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Oct 2, 2007, 4:06:20 AM10/2/07

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is godel lieing when he states

Godel states that he is going to use the system of PM

“ 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)

but peter smith who has written a book on godel says that godel does not

use the system of PM ie theory of types axiom of reducibility axiom of

choice

so is peter smith correct and is Godel lieing

or

is peter smith wrong and godel does use the system PM

Oct 2, 2007, 6:37:53 AM10/2/07

to

On Oct 2, 4:06 pm, "elsiemelsi" <cyprin...@nosam.yahoo.com> wrote:

> is godel lieing when he states

>

> Godel states that he is going to use the system of PM

> " 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> is godel lieing when he states

>

> Godel states that he is going to use the system of PM

> " before we go into details lets us first sketch the main ideas of 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

>

> "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)

>

> but peter smith who has written a book on godel says that godel does not

> use the system of PM ie theory of types axiom of reducibility axiom of

> choice

>

> so is peter smith correct and is Godel lieing

> or

> is peter smith wrong and godel does use the system PM

Goedel's not lying. He discusses a system called P, which is closely

related to Russell and Whitehead's system. There are some changes

which make Goedel's proof easier, they are not essential to the

argument and Goedel gives fair notice of them. Goedel's system P is

equi-interpretable with PM with the axiom of infinity in the form

"there exist denumerably many individuals" and the axiom of

reducibility for all types. It hasn't got the axiom of choice, by the

way. I don't remember Goedel saying he included the axiom of choice in

his 1931 paper, although he did include the axiom of choice when he

announced his results in a notice prior to the 1931 paper. The proof

works fine whether you include the axiom of choice or not.

Oct 2, 2007, 6:56:16 AM10/2/07

to

On Tue, 02 Oct 2007 04:06:20 -0400, "elsiemelsi"

<cypr...@nosam.yahoo.com> wrote:

<cypr...@nosam.yahoo.com> wrote:

>is godel lieing when he states

>

>Godel states that he is going to use the system of PM

>“ 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)

>

>but peter smith who has written a book on godel says that godel does not

>use the system of PM

Nothing above indicates that Godel _is_ using the system of PM.

Peter explained this very clearly: Godel is about to prove things

_about_ that system. Before attempting to prove things about

that system he explains some key aspects of what the system _is_.

Proving something _about_ a system is not the same thing as

_using_ the system.

You're really being very slow here. It's as though I wrote a paper

proving that unicorns do not exist. You give a "refutation" -

you carefully quote the part where I explain exactly what I

mean by "unicorn", then you claim that my proof is invalid

because I'm using unicorns in the proof.

>ie theory of types axiom of reducibility axiom of

>choice

>

>so is peter smith correct and is Godel lieing

>or

>is peter smith wrong and godel does use the system PM

************************

David C. Ullrich

Oct 2, 2007, 7:02:39 AM10/2/07

to

you say

I don't remember Goedel saying he included the axiom of choice in

his 1931 paper

but you are wrong

godel uses AC just as he said he would do

quote

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.) Quite clearly the axiom of choice is part

of the meta-theory used in the deduction

I don't remember Goedel saying he included the axiom of choice in

his 1931 paper

godel uses AC just as he said he would do

quote

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,

of the meta-theory used in the deduction

have a look at deans work

"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."

http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf

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

Oct 2, 2007, 7:55:35 AM10/2/07

to

you say

Nothing above indicates that Godel _is_ using the system of PM.

Peter explained this very clearly: Godel is about to prove things

_about_ that system. Before attempting to prove things about

that system he explains some key aspects of what the system _is_.

Proving something _about_ a system is not the same thing as

_using_ the system.

he clearly uses the says he is going to use the axioms of PM in his proof

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)

which he goes on and does in axiom 1V and formula 40

quote

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

and in axiom of choice quote

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.) Quite clearly the axiom of choice is part

of the meta-theory used in the deduction

and 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 avoid the

serious problems with the theory of types and to make the theory of types

work.- without the axiom of reducibility virtually all mathematics breaks

down. (http://planetmath.org/encyclopedia/AxiomOfReducibility.html)

As he states “ We now describe in some detail a formal system which will

serve as an example for what follows …We shall depend on the theory of

types as our means for avoiding paradox. .Accordingly we exclude the use

of variables running over all objects and use different kinds of variables

for different domians. Speciically p q r... shall be variables for

propositions . Then there shall be variables of successive types as

follows

x y z for natural numbers

f g h for functions

Different formal systems are determined according to how many of these

types of variable are used...

(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.). Clearly Godel is using the theory

of types as part of his meta-theory to show something in his object theory

i.e. his formal system example.

the problem is all you mathematical genius can prove godel with your eyes

closed but you dont know what you are proving you dont know what godel was

doing and how he did it -even though you can prove it you all have no idea

what you are doing

you are all orgasaming over how brilliant the logic is but you have no

idea what he uses this logic on

Oct 2, 2007, 9:14:47 AM10/2/07

to

elsiemelsi wrote:

> you are all orgasaming over how brilliant the logic is but you have no

> idea what he uses this logic on

> you are all orgasaming over how brilliant the logic is but you have no

> idea what he uses this logic on

He "uses this logic" on some heavy-duty psychedelics, apparently.

--

Aatu Koskensilta (aatu.kos...@xortec.fi)

"Wovon man nicht sprechen kann, daruber muss man schweigen"

- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

Oct 2, 2007, 9:23:35 AM10/2/07

to

all you mathematical geniuses can add 1+1 =2

but you dont even know what numbers are

same with godels theorems

you can use your mathematical logic on his axioms and formula but you

dont know what they mean

but you dont even know what numbers are

same with godels theorems

you can use your mathematical logic on his axioms and formula but you

dont know what they mean

example

godels says he uses propositions that refer to themselves but done of you

know which are those propositions

quote 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.)

you all might be mathematical geniuses but it takes a philosopher to tell

you what your axioms formula etc mean

Oct 2, 2007, 4:05:54 PM10/2/07

to

Geeze dude, you got an axe to grind over Godel....What, did he steal

your girlfriend in grad school?

your girlfriend in grad school?

On Oct 2, 4:06 am, "elsiemelsi" <cyprin...@nosam.yahoo.com> wrote:

> is godel lieing when he states

>

> Godel states that he is going to use the system of PM

> " 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

Oct 2, 2007, 7:49:17 PM10/2/07

to

On Oct 2, 7:02 pm, "elsiemelsi" <cyprin...@nosam.yahoo.com> wrote:

> you say

> I don't remember Goedel saying he included the axiom of choice in

> his 1931 paper

> but you are wrong

> godel uses AC just as he said he would do

> you say

> I don't remember Goedel saying he included the axiom of choice in

> his 1931 paper

> but you are wrong

> godel uses AC just as he said he would do

No, I'm not wrong. The system P which is his object theory does not

have the axiom of choice. He later notes, as you observe below, that

even if we add the axiom of choice to his object theory his theorem

remains true.

> quote

> 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.) Quite clearly the axiom of choice is part

> of the meta-theory used in the deduction

>

Nonsense. The axiom of choice most certainly is not needed in the

*metatheory*.

> have a look at deans work

>

> "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."

>

No. Goedel's theorem can be proved in Bounded Arithmetic. It is as

secure as a mathematical theorem can be. Incidentally, there is no

reason to think that even ZFC is inconsistent. ZFC is accepted by

mathematicians as the "gold standard" of rigour.

> http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf

>

> 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

blah blah blah...

Oct 2, 2007, 7:51:15 PM10/2/07

to

On Oct 2, 7:55 pm, "elsiemelsi" <cyprin...@nosam.yahoo.com> wrote:

> you say

>

> Nothing above indicates that Godel _is_ using the system of PM.

> Peter explained this very clearly: Godel is about to prove things

> _about_ that system. Before attempting to prove things about

> that system he explains some key aspects of what the system _is_.

> Proving something _about_ a system is not the same thing as

> _using_ the system.

>

> he clearly uses the says he is going to use the axioms of PM in his proof

> 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> you say

>

> Nothing above indicates that Godel _is_ using the system of PM.

> Peter explained this very clearly: Godel is about to prove things

> _about_ that system. Before attempting to prove things about

> that system he explains some key aspects of what the system _is_.

> Proving something _about_ a system is not the same thing as

> _using_ the system.

>

> he clearly uses the says he is going to use the axioms of PM in his proof

> quote

> before we go into details lets us first sketch the main ideas of the

> system PM)

>

> which he goes on and does in axiom 1V and formula 40

> quote

>

> 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

>

> and in axiom of choice quote

> 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.) Quite clearly the axiom of choice is part

> of the meta-theory used in the deduction

>

> and 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 avoid the

> serious problems with the theory of types and to make the theory of types

> work.- without the axiom of reducibility virtually all mathematics breaks

> down. (http://planetmath.org/encyclopedia/AxiomOfReducibility.html)

> As he states " We now describe in some detail a formal system which will

> types as our means for avoiding paradox. .Accordingly we exclude the use

> of variables running over all objects and use different kinds of variables

> for different domians. Speciically p q r... shall be variables for

> propositions . Then there shall be variables of successive types as

> follows

> x y z for natural numbers

> f g h for functions

>

> Different formal systems are determined according to how many of these

> types of variable are used...

> (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.). Clearly Godel is using the theory

> of types as part of his meta-theory to show something in his object theory

> i.e. his formal system example.

>

No. The metatheory can be Bounded Arithmetic.

Oct 2, 2007, 11:56:51 PM10/2/07

to

you say

No, I'm not wrong. The system P which is his object theory does not

have the axiom of choice. He later notes, as you observe below, that

even if we add the axiom of choice to his object theory his theorem

remains true.

Nonsense. The axiom of choice most certainly is

not needed in the

*metatheory*.

you are wrong

russell tells us he is going to use the axims etc of system PM

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

“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)”

on page 7 he states

"now we obtain an undecidable proposition of the system PM"

clearly this undecidable proposition comes about due the the axioms etc

which PM uses

he goes on

"the ternary relation z=[y;z] also turns out to be definable in PM"

he goes on

"since the concepts ocurring in the definiens are all definable in PM"

he has told us PM is made up of axiom reducibility axiom of choice etc so

these definiens must be defined interm of these axioms

he goes on

"we now show that the proposition [R(q);q] is undecidable in PM" - again

this must mean undecidable within PMs system ie its axioms etc

further

he goes on

"we pass now to the rigourous execution of the proof sketched aboveand we

first give a precise description of the formal system P for which we wish

to prove the existence of undecidable propositions"

you call this system P the object theory but you are wrong in part

for he goes on

"P is essentially the system which one obtains by building the logic of PM

around Peanos axioms..."

thus P uses as its meta-theory the system PM ie its axioms of choice

reducibility etc (he has told us this is what PM SYSTEM IS)

thus P is made up of the meta-theory of PM and peanos axioms

thus by being built on the meta-theory of PM it must use the axioms of PM

etc and these axioms are choice reducibility etc

if godel tells us he is going to using the axioms of PM but only use some

of them in fact

then he is both wrong and lieing when he tells us that

"we now show that the proposition [R(q);q] is undecidable in PM"

and

"the proposition undecidable in the system PM is thus decided by

metamathemaical arguments"

thus simply

he tells us

1) he is useing the axioms of PM

2) the proposition is undecidable in the system PM

2)P uses as its metasystem the axioms of PM

3) so the proof in P must use PMs axioms

3) if he does not use all the axioms of PM then he is lieing to us when he

say "there are undeciable propsitions in PM, and P

Oct 3, 2007, 12:42:06 AM10/3/07

to

On Oct 3, 11:56 am, "elsiemelsi" <cyprin...@nosam.yahoo.com> wrote:

> you say

>

> No, I'm not wrong. The system P which is his object theory does not

> have the axiom of choice. He later notes, as you observe below, that

> even if we add the axiom of choice to his object theory his theorem

> remains true.

>

> Nonsense. The axiom of choice most certainly is

> not needed in the

> *metatheory*.

>

> you are wrong

> russell tells us he is going to use the axims etc of system PM

>

> you say

>

> No, I'm not wrong. The system P which is his object theory does not

> have the axiom of choice. He later notes, as you observe below, that

> even if we add the axiom of choice to his object theory his theorem

> remains true.

>

> Nonsense. The axiom of choice most certainly is

> not needed in the

> *metatheory*.

>

> you are wrong

> russell tells us he is going to use the axims etc of system PM

>

Russell? Do you mean Goedel?

Yes, the system P is a modified version of PM, but it doesn't have the

axiom of choice. You seem to have a copy of the paper, so it wouldn't

be difficult for you to verify this point by looking at the

description of the system P, if you had any competence in mathematical

logic.

> 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

>

> "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)"

>

I haven't got a copy of the paper in front of me. I'm in China at the

moment and my copy is back in Australia. If he says "choice", then

he's just alluding to the fact that the argument would still go

through if he did include the axiom of choice in the object theory.

The system P which he discusses in the main argument does not include

the axiom of choice. But it doesn't matter. If it did the argument

would still be essentially the same.

The main point is that the metatheory does not include the axiom of

choice, in fact the metatheory can be Bounded Arithmetic, which is

about as weak a metatheory as you can get.

> on page 7 he states

> "now we obtain an undecidable proposition of the system PM"

>

> clearly this undecidable proposition comes about due the the axioms etc

> which PM uses

>

The argument applies to a very large class of formal systems. Goedel

discusses this.

Have you read and understood the paper? Obviously not. Why don't you

apply yourself to the task of understanding the arguments in the

paper?

> he goes on

> "the ternary relation z=[y;z] also turns out to be definable in PM"

>

> he goes on

> "since the concepts ocurring in the definiens are all definable in PM"

>

> he has told us PM is made up of axiom reducibility axiom of choice etc so

> these definiens must be defined interm of these axioms

>

The above statements would still hold, and the argument would still be

the same, in any extension of Robinson Arithmetic. The fact that PM

includes the axiom of reducibility and the axiom of choice is

irrelevant to the argument. (Also, as a matter of fact the system P

which Goedel actually uses for the purposes of the main argument

doesn't include the axiom of choice).

> he goes on

> "we now show that the proposition [R(q);q] is undecidable in PM" - again

> this must mean undecidable within PMs system ie its axioms etc

>

But he establishes that it holds in any omega-consistent recursively

enumerable extension of second-order Peano Arithmetic (he comes pretty

close to making that first-order Peano Arithmetic), and it was

established shortly after his paper that it holds in any consistent

recursively enumerable extension of Robinson Arithmetic.

Why don't you just read the paper, instead of pretending you know what

you are talking about?

> further

> he goes on

> "we pass now to the rigourous execution of the proof sketched aboveand we

> first give a precise description of the formal system P for which we wish

> to prove the existence of undecidable propositions"

>

> you call this system P the object theory but you are wrong in part

> for he goes on

> "P is essentially the system which one obtains by building the logic of PM

> around Peanos axioms..."

>

Yes, that's right. It's the object theory. The metatheory can be

Bounded Arithmetic. Goedel certainly knew that the metatheory could be

very weak, for he observes that his argument can be made to satisfy

"all the requirements of the finitists and constructivists." I could

locate the exact quote for you if I had the paper in front of me. You

really should read the paper. Or starting learning the necessary

background knowledge that would be required for you to read the paper.

> thus P uses as its meta-theory the system PM ie its axioms of choice

> reducibility etc (he has told us this is what PM SYSTEM IS)

>

Nonsense. P is *not* the metatheory. It is the object theory. The

metatheory can be Bounded Arithmetic.

There really is no hope for you until you get that remarkably simple

point into your thick skull.

> thus P is made up of the meta-theory of PM and peanos axioms

>

Garbage. Do you even know what "object theory" and "metatheory" mean?

> thus by being built on the meta-theory of PM it must use the axioms of PM

> etc and these axioms are choice reducibility etc

>

> if godel tells us he is going to using the axioms of PM but only use some

> of them in fact

> then he is both wrong and lieing when he tells us that

> "we now show that the proposition [R(q);q] is undecidable in PM"

>

Garbage. He demonstrates, in Bounded Arithmetic, that if PM is omega-

consistent then the proposition [R(q);q] is undecidable in PM.

If you want to discuss this paper, start learning some mathematical

logic and get to the point where you can actually read the paper.

> and

> "the proposition undecidable in the system PM is thus decided by

> metamathemaical arguments"

>

On the assumption that PM is omega-consistent, yes.

> thus simply

> he tells us

> 1) he is useing the axioms of PM

> 2) the proposition is undecidable in the system PM

> 2)P uses as its metasystem the axioms of PM

*No*. No, no, no, no, no. None of the quotes you have given support

that contention. It is *wrong*. The metatheory is a weak fragment of

finitary number theory.

> 3) so the proof in P must use PMs axioms

> 3) if he does not use all the axioms of PM then he is lieing to us when he

> say "there are undeciable propsitions in PM, and P

Meaningless babble.

The *metatheory* is a weak fragment of finitary number theory.

The *object theory* is P.

In the metatheory, we demonstrate that if P is omega-consistent then

there are undecidable propositions in P.

There is no problem here.

You apparently are not capable of understanding this.

Oct 3, 2007, 1:21:23 AM10/3/07

to

you say

The *metatheory* is a weak fragment of finitary number theory.

The *object theory* is P.

The *metatheory* is a weak fragment of finitary number theory.

The *object theory* is P.

sorry you are wrong

he states he is going to use the system of PM in P with peanos axioms

System Pm is clearly his meta-theory through which he does his proof

you are wrong

he tells us clearly

1) he is useing the axioms of PM

2) the proposition is undecidable in the system PM

2)P uses as its metasystem the axioms of PM

thus

3) so the proof in P must use PMs axioms

3) if he does not use all the axioms of PM then he is lieing to us when he

say "there are undecidable propositions in PM, and P

godels meta-theory is PM it is through and by this meta-theory that he

prooes P and says

"the proposition undecidable in the system PM "

PM - its system -is clearly the bedrock of his whole argument

Oct 3, 2007, 2:57:49 AM10/3/07

to

On 3 Oct, 06:21, "elsiemelsi" <cyprin...@nosam.yahoo.com> wrote:

> godels meta-theory is PM

This is, of course, complete and utter bollocks (to use the technical

term).

PM -- or rather the simplied version Gödel calls P -- is the object

theory (the theory his is talking about). His metatheory (the body of

assumptions he brings to bear in talking about the object theory) is,

as you've been told a dozen times, very, very much weaker.

If you can't understand that very elementary, and purely technical,

point (it isn't some disputable matter of philosophical

interpretation, it is just an elementary purely mathematical fact

about the proof) after it has been explained to you a number of times

very clearly by a number of patient people, then you not only reveal

yourself as exceedingly thick (or a troll!), but you entirely

disqualify yourself as a commentator on the significance of Gödel's

theorem.

Oct 3, 2007, 2:58:15 AM10/3/07

to

On Oct 3, 1:21 pm, "elsiemelsi" <cyprin...@nosam.yahoo.com> wrote:

> you say

> The *metatheory* is a weak fragment of finitary number theory.

> The *object theory* is P.

>

> sorry you are wrong

> you say

> The *metatheory* is a weak fragment of finitary number theory.

> The *object theory* is P.

>

> sorry you are wrong

Sorry, I'm not. You clearly don't have the first clue what you're

talking about.

> he states he is going to use the system of PM in P with peanos axioms

He states that he is going to be reasoning *about* it. He clearly

intends to use it as his *object* theory, not his metatheory. He is

reasoning *about* P, not *in* P. He doesn't even need to understand

the language of P in order for his argument to work. P could just be a

meaningless game we play with symbols. For the purposes of his

argument, P is just a formal calculus for manipulating symbols and we

reason about the properties of this system using a weak fragment of

finitary number theory.

> System Pm is clearly his meta-theory through which he does his proof

>

Only someone who didn't have the first clue what he was talking about

would say such a thing. It clearly is his object theory, not his

metatheory. No-one who read the paper with any understanding would

deny that.

> you are wrong

> he tells us clearly

>

'Fraid not. You're not competent to read work like this. Learn some

logic to the point where you're capable of reading his paper, then

come back.

> 1) he is useing the axioms of PM

> 2) the proposition is undecidable in the system PM

> 2)P uses as its metasystem the axioms of PM

>

*Wrong*.

> thus

> 3) so the proof in P must use PMs axioms

> 3) if he does not use all the axioms of PM then he is lieing to us when he

> say "there are undecidable propositions in PM, and P

>

> godels meta-theory is PM it is through and by this meta-theory that he

> prooes P and says

>

You keep saying this over and over again, but you have not provided

the slightest shread of evidence for it, and no-one who read the paper

with any understanding would agree with you.

> "the proposition undecidable in the system PM "

> PM - its system -is clearly the bedrock of his whole argument

It is the *object theory*. It is the system which we reason *about*.

It is not the metatheory. It is not the system we *use* to do our

reasoning in.

He also mentions that the argument would still work even if we added

the generalized continuum hypothesis for PM. Now, in order to

appreciate this point, you don't have to believe in the generalized

continuum hypothesis.

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