Godel did not destroy the Hilbert Frege Russell programme

[zamac]

The Australian philosopher colin leslie dean shows that

 

Godel did not destroy the Hilbert Frege Russell programme to create a

unitary deductive system in which all mathematical truths can can be

deduced from a handful of axioms

 

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

 

Godel is said to have shattered this programme in his paper called "On

formally undecidable propositions of Principia Mathematica and related

systems"

 

but this paper it turns out had nothing to do with Principia Mathematica

and related systems" but instead with a completly artificial system

called P Godel uses axioms which where not in his version of PM thus his

proof/theorem cannot apply to PM thus he cannot have destroyed the Hilbert

Frege Russell programme and also his system P is artificial and applies to

no system anyways

 

colin leslie dean shows that Godel constructs an artificial system P made

up of Peano axioms and axioms including the axiom of reducibility-

which is not in the edition of PM he says he is is using. This system is

invalid as it uses the invalid axiom of reducibility. Godels theorem has

no value out side of his system P and system P is invalid as it uses the

invalid axiom of reducibility

 

 

godel uses the axiom of reducibility

he tell us he is going to use it

 

“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)”

 

NOTE HE

SAYS HE IS USEING 2ND ED PM -where the axiom of reducibility was

repudiated given up and dropped

 

 

 

and he uses it in his axiom 1v and formular 40

 

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

 

“ [40. R-Ax(x) ≡ (∃u,v,y,n)[u, v, y, n <= x & n Var v & (n+1)

Var u

& u Fr y & Form(y) & x = u ∃x {v Gen [[R(u)*E(R(v))] Aeq y]}]

 

x is a formula derived from the axiom-schema IV, 1 by substitution

“

 

 

 

http://www.math.ucla.edu/~asl/bsl/1302/1302-001.ps.

 

 

"The system P of footnote 48a is Godel’s

streamlined version of Russell’s theory of types built on the

natural numbers as individuals, the system used in [1931]. The last

sentence ofthe footnote allstomindtheotherreferencetosettheoryinthatpaper;

KurtGodel[1931,p. 178] wrote of his comprehension axiom IV,

foreshadowing his approach to set theory, “This axiom plays the role of

[Russell’s] axiom of reducibility (the comprehension axiom of set

theory).”

 

 

(BUT

 

IT MUST BE NOTED THAT GODEL IS USING 2ND ED PM BUT RUSSELL TOOK THE AXIOM

OF REDUCIBILITY OUT OF THAT EDITION – which Godel must have known.

 

The Cambridge History of Philosophy, 1870-1945- page 154

 

http://books.google.com/books?id=I0...WOzml_RmOLy_JS0

Quote

 

“In the Introduction to the second edition of Principia, Russell

repudiated Reducibility as 'clearly not the sort of axiom with which we

can rest content'…Russells own system with out reducibility was

rendered incapable of achieving its own purpose”

 

quote page 14

http://www.helsinki.fi/filosofia/gts/ramsay.pdf.

 

Russell gave up the Axiom of Reducibility in the second edition of

Principia (1925)”

 

 

 

http://books.google.com.au/books?id...sh0US6QrI&hl=en

Phenomenology and Logic: The Boston College Lectures on Mathematical

Logic and Existentialism (Collected Works of Bernard Lonergan) page 43

 

"in the second edition Whitehead and Russell took the step of using the simplified theory of types DROPPING THE AXIOM OF REDUCIBILITY and not worrying to much about the semantical difficulties"

 

 

 

 

Godels paper is called

 

ON FORMALLY UNDECIDABLE PROPOSITIONS

 

OF PRINCIPIA MATHEMATICA AND RELATED

 

SYSTEMS

 

but he uses an axiom that was not in PRINCIPIA MATHEMATICA thus his

proof/theorem has nothing to do with PRINCIPIA MATHEMATICA AND RELATED

SYSTEMS at all

 

Godels proof is about his artificial system P -which is invalid as it uses

the ad hoc invalid axiom of reducibility

 

 

system P is the system from which he derives his incompleteness theorem

quote from the van Heijenoort translation

 

 

”Theorem XI. Let κ be any recursive consistent63 class of

FORMULAS;

then the SENTENTIAL FORMULA stating that κ is consistent is not

κ-PROVABLE; in particular, the consistency of P is not provable in

P,64provided P is consistent (in the opposite case, of course, every

proposition is provable [in P])". (Brackets in original added by

Gödel“to help the reader”, translation and typography in van

Heijenoort1967:614)

 

Godel tells us

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

around Peanos axioms..."

 

and

system P contain the axiom of reducibility

 

 

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)”

 

http://www.math.ucla.edu/~asl/bsl/1302/1302-001.ps.

 

 

"The system P of footnote 48a is Godel’s

streamlined version of Russell’s theory of types built on the natural

numbers as individuals, the system used in [1931]. The last sentence ofthe

footnote allstomindtheotherreferencetosettheoryinthatpaper;

KurtGodel[1931,p. 178] wrote of his comprehension axiom IV, foreshadowing

his approach to set theory, “This axiom plays the role of [Russell’s]

axiom of reducibility (the comprehension axiom of set theory).”

 

but

the axiom of reducibility was dropped from 2 nd ed PM

 

"in the second edition Whitehead and Russell took the step of using the simplified theory of types DROPPING THE AXIOM OF REDUCIBILITY and not worrying to much about the semantical difficulties"

 

EVERY ONE KNEW THAT AR WAS NOT IN 2ND ED PM EVEN

 

GODEL BUT NO ONE SAID

ANYTHING

 

thus Godel could not have destroyed the Hilbert Frege Russell programme in his paper as his proof theorem has nothing to do with PM

but

only with his artificial system P -that applies to no other system at all

[bascule]

Urrrrgh, this troll is back. Can one of the admins please do something? Like, uhh, ban with extreme prejudice?

[zamac]

Urrrrgh, this troll is back

 

what are you talking about

i thought this is a science forum

an important finding I thought you all would find interesting

 

regardless of what troll you are talking about

i get the impression calling troll is just an attempt to stop discussion

[the tree]

Dude, calm down. No-one cares. I second the motion to ban with extreme prejudice.

[zamac]

Dude, calm down. No-one cares. I second the motion to ban with extreme prejudice.

 

follow the sheep mentality

i thought science was about objectivity and facts

you show it is only about closed minds and follow the lead

SHAME ON YOU ALL no wonder they say our education systems are turning out

idiots

SHAME with your mentality true science is dead

 

why do i waste my time with fools

if you cant see and comment on a revolutionary finding

then this is not a science forum at all

 

 

why do i waste my time with fools

if you cant see and comment on a revolutionary finding

then this is not a science forum at all

[Royston]

why do i waste my time with fools

if you cant see and comment on a revolutionary finding

then this is not a science forum at all

 

Colin, your crap can be found all over the net, your argument has been addressed several times by people clearly more proficent in math than you, IOW repeating yourself won't change anybodies mind. Kindly take your crackpottery elsewhere.

[Phi for All]

follow the sheep mentality

Classic crackpot.

i thought science was about objectivity and facts

But you're assuming your ideas are already fact. That's not how science works.

you show it is only about closed minds and follow the lead

I think it's more like nobody agrees with you, for reasons they've posted in other threads and even other forums. You're the one closing his mind.

SHAME ON YOU ALL no wonder they say our education systems are turning out

idiots

SHAME with your mentality true science is dead

More crackpot classics. It *must* be everybody else's lack of education.

 

why do i waste my time with fools

if you cant see and comment on a revolutionary finding

then this is not a science forum at all

Everybody else is wondering the same thing, why do you waste your time? You just keep repeating the same junk and don't listen when someone makes a valid criticism. Repetition doesn't make your ideas any less wrong.

 

why do i waste my time with fools

if you cant see and comment on a revolutionary finding

then this is not a science forum at all

Repetition makes your ideas seem shallow and ill-formed. Like they'll fall down if you don't say them exactly the same way each time.

[zamac]

you see you show your incompetence by not attacking the arguments

by ad hominums you show you have not the intelligence to critique the views

 

come on let see some thinking rather than following the leader

[Cap'n Refsmmat]

[thread]29703[/thread]

[thread]29661[/thread] (post #19)

 

I see you're responsible for most of the threads on Godel here on SFN. Clearly you'd be familiar with the past ones, then. Why not look back and see what others have told you before?

 

Now stop posting the same thread over and over. We're getting sick of it.

[zamac]

Why not look back and see what others have told you before?

 

sorry no one has said anything except ad hominums

no one has offered a reasoned rebutal

ie

what you got to say about godel using an axiom which is invalid which is not in PM

 

"in the second edition Whitehead and Russell took the step of using the simplified theory of types DROPPING THE AXIOM OF REDUCIBILITY and not worrying to much about the semantical difficulties"

 

godel tells us AR is in 2nd ED PM

but it is not

 

“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)”

come give a reasoned reply to this fact

 

how about a reasoned reply to this fact

 

godel uses AR in his proof it is his axiom 1v

 

"The system P of footnote 48a is Godel’s

streamlined version of Russell’s theory of types built on the natural

numbers as individuals, the system used in [1931]. The last sentence ofthe

footnote allstomindtheotherreferencetosettheoryinthatpaper;

KurtGodel[1931,p. 178] wrote of his comprehension axiom IV, foreshadowing

his approach to set theory, “This axiom plays the role of [Russell’s]

axiom of reducibility (the comprehension axiom of set theory).”

 

Godels paper is called

 

ON FORMALLY UNDECIDABLE PROPOSITIONS

 

OF PRINCIPIA MATHEMATICA AND RELATED

 

SYSTEMS

 

yet it AR is not in PM

 

Russell gave up the Axiom of Reducibility in the second edition of Principia (1925)”

so his proof cant be about UNDECIDABLE PROPOSITIONS OF PRINCIPIA MATHEMATICA

 

how about a reasoned reply to this -if you have the inteligence

[the tree]

what you got to say about godel using an axiom which is invalid which is not in PM

Gödel's Incompleteness Theorems are not specific to the Principia Mathematica or any other book, they are about all formal logic systems (including the Principia Mathematica) no matter what axioms those systems may or may not use.

 

An axiom can only be invalid if it leads to a contradiction with the other axioms used in the same theorem. You already know this because you've been told enough times.

[zamac]

Gödel's Incompleteness Theorems are not specific to the Principia Mathematica or any other book, they are about all formal logic systems (including the Principia Mathematica) no matter what axioms those systems may or may not use.

 

An axiom can only be invalid if it leads to a contradiction with the other axioms used in the same theorem. You already know this because you've been told enough times.

 

sorry u have not answered the question

godels paper is called

ON FORMALLY UNDECIDABLE PROPOSITIONS OF PRINCIPIA MATHEMATICA AND RELATED

 

SYSTEMS

 

so his proof is about PM and related systems

but he uses an ad hoc axiom that is not part of PM thus his proof cannot be about PM and related systems

 

even if it applies to other systems that is just mere chance for it cannot apply to PM

and cannot have destroyed the hilbert frege russell proramme

 

even if AR is valid it was not in the ed of PM godel is using

so his proof cannt appliy to PM and related systems

CANT YOU GET IT

IT IS ABOUT WHAT GODEL DID DUMB NUMN..TS AND NOT WHAT OTHERS HAVE SHOWN

 

 

 

 

 

important mathematician say AR is invalid

ramsey

Such an axiom has no place in mathematics

 

the standford encyclopdeia of philosophy says of AR

 

http://plato.stanford.edu/entries/principia-mathematica/

 

“many critics concluded that the axiom of reducibility was simply too ad hoc to be justified philosophically”

 

and even godels complete works

From Kurt Godels collected works vol 3 p.119

 

http://books.google.com/books?id=gDzbuUwma5MC&pg=PA119&lpg=PA119&dq=godel+axiom+of+reducibility&source=web&ots=-t22NJE3Mf&sig=idCxcjAEB6yMxY9k3JnKMkmSvhA#PPA119,M1

 

“the axiom of reducibility is generally regarded as the grossest philosophical expediency “

 

go study up on the problems of AR before you keep spouting crap

 

 

 

 

ramsey

Such an axiom has no place in mathematics

 

the standford encyclopdeia of philosophy says of AR

 

http://plato.stanford.edu/entries/principia-mathematica/

 

“many critics concluded that the axiom of reducibility was simply too ad hoc to be justified philosophically”

 

and even godels complete works

From Kurt Godels collected works vol 3 p.119

 

http://books.google.com/books?id=gDzbuUwma5MC&pg=PA119&lpg=PA119&dq=godel+axiom+of+reducibility&source=web&ots=-t22NJE3Mf&sig=idCxcjAEB6yMxY9k3JnKMkmSvhA#PPA119,M1

 

“the axiom of reducibility is generally regarded as the grossest philosophical expediency “

 

go study up on the problems of AR before you keep spouting crap

[the tree]

Oh for fucks sake. Euclid's 5^th postulate wasn't invalid, it was just ugly and consistent geometries have been created without it. How can you not catch on with that? Are you completely sure you know what an axiom is?

 

'related systems' refers to every non trivial formal system (come on, this is basic stuff), but when you use it in reference to the Principia Mathematica itself then there is absolutely no reason why a theorem about the system should have a single axiom in common with the system itself.

 

If you want to actually learn about formal systems, then you need to calm the fuck down, have a cup of tea and read some Hofstadter. If you don't want to learn, then I recommend unplugging your network cable and leaving everyone else to it.

[zamac]

you say

An axiom can only be invalid if it leads to a contradiction with the other axioms used in the same theorem

which is bullsh..t

 

as euclids 5th axiom is invalid and is not in contradiction with his other axioms

you have absoLutly have no fu..ing idea about the problems of AR

you keep talking about this and it has been shown an axiom can be invalid ie euclids 5th without being in contradiction with other axioms

 

 

The independence of the parallel postulate from Euclid's other axioms was finally demonstrated by Eugenio Beltrami in 1868.

 

 

but it is invalid

so godel could have made up an axiom ie 1+1=7 independent of all his other axioms

and you would say his proof was valid- not talk crap you and every one else would say the proof was rubbish

 

so now dont change the gaol post like you all do when proven wrong

you said

An axiom can only be invalid if it leads to a contradiction with the other axioms used in the same theorem

and i showed you that euclids 5th does not contradict the other axioms but is invalid so i have disproven your claim against AR

 

but come on change the goal post

but you want say the same about godel proof

important mathematician say AR is rubbish and invalid just like 1+1=7

 

Oh for ****s sake. Euclid's 5th postulate wasn't invalid, it was just ugly and consistent geometries have been created without it. How can you not catch on with that? Are you completely sure you know what an axiom is?

 

'related systems' refers to every non trivial formal system (come on, this is basic stuff), but when you use it in reference to the Principia Mathematica itself then there is absolutely no reason why a theorem about the system should have a single axiom in common with the system itself.

 

go learn geometry euclids 5th is invalid every heard of non-euclidian geometries

for **** sake

godel used an axiom that was not in the ed of PM he is using so his proof cannot be about PM

it is not about what others have proved but what godel proved and his proof is not about PM or systems related to PM as his proof uses axioms not even in PM

for **** sake

 

Oh for ****s sake. Euclid's 5th postulate wasn't invalid, it was just ugly and consistent geometries have been created without it. How can you not catch on with that? Are you completely sure you know what an axiom is?

 

'related systems' refers to every non trivial formal system (come on, this is basic stuff), but when you use it in reference to the Principia Mathematica itself then there is absolutely no reason why a theorem about the system should have a single axiom in common with the system itself.

 

go learn geometry euclids 5th is invalid every heard of non-euclidian geometries

for **** sake

godel used an axiom that was not in the ed of PM he is using so his proof cannot be about PM

it is not about what others have proved but what godel proved and his proof is not about PM or systems related to PM as his proof uses axioms not even in PM

for **** sake

 

but when you use it in reference to the Principia Mathematica itself then there is absolutely no reason why a theorem about the system should have a single axiom in common with the system itself.

dont talk shit

even godel new that to show PM is undecidable he had to use the PM system

you talk utter crap

i dont think you have even read godels prof j

 

but when you use it in reference to the Principia Mathematica itself then there is absolutely no reason why a theorem about the system should have a single axiom in common with the system itself.

 

you dont know what you are talking about

 

godels proof is about system p

 

”Theorem XI. Let κ be any recursive consistent63 class of FORMULAS;then the SENTENTIAL FORMULA stating that κ is consistent is not

κ-PROVABLE; in particular, the consistency of P is not provable in P,64

provided P is consistent (in the opposite case, of course, every

proposition is provable [in P])". (Brackets in original added by Gödel

“to help the reader”, translation and typography in van Heijenoort

1967:614)

 

P is made up of Peano axioms and axioms from PM

 

"P is essentially the system which one obtains by building the logic of PM around Peanos axioms..." K Godel , On formally undecidable propositions of principia mathematica and related systems in The undecidable , M, Davis, Raven Press, 1965,, p.10)

 

but he use an axiom not PM so it cant be about PM

just like if he used axioms not in Peano then his system P could not be about Peano axioms

 

so his system P is completly artifical and relates to no known other system at all

 

for no others systems use AR

[YT2095]

any more Bad language or lack of Temper restraint will result in time spent in the Cooler!

 

now Smarten UP!

[zamac]

sorry

i have just realised that no one here has read godels proof

or read the iniatial post at all

 

you say an axiom is vallid untill it contradicts the other axioms in the system

that is not correct

for

i could make up any axioms which are independent of each other and oprove anything

ir fermets last theorem

e=mc3

anything

you cannot just bring ad hoc axioms into a proof as godel did

for if you could then

every thing can be proved

to give a ridiculous example

i will make two independent axioms and prove einstiens theories are wrong

1) the proof made by an idiot is wrong

2) einstien was an idiot

therefore einsteins theories are wrong

 

or axiom

1+1=7

 

2 apples + one orange + 3 plums + 1 grape

= 2+1+3+1= 2+1+1+3= 12

[bascule]

Do Not Feed The Trolls

[Phi for All]

sorry

Apology accepted. Please go somewhere else because you are inconsistent with our purpose here.