HB initial response is posted in the 'Are you religious thread' in this

message. It does not contain any formal comment on or extension of Godel's Incompleteness Theorems.

I have always understood that infinity means that there is no god. If there is a 'god' in a religious sense then infinity ends... The characteristics applied to 'god the unknown' are man made...like this sentence is true, the one true god, etc.. it goes on... Cogi, You have no idea what exists outside of the system. 'Outside' is an endless paradox...

In other peoples words:

"Gödel's Incompleteness Theorem demonstrates that it is impossible for the Bible to be both true and complete."

Gödel's First Incompleteness Theorem applies to any consistent formal system which:

Is sufficiently expressive that it can model ordinary arithmetic

Has a decision procedure for determining whether a given string is an axiom within the formal system (i.e. is "recursive")

Gödel showed that in any such system S, it is possible to formulate an expression which says "This statement is unprovable in S."

If such a statement were provable in S, then S would be inconsistent. Hence any such system must either be incomplete or inconsistent. If a formal system is incomplete, then there exist statements within the system which can never be proven to be valid or invalid ("true" or "false") within the system.

Essentially, Gödel's First Incompleteness Theorem revolves around getting formal systems to formulate a variation on the "Liar Paradox." The classic Liar Paradox sentence in ordinary English is "This sentence is false."

Note that if a proposition is undecidable, the formal system cannot even deduce that it is undecidable. (This is Gödel's Second Incompleteness Theorem, which is rather tricky to prove.)

The logic used in theological discussions is rarely well defined, so claims that Gödel's Incompleteness Theorem demonstrates that it is impossible to prove (or disprove) the existence of God are worthless in isolation.

One can trivially define a formal system in which it is possible to prove the existence of God, simply by having the existence of God stated as an axiom. (This is unlikely to be viewed by atheists as a convincing proof, however.)

It may be possible to succeed in producing a formal system built on axioms that both atheists and theists agree with. It may then be possible to show that Gödel's Incompleteness Theorem holds for that system. However, that would still not demonstrate that it is impossible to prove that God exists within the system. Furthermore, it certainly wouldn't tell us anything about whether it is possible to prove the existence of God generally.

Note also that all of these hypothetical formal systems tell us nothing about the actual existence of God; the formal systems are just abstractions.

Another frequent claim is that Gödel's Incompleteness Theorem demonstrates that a religious text (the Bible, the Book of Mormon or whatever) cannot be both consistent and universally applicable. Religious texts are not formal systems, so such claims are nonsense.