Gödel's theorem

[tkorrovi]

Epimenides paradox is that Epimenides was a Cretan and said that all Cretans were liars. It is logical to think that it goes into the loop, ie Cretans are liars, therefore Epimenides is liar, therefore Cretans are not liars, therefore Epimenides is not liar, therefore Cretans are liars etc. As a loop, it can be part of a system and a lot of programs contain such loops. Gödel made a formal system what supposed to represent every possible system, and then he did show that such formal system may be inconsistent, from what comes that there are systems what cannot be modelled by the computer. But one of the several refutations of the Gödel's theorem at homepage.mac.com/ardeshir/Godel-SimpleRefutation.html as I understand shows that such self-reference as Epimenides paradox cannot be part of the Gödel's formal system and therefore Gödel's theorem is true only for systems what don't go into such loops.

[tkorrovi]

This is what I wrote in other forums.

ON FORMALLY UNDECIDABLE PROPOSITIONS OF PRINCIPIA MATHEMATICA AND RELATED SYSTEMS
home.ddc.net/ygg/etext/godel/godel3.htm

This is the Gödel's original paper. This is how the reference of series of basic signs is calculated "Furthermore, variables of type n are given numbers of the form pn (where p is a prime number > 13). Hence, to every finite series of basic signs (and so also to every formula) there corresponds, one-to-one, a finite series of natural numbers. These finite series of natural numbers we now map (again in one-to-one correspondence) on to natural numbers, by letting the number 2n1, 3n2 … pknk correspond to the series n1, n2, … nk, where pk denotes the k-th prime number in order of magnitude. A natural number is thereby assigned in one-to-one correspondence, not only to every basic sign, but also to every finite series of such signs. We denote by F(a) the number corresponding to the basic sign or series of basic signs a." Now to have a loop, we supposed to have such reference in the formula, but then the reference to the formula would be bigger than that reference and there's supposed to be no way how we can write such loop (iteration) in Gödel's formal system, but most of the algorithms need iterations.
homepage.mac.com/ardeshir/Godel-SimpleRefutation.html
www.deducing.com/rotg.html