Thursday, September 30, 2010

Goedel's Theorems and Christian Philosophy

What Einstein did for Physics, Godel did for Mathematics. However, what the latter did in his proofs has more application in philosophy, and specially Christian Philosophy.

One of Godel's Theorem which affect arithmetic is that (in lay man's terms) there are things that are true, or there are statements that are true but there is no proof of it. There are true statements in a system that have no proofs in that system. So how does it apply to Christianity?

Well this applies to the idea of God. Think about it for the moment. That means faith in God is plausible, to say the least. In fact, Godel had a mathematical proof for the existence of God but it only got published posthumously. He knew he would be persecuted if he came out of the closet as a Christian believer (incidentally his biographers say he was Lutheran). He knew other issues would cloud his mathematical involvement and he would be carried out to other debates had he made noises.

At any rate, one of the things that came around his theorems is the matter of consistency.

Many people think that if a system of belief is consistent, that means it is true! Not so in mathematics. So when I hear Islamic apologists criticize the Bible for alleged inconsistencies and they claim that the Qu'ran has not got them, who are they trying to impress? One does not have to have divine intervention to have a system that is consistent. Mathematicians are doing that for centuries now. I think the Calvinists should listen to this too. Consistency does not imply truth necessarily. However, truth implies consistency.

Hence, I dare say, the Word of God is true and therefore consistent. Jesus says so. Think about that once again.

Then there is also the RC apologists who is able to prove many things from Catholic dogma, as if this is a tower of strength. This is false notion too. For in mathematics, if your system is able to prove any statement under the sun, something is wrong, it is inconsistent. For a system to be consistent, there must be statements it cannot prove or pry on. The sophist motto is ex falso quod libet. From a contradiction prove anything. If you are operating on this mode, watch out your system of belief has a contradiction and that will compound more confusion.

Concordian thinking, at times, pleads ignorance, which is a good thing and a correct thing to do. Go only so far as Scripture. Because, fools rush in where angels fear to thread.

On the other hand, if we plead ignorance in all things, well... I think this not Christian either.



15 comments:

Brett Meyer said...

Wrapping my head around your post. This statement is interesting in regards to mathematics, "One of Godel's Theorem which affect arithmetic is that (in lay man's terms) there are things that are true, or there are statements that are true but there is no proof of it. There are true statements in a system that have no proofs in that system."

Question, in mathematics if someone claims that a statement is true but cannot provide proof for it and likewise there are no statements to refute it, does it become accepted as true on that basis alone? How is one to "prove" an unsubstantiated statement?

Can you post such a statement?

LPC said...

Hi Brett,

Thanks for this.

Question, in mathematics if someone claims that a statement is true but cannot provide proof for it and likewise there are no statements to refute it, does it become accepted as true on that basis alone?

This is a very good question and comes to the subject of axioms.

In Maths, axioms are statements that we regard as true but we have no proof of them. For example one of the axioms is (A->(B->A)).

This axiom says that A implies that something implies A. This is true and somewhat obvious. in causal talk, something is caused by something. In the ultimate sense it is true, except for God correct?

For example either A or NOT A. This is an axiom.

This self evident truth is very much seen in the subject of set theory which has lots of axioms that are assumed to be true.

With Goedel's Theorem, he proved that there are true statements aside from the axioms that are true but have no proof or you could not find a proof of it.

Example, in our language is this...
"This statement is false".

The implication of Goedel is that for the case of the existence of God, if one does not for a moment consider Scripture and Jesus as evidence, to posit His existence is plausible, because this could be one statement that has no proof, physically.

Actually we do have lots of proof that God is there and exists but our proofs are not accepted by science.

Another answer to the question is that the statement is reduced to a conjecture, and so faith takes over. Thus some mathematicians believe in the conjecture, some do not pay any cents on it.

Goedel's result is philosophically detrimental to atheist and atheist scientists, that is the short of it.

I will try an post an actula idea in arithmetic may be about prime numbers etc.

Your question has stimulated me Brett. Do send me some more.

LPC

Brett Meyer said...

This is fun. Reading your answer brought this question/statement to mind.

You state, "For example either A or NOT A. This is an axiom."
Your definition of an axiom is, "axioms are statements that we regard as true but we have no proof of them."

Isn't "A or NOT A" a self evident truth and thus proves itself. Thus "A or NOT A" is not an axiom but a ....? Not sure what it would be called but something that is self evident seems to substantiate itself and thus is proved by it's own clarity or simplicity. If it can be proved then it's not an axiom.

This line of thought extends to the point of "what is the necessity of axioms if they can't be proven and if they can't be proven how can they be used to shed light on anything else? Doesn't it become a case of chasing ones own tail for an answer when the tools to find the answer may or may not be applicable and true.

In a way this seems to relate to UOJ's insistance that God must provide something already completed for the Holy Spirit's faith to cling to, to grasp, otherwise the God's justification of the sinner won't work. UOJ says faith must cling to forgiveness distributed and cannot cling to the promise of forgiveness. I think this is another example of UOJ's perversion of faith and it's real confession that faith is truly of man - thus they can't believe man's faith can cling to a promise but must have a firm completed act to cling to - it's really a doubting Thomas thing.

Thinking through this as I type but I think there's something to that line of reasoning.

Christ's blessings to you and yours Lito - you've certainly been a blessing to me, by the grace and mercy of God.

In Christ,
Brett

LPC said...

Brett,

Ahh..
Actually , I have to correct myself and your question and comment is quite wise. I made a mistake in citing A or NOT A as an axiom. Actually A or NOT A is not an axiom but a rule of inference.

In otherwords, self-evident truth requires no proof and we do not bother as mathematicians to find proof of it, because as you said, it is obviously true. I forgot to say this but you alerted me to it, so thank you.


In a way mathematics is actually a Christian endeavour. Why ? because Scripture says, by faith we understand.
And this is what unknown to mathematicians are doing. Philosophically they have faith in their axioms!

So the mathematician says - here are the axioms of arithmetic, trust it and see that if you proceed from the axioms the whole system works, and it does....

ALso it affirms that faith is the foundation of knowledge. In a way in maths, we cannot present knowledge if we have no proof of the information we are displaying, except for axioms which are self-evident truth that we already know.


I donot like to stretch the analogy too much but the whole Scripture can be seen as God's axioms for us. They are true because God breathed it out.

This analogy is so strong so much so that in some light hearted way mathematicians even atheistic ones, say that if there is a God, they would be quite sure, He invented Maths! In light hearted mood, so say God is a Mathematician. The whole pardigm of the discipline mimics Christian Philosophy/ Discipline.

I was laughing one time when an author Howard Delong even introduced Jesus and Original Sin into his book The Profile of Mathematical Logic. I enjoyed his analogy. I will try and replicate it here.

Re:UOJ. I do not believe UOJers can claim the mathematical method for themselves. Because they violate one theorem straight away, namely: If something is true, then it must be consistent. The equivalent of this is : If something is inconsistent, then it is NOT TRUE.

We have proven time and again and from your exposition that UOJ is inconsistent with Scripture. Clearly it present God as not knowing if he has already forgiven all then requires people to believe that forgiveness so that they are forgiven etc.

Since UOJ is inconsistent, then it is NOT TRUE.

Now UOJers want to call their belief a paradox. There is a difference between a paradox and something inconsistent. Let me give an analogous statement which is a paradox:

Let A be the statement = This statement is false.

A is not true and not false at the same time. Either it is true or false, we just do not know.

UOJ is not a paradox but an inconsistency, because it affirms the statement : we are all forgiven ALREADY and we are all not forgiven YET, at the same time and in the same sense.

It was my training in maths that made me question UOJ and with your help and that of Pr GJ rejected it.

In maths, we are not suppose to collapse categories unless we have evidence to do so. For example, we cannot say one object is the same as another with out proof of isomorphism (meaning same nature just different presentation or way of viewing)? At every turn, the proof that justification = atonement always collapses, absolutely... and convincingly.

God's promises are true even it is still yet to come because God's word are axioms, they are true by virtue of the one saying it, God himself.

UOJ says something must be already completed inorder for it to be believed. This is surely false, because we cannot believe in Jesus' coming again if faith is that way. This is a blunder.

This is human reasoning and using human analogy, it is a blunder because the Bible does not depict faith that way. Abraham believed in Christ even though he has not seen Christ, he believed God's promise. Abraham looked forward to the Atonement and was justified. We look backward to the Atonement and like Abraham we get justified by faith. Correct?

God bless you bro.

LPC

Brett Meyer said...

A point to bring out about the whole doctrine of UOJ is that even though it is, in itself, inconsistent. More than that it is opposed to the clearly revealed Word of God. When I've said that UOJ is inconsistent it may sound as though UOJ has proferred additional doctrinal points that God does not reveal (it does do that) and so shines light on something new. In fact the 99% of UOJ's inconsistencies are truly perversions of what God has clearly revealed in Scripture.

I have (W)ELS quotes which claim, "the fact that we can't understand how God can at the same moment declare the whole unbelieving world righteous, forgiven, justified, guiltless AND condemned for their sin, proves that the doctrine is true. Simply because we can't understand it proves it's true." This is in fact, one reason why they reject Justification by Faith Alone, because it is consistent with Scripture. All part of the game the devil plays with them in their unbelief.

You state, "UOJ is not a paradox but an inconsistency, because it affirms the statement : we are all forgiven ALREADY and we are all not forgiven YET, at the same time and in the same sense. Yes, exactly (and more succinct)

UOJ says something must be already completed inorder for it to be believed. This is surely false, because we cannot believe in Jesus' coming again if faith is that way. This is a blunder.
I agree, Abraham could not have been forgiven/saved by the UOJists faith. And unfortunately for them, neither can they.

Mathematics looks more beautiful to me now. I very much appreciate this post.

In Christ,
Brett

LPC said...

Brett,

UOJers are quite cultic if you ask me. They are also quite arrogant in that they think those who question it must surely be blinded.

Cults and other religions also try to keep themselves afloat by masking their inconsistency by relabeling it as paradox.

If you study Budhism and Taoism it has lots of inconsistencies. Yet they make these inconsistencies sound so noble and sound so heavenly. Absurdity gets glorified. This will not work in mathematics, because the whole purpose of mathematics is to be precise in your ideas and in your knowledge.

Observe UOJers how they allow lots of inconsistencies in doctrine and Christian life. Observe how anything eventually goes. That is the fruit of inconsistency, confusion. Yet God is not the God of it but the God of order. Confusion is the devil's work. Clarity and precision is God's work.

LPC

Pr Mark Henderson said...

Hey Lito,
Has anyonee ver told you, you look just like Goedel! It's uncanny ;0)

I'm afraid that's the best response I can make - I'm an arts and humanities person, not maths and sciences. It's all way above my head.

Brett Meyer said...

Clarity and precision is God's work.

This is a great point. The sophists and false teachers will talk of how the Scriptures are muddy or gray, that we must determine the concepts and thoughts of Scripture and then deduct our doctrines from that. Really being from their own reasoning. Luther confirmed that Scripture is and must be the most clear revelation of Christian doctrine since it is literally God's Word from which all truth flows. Thus it is that the final say always goes to Scripture. For orthodox Lutherans Scripture is the Norm and the Confessions the normed norm.

And so it is with Justification by faith alone. It is precise in perfect, God designed, harmony with all the chief articles of Christian faith. UOJ and the other false man made doctrines are not precise they are sloppy, contradictory to the chief articles of Christian faith and only live by paradox and inconsistencies. Even those who promote the false gospel of UOJ cannot speak or write clearly and having sold their souls to the devil for a new path to righteousness they glory in the confusion their doctrine creates.

Clarity and precision. UOJ can only hope to attain the precision of a wasp's nest yet they only achieve a dung pile. Note how few there are who will debate the doctrine anymore. Now they delete their comments in the dark of night.

LPC said...

Pr. Mark,

I do have some bunch of white hair being now in my 50s.

Goedel though died of mental health issues. He became a hypro-condriac. In some ways I am not surprized because if one looks at his proof of his theorems, the arguments are fairly extended. This I believe took a toll on his mental health in his later age.

I do not know how far he went with his Christianity. His biographers published his proof of the existence of God after he died in logic.

Also he was originally Czech but he took on Austrian citizenship, this is why being Austrian and Lutheran people may find unusual. That Lutheran line came from his German Czech background.

LPC

LPC said...

Oh btw, Einstein and Goedel where best friends. Einstein says it was only Goedel who understood him and missed him when Goedel died. However, many peopld do not know this, but Goedel took Einstein's theory and originated the idea of time travel at the speed of light. Also what Goedel did with Einstein's theory of relativity and time has some Christian implications in a positive way.

LPC

LPC said...

Brett,

UOJ actually glorifies absurdity and thus glorifies eventually false doctrine of other religions.

In my young years as a converted atheist who became a theist but not Christian, I read eastern religious books and this is what you get, a glorification of nonsense as if nonsense is deep theology.

For example, you must have heard of the "sound of one hand clapping".

That is a sample of absurdity glorified.

LPC

LutherRocks said...

This is a great thread. I appreciate the straightforward, pragmatic and logical approach to Scripture. As Jesus said when he was blessing the children...unless you have faith such as these, you can not enter into the kingdom of Heaven. What little child is going to grasp UOJ?

"Observe UOJers how they allow lots of inconsistencies in doctrine and Christian life. Observe how anything eventually goes. That is the fruit of inconsistency, confusion. Yet God is not the God of it but the God of order. Confusion is the devil's work. Clarity and precision is God's work."

Thanks for that, Lito, I needed it. I am mustering the strength to approach the leadership of my church on some issues.

Intrepid Lutherans are sure quiet...I can't help thinking there is a dung storm going on behind the scenes...

Peace in Jesus everyone as we approach the all important anniversary of the Reformation.

Joe

LPC said...

Joe,

What little child is going to grasp UOJ?

That is another good insight from you.

It will not be surprise that there is a dung storm, there in the US, some parts (and even here) are behaving like clique which is cultic if you'd ask me.

Peace in the Lord Joe. God bless us this Reformation anniversary.

LPC

Pr Mark Henderson said...

Sometimes, I think, post-Christians are running away not from the Christian faith, but from a system which attempts to explain everything, i.e. either Calvinism or Catholicism. Not that they have always studied those systems, but they have been raised under their influence, and reject it.
On the other hand, Lutherans have their share of "wild children" as well: Marx, Nietzsche, Kiekegaard et al. Sometimes, of course, it was a very debased form of Lutheranism they had rejected.
It would be intersting to explore Goedel's Lutheran background.

LPC said...

Pr. Mark,

The result of Goedel's Theorems is the devastation of the white hope in science. The conclusion of his theorems is that mathematicians do not know what they are talking about although they now know on a higher plane that they are ignorant. It is a humbling state of affairs, something that sometimes theologians should learn.

However, Hawking does not know what he is talking about too, because if he knew that his physics which is founded on math has areas which it does not know, i.e. it cannot decide, then he would not be so arrogant as a pig as he is now.

Hawking's theory is really rubbish in the light of Goedel's Theorems. I grant that Goedel's Theorem does not outright prove in a human way the existence of God, but his theorem shows that the plausibility and sensibility of positing God is wise and not foolish at all. Of course nature can only point to God as in general revelation, unless Jesus "descends" on us, we would not know who this God is.


LPC