colin leslie dean's attack on godel STANDS any more attempt

[ladyjane]

After debating aporia on colin leslie dean’s claims that godels proof is invalid he finally said

ok

thus colin leslie dean’s attack on godel STANDS

so any more who want to try - and fail

hahahaha

[aporia]

you would make a great politician dean
you constantly take quotes out of context and suggest that they say much more than they actually do
my “ok” was only assenting that godel was using axiom of reducibility
it does not follow that godel’s proof is wrong or worthless as i discuss in the thread

[ladyjane]

my “ok” was only assenting that godel was using axiom of reducibility

godels proof is as worthless as if his proof used a sstem in which was an axiom 1+1=7
all very interesting but in fact worthless

for at least 2 reasons
but godel extended/generalized his proof to other systems based on an invalid system

During the proof of theorem VI we did not use any other properties of the system
P than the following:

1. The class of axioms and deduction rules (i.e. the relation “immediate conse-
   quence”) are primitive recursively definable (as soon as you replace the basic
   signs by numbers in some way).
2. Every primitive recursive relation is definable within the system P (in the sense
   of theorem V).

Hence there are undecidable propositions of the form ∀x.F(x) in every formal
system that fulfills the preconditions 1, 2 and is ω-consistent, and also in every extension
of such a system by a primitive recursively definable, ω-consistent class of axioms. To
[191]
this kind of systems belong, as one can easily confirm, the Zermelo-Fraenkelian axiom-
system and the von Neumannian system of set-theory,

and he based his proof on an abandoned system PM
he would have known russell rejected abandoned system PM which used the axiom of reduciblity

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

books.google.com/books?id=I09hCI … _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
helsinki.fi/filosofia/gts/ramsay.pdf.

“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
books.google.com.au/books?id=Pd5 … 6QrI&hl=en
“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

books.google.com.au/books?id=lgD … nOYs&hl=en
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

[/quote]

[aporia]

this post is superfluous and should be locked
it just contains dean/ladyjane’s premature victory dance
the conversation continues in the original thread