Godel did not destroy the Hilbert Frege Russell programme to create a unitary deductive system in which all mathematical truths can be deduced from a handful of axioms
htt ://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 completely artificial system called P
Godel uses axioms which where abandoned rejected dropped in 2nd ed PM. Godel used a text in PM that based on Russells revised version of PM in 2nd ed PM Russell had rejected abandoned dropped as stated in the introduction. Godel used a text with the axiom of reducibility in it but Russell had abandoned rejected dropped this axiom as stated in the introduction.
Godel used a rejected text as it used the rejected axiom of reducibility. 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
IT MUST BE NOTED THAT GODEL IS USING 2ND ED PM BUT RUSSELL ABANDONED REJECTED GAVE UP DROPPED THE AXIOM OF REDUCIBILITY IN THAT EDITION – which Godel must have known. Godel used a text in PM that based on Russells revised version of PM in 2nd ed PM Russell had rejected abandoned dropped as stated in the introduction. Godel used a text with the axiom of reducibility in it but Russell had abandoned rejected dropped this axiom as stated in the introduction. Godel used a rejected text as it used the rejected axiom of reducibility.
The Cambridge History of Philosophy, 1870-1945- page 154
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
“Russell gave up the Axiom of Reducibility in the second edition of
Principia (1925)”
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”
In Godels collected works vol 11 page 133
it says AR is dropped
quote
In the second edition of Principia (at least in the introduction) ...the axiom of reducibility is dropped
Godels paper is called
ON FORMALLY UNDECIDABLE PROPOSITIONS
OF PRINCIPIA MATHEMATICA AND RELATED
SYSTEMS
but he uses an axiom that was abandoned rejected given up 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
Godel constructs an artificial system P made up of Peano axioms and axioms including the axiom of reducibility- which is ABANDONED REJECTED GAVE UP DROPPED 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
Russell following Wittgenstein took it out of the 2nd ed due to it being invalid. Godel would have known that. Russell Ramsey and Wittgenstein new Godel used it but said nothing .Ramsey points out AR is invalid before Godel did his proof. Godel would have known Ramsey’s arguments Ramsey would have known Godel used AR but said nothing. Every one knew AR was invalid and was dropped from 2nd ed PM they all knew godel used it but nooooooooooooo one said -or has said anything for 76 years.
htt ://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 completely artificial system called P
Godel uses axioms which where abandoned rejected dropped in 2nd ed PM. Godel used a text in PM that based on Russells revised version of PM in 2nd ed PM Russell had rejected abandoned dropped as stated in the introduction. Godel used a text with the axiom of reducibility in it but Russell had abandoned rejected dropped this axiom as stated in the introduction.
Godel used a rejected text as it used the rejected axiom of reducibility. 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
IT MUST BE NOTED THAT GODEL IS USING 2ND ED PM BUT RUSSELL ABANDONED REJECTED GAVE UP DROPPED THE AXIOM OF REDUCIBILITY IN THAT EDITION – which Godel must have known. Godel used a text in PM that based on Russells revised version of PM in 2nd ed PM Russell had rejected abandoned dropped as stated in the introduction. Godel used a text with the axiom of reducibility in it but Russell had abandoned rejected dropped this axiom as stated in the introduction. Godel used a rejected text as it used the rejected axiom of reducibility.
The Cambridge History of Philosophy, 1870-1945- page 154
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
“Russell gave up the Axiom of Reducibility in the second edition of
Principia (1925)”
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”
In Godels collected works vol 11 page 133
it says AR is dropped
quote
In the second edition of Principia (at least in the introduction) ...the axiom of reducibility is dropped
Godels paper is called
ON FORMALLY UNDECIDABLE PROPOSITIONS
OF PRINCIPIA MATHEMATICA AND RELATED
SYSTEMS
but he uses an axiom that was abandoned rejected given up 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
Godel constructs an artificial system P made up of Peano axioms and axioms including the axiom of reducibility- which is ABANDONED REJECTED GAVE UP DROPPED 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
Russell following Wittgenstein took it out of the 2nd ed due to it being invalid. Godel would have known that. Russell Ramsey and Wittgenstein new Godel used it but said nothing .Ramsey points out AR is invalid before Godel did his proof. Godel would have known Ramsey’s arguments Ramsey would have known Godel used AR but said nothing. Every one knew AR was invalid and was dropped from 2nd ed PM they all knew godel used it but nooooooooooooo one said -or has said anything for 76 years.