) was the first to notice that the
> axiom of reducibility in effect collapses the hierarchy of levels, so that
> the hierarchy is entirely superfluous in presence of the axiom.
>
> AXIOM OF CHOICE
> Godel states he uses the axiom of choice "this allows us to deduce that

> even with the aid of the axiom of choice (for all types) ... not all
> sentences are decidable..." (K Godel , On formally undecidable propositions

> of principia mathematica and related systems in The undecidable , M,
> Davis, Raven Press, 1965. p.28.)
> ("The Axiom of Choice (AC) was formulated about a century ago, and it was
> controversial for a few of decades after that; it may be considered the

> last great controversy of mathematics.... A few pure mathematicians and many

> applied mathematicians (including, e.g., some mathematical physicists) are
> uncomfortable with the Axiom of Choice. Although AC simplifies some parts
> of mathematics, it also yields some results that are unrelated to, or
> perhaps even contrary to, everyday "ordinary" experience; it implies the
> existence of some rather bizarre, counterintuitive objects. Perhaps the

> most bizarre is the Banach-Tarski Paradox "-http://www.math.vanderbilt.edu/~schectex/ccc/choice.html)

>
> Godel used impredicative definitions - but these are regarded as an evil
> in mathematics
>
> Quote from Godel
> " 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

> quantify over all predicates of real numbers..., not only of those of a

> given level. In order to overcome this, Russell and Whitehead introduced

> in PM the so-called axiom of reducibility - but as we have seen this Axiom

### Jesse F. Hughes

Oct 4, 2007, 2:57:39 PM10/4/07
to
"elsiemelsi" <cypr...@nosam.yahoo.com> writes:

> Peter smith you once said godel did not use the axiom of reducibility i
> proved you wrong by pointing out he used it in formula 40
> YOU WHERE WRONG HERE

Is there any reason you provide exactly the same unconvincing
quotations post after post? Do you really believe that you'll change
someone's mind this go-round?

Give us some new material, would you? Perhaps you (or Dean or
whoever) can have a go at Cantor or something.

--
Jesse F. Hughes

"We will run this with the same kind of openness that we've run
Windows." Steve Ballmer, speaking about MS's new ".Net" project.

### Jesse F. Hughes

Oct 4, 2007, 2:55:32 PM10/4/07
to
Peter_Smith <ps...@cam.ac.uk> writes:

> elsiemelsi wrote:
>> The Australian philosopher colin leslie dean argues what Gödel proved he
>> proved this with flawed and invalid axioms
>
> And "philosopher" (ho! ho! ho!) Dean is plain wrong, for the reasons
> that have been repeatedly explained here.

I do wonder why elsiemelsi sells Dean so short. Why refer to him as a
mere philosopher, when he is also a damn fine erotic poet? "Is your
cunt hairy 2?" was a particularly fine example and with very
interesting font choices, too.

Dean is a renaissance man.

--
Jesse F. Hughes

"It is a brilliant proof you, you math haters!!!"
-- James S. Harris