Ponicare Russell et al said self referencing statements ie impredicative
definitions are invalid
texts books on logic tell us self referencing ,statements (petitio
principii) are invalid
Godel uses at least 2 in his incompleteness theorem 1
The general result as to the existence of undecidable propositions reads:
Proposition VI: To every ω-consistent recursive class c of formulae
there correspond recursive class-signs r, such that neither v Gen r nor
Neg (v Gen r) belongs to Flg© (where v is the free variable of r).
Godel gives a prof of this
he uses in that proof forumlas 1-45
formula 16 is self referencing
16. 0 N x ≡ x
(n+1) N x ≡ R(3) * n N x
note N x appears on both sides of the formular
formula 28 which is defined from formular 16 is self referencing
28. 0 St v,x ≡ ε n {n <= l(x) & v Fr n,x & not (∃p)[n <=
l(x) & v Fr p,x]}
(k+1) St v,x ≡ ε n {n ∃p)[n < p < k St v,x & v Fr p,x]}
note St v,x appears on both sides of the formular
thus his incompleteness theorem is derived from 2 invalid self referencing
statements and according to colin leslie dean his theorem is thus
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
By
COLIN LESLIE DEAN
B.SC, B.A, B.LITT (HONS), M.A, B,LITT (HONS), M.A,
M.A (PSYCHOANALYTIC STUDIES), MASTER OF PSYCHOANALYTIC STUDIES, GRAD CERT
(LITERARY STUDIES)
GAMAHUCHER PRESS WEST GEELONG, VICTORIA AUSTRALIA
2007