What impact does Godel's Incompleteness Theorem have to the Catholic faith?

[Ben_Sinner]

I brushed on this topic a little in a different thread, but I will make it the main focus on this thread.

What impact does Godel’s Incompleteness Theorem have on the Catholic faith?

Some people have used it to prove that we cannot know absolute truth, others have used it to prove the existence of God.

From what I understand of it, it states that our logic is inconsistent and we can never prove that what we actually conclude in our logic can never be proven.

An example of the theorem goes like this.

**1) Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.

1. Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.
2. Smiling a little, Gödel writes out the following sentence: “The machine constructed on the basis of the program P(UTM) will never say that this sentence is true.” Call this sentence G for Gödel. Note that G is equivalent to: “UTM will never say G is true.”
3. Now Gödel laughs his high laugh and asks UTM whether G is true or not.
4. If UTM says G is true, then “UTM will never say G is true” is false. If “UTM will never say G is true” is false, then G is false (since G = “UTM will never say G is true”). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
5. We have established that UTM will never say G is true. So “UTM will never say G is true” is in fact a true statement. So G is true (since G = “UTM will never say G is true”).
6. “I know a truth that UTM can never utter,” Gödel says. “I know that G is true. UTM is not truly universal.” **

My question is, what implications does this have for the faith? People have used it to defend the faith and others have used it to refute the faith. Some have used it to say that we cannot ever truly know our own minds, etc.

Would God be bound by this theorem? If yes, would he still be ultimate truth?

How does this coincide or contradict with the Catholic teaching of absolutes and our ability to know them?

What are the criticisms of this theorem?

 

[Vic_Taltrees_UK]

Outside the present universe, apparently, is one with no fewer than four dimensions of space alone, not considering time etc.

Picture some of their version of California Redwoods out there and try to measure them with your mum’s tape measure!

Or, ferry a Fiat 500 - old style - not Abarth - out there and enter it in one of their Grand Prix races!

 

[Bob_Crowley]

…

An example of the theorem goes like this.

**1) Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.

1. Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.
2. Smiling a little, Gödel writes out the following sentence: “The machine constructed on the basis of the program P(UTM) will never say that this sentence is true.” Call this sentence G for Gödel. Note that G is equivalent to: “UTM will never say G is true.”

…

**

If we allegorise the Creator as the UTM, then Godel is claiming he’s got the program that requires God to act in certain ways.

Which is rubbish. God is infinite, and his thought processes are infinite. If we allegorise God as needing a program to think, then His program is infinite.

Godel couldn’t write a sentence upon which God could not pronounce true judgement.

Godel can’t get hold of the program.

In any case a machine that can answer “any question at all” would require an infinite program, since there is an infinite number of questions that could possibly be asked.

And I fail to see how this proves or disproves Catholicism. What’s the relevant question?

 

[multitude]

Using Godel’s Incompleteness Theorem to prove God is iffy; it also works the other way round. But it actually shows that you can’t just rely on reason alone. So no, it has no real impact on religious faith, because faith and reason are not opposed.

 

[Ben_Sinner]

If we allegorise the Creator as the UTM, then Godel is claiming he’s got the program that requires God to act in certain ways.

Which is rubbish. God is infinite, and his thought processes are infinite. If we allegorise God as needing a program to think, then His program is infinite.

Godel couldn’t write a sentence upon which God could not pronounce true judgement.

Godel can’t get hold of the program.

In any case a machine that can answer “any question at all” would require an infinite program, since there is an infinite number of questions that could possibly be asked.

And I fail to see how this proves or disproves Catholicism. What’s the relevant question?

Because it is trying to prove that any logical system is inconsistent, which would mean that what we know about God, ourselves, and the laws of logic may also be flawed as well. Thats why I entered the proof or disproof of Catholicism in the question.

 

[inocente]

Because it is trying to prove that any logical system is inconsistent, which would mean that what we know about God, ourselves, and the laws of logic may also be flawed as well. Thats why I entered the proof or disproof of Catholicism in the question.

Might be your choice of words, but the theorems don’t prove that logical systems are inconsistent, they instead show that it’s impossible to completely prove that any system is consistent:

“Gödel’s two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories. The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F. According to the second incompleteness theorem, such a formal system cannot prove that the system itself is consistent (assuming it is indeed consistent).” - plato.stanford.edu/entries/goedel-incompleteness/

 

[fisherman_carl]

Because it is trying to prove that any logical system is inconsistent, which would mean that what we know about God, ourselves, and the laws of logic may also be flawed as well. Thats why I entered the proof or disproof of Catholicism in the question.

If that were true then Godel’s theorem would contradict itself since doesn’t it rely on logic?

If Godels theorem is true then logic is inconsistent.
Godels theorem uses logic.
Therefore if it is true then it is itself inconsistent.
Therefore Godels theorem is not true.