Showing posts with label logicalism. Show all posts
Showing posts with label logicalism. Show all posts

Saturday, December 14, 2013

Merry Christmaths

My postings have been scarce this year.

It will be even more so because I am writing a booklet for first year maths students on proofs. I got dismayed when I encountered senior maths majors having no clue and no rigour when writing proofs.

God's blessings for Christmas to those who often come here.

LPC

Saturday, February 09, 2013

The fallacy of C F W Walther and his disciple Jack "The Strawman" Kilcrease

Universal Objective Justification (UOJ) started with a fallacy and so it still produces more fallacies even today. JBFA people discussing UOJ errors with a UOJ adherent need to first step back and give the UOJ adherent a course on Critical Thinking 101. When you point to a UOJ a fallacy, the UOJer treats it like water off a duck's back, it just does not hit them like normal people would.

In fact if you examine the posts and comments here and you look at how a UOJers interact with us, you will soon discover UOJers do not have a capacity to evaluate a fallacy.

For a clue on logical fallacies you can find a good read here.


A few days ago, I responded to a post by found at Intrepid Lutherans found here.

There I was responding to a comment that the BoC Writers may have fallen into error in their own writings. In the election controversy ignited by C. F. W. Walther and based on his on account, his opponents were quoting to him the understanding of the BoC Lutheran “Fathers”. Here is what he said…

The principal means by which our opponents endeavor to support their doctrine, consists in continually quoting passages from the private writings of the fathers of our Church, published subsequent to the _Formula of Concord_. But whenever a controversy arises concerning the question, whether a doctrine is Lutheran, we must not ask: "What does this or that 'father' of the Lutheran Church teach in his private writings?" for he also may have fallen into error;

Indeed they may have, but the issue is not to state what in general is possible, but to demonstrate clearly in actuality where they erred against Scripture on a particular subject. The fallacy of Walther above is what can be called “If you do not believe me you are a heretic” fallacy. This is another force of argumentum ad baculum. This is a form of bullying, psychological bullying.

What else was Walther saying – if the Fathers disagreed with me, it is they that is in error not me. The test is not to put the Fathers first on the stand, rather the test is first put Walther on the stand.

Walther was an arrogant churchman, and so is his modern fan – Dr. Jack “Fallacious” Kilcrease, to which I now turn.

In his post found here, he titled it To Reject Objective Justification is to Reject Election.

As usual, Jack’s post is overflowing with fallacy, it is a lot of fun dissecting it and using it when I give a course in Critical Thinking. He provides me plenty of material for a seminar I would like to give and I would entitle as – How to argue like a bad Theologian.  I do not have time that is why this took a few days to write but I will give you a few samples. These few examples are warning enough for you not to be misled by false reasonings:
1.     The first fallacy is found by observing the title of the post. Remember I just spoke about argumentum ad baculum? The title sets the reader up to swallow a fallacy called argumentum ad consequentiam, the negative form.
2.     The false testimony “He [me, LPC] does not believe in it [election]” is so pregnant with fallacy, in fact a very abysmal attempt to put me – an anti-UOJer in a bad light.  He was able to conclude this because of the quote I just made?  This is the usual tertium non datur fallacy, the denial of a 3rd possibility fallacy. Jack “The Strawman” Kilcrease wants you to believe there is a false dilemma.  It is just like saying  - if you do not believe in the Democratic Party’s policies, then you must be a Republican. Huh? Are there not independents in USA? That is the form of reasoning Dr. Strawman wants you to follow.
3.     He then says Believers are only bound to writings that serve as a public confessions of faith and not necessarily to the private writings of a particular theologian”. This is the non sequitur fallacy. I do not subscribe to the private writings of particular theologians as if they were a confession also.  This is jumping the shark fallacy.  Jack is the one who misunderstands when one uses the quotation of the Fathers and so Walther misunderstood too in quickly dismissing them. Rather the writings were being used to support an argument, it is not because the opponents of Walther subscribe to them as a confession. This is Jack’s favorite fallacy – The Strawman fallacy. He makes arguments on my behalf or asserts them as if I was doing them and then tares them down. Voila!  The point is disposed (so he thinks).
4.     He then says, “In other words, if in response to Christ's death God does not speak forth a universal word of reconciliation, but simply pronounces reconciliation on those who believe, we are left with two options”, he is again setting up the believer to accept false dichotomy. Let me illustrate, they say if you reject OJ you must believe in Limited Atonement. Do Brett Meyer, Dr. Jackson and Pr. Rydecki and Pr. Bickel believe in Limited Atonement(LA)? I was a Calvinist! I know what Limited Atonement is when I see one. Jack has no clue as to the Scriptural arguments being used by Calvinists to support LA.
5.     Lastly Jack shows his own self-negation of his title post which is a thesis he believes in. He says, “In a word: rejection of OJ also compromises the Lutheran doctrine of election (something I do not think Paul Rydecki appreciates, since he still claims to believe in election!)”. Dear folks, here he provides a counter-example to his own thesis, by his admission! We know Rev. Rydecki rejects OJ yet by Jack’s very own admission, he states Pr. Paul still believes in election. A fish is caught in the mouth. Jack negated the thesis title of his post. So Jack illustrates how fallacious he himself is.

I see he has lots of registered followers. I pity those folk who admire him.They do not know they are following a "blind man".

Thursday, March 01, 2012

A proof for the existence of God

I am just having some rest and recreation, my doctor says I must rest after they placed a stent in one of my heart arteries. What an irony, the one that is supposed to be giving me health (food) is the one that is killing me.

Here goes the proof....consider the following sentences:
1.) God exists
2.) None of the sentences in this pair is true.

Let us call sentence 1 and 2 as G and N respectively. Then we have the following conjunction of sentences as a pair, G & N.

Now G or N may be true or false, we do not know which is which.

Assume first that N is true. If so, then we have a contradiction because there is supposed to be no sentence in the pair that is true, and so the value of G is irrelevant. Whatever it is G & N is inconsistent.

Assume now that N is false. If so, then the negation of N means at least one of the pair is true. Since there are only two sentences, G and N and we know N is false, it must be G that is true.

Thus in order for statement G & N to make sense or for it to be consistent, G must be true.

Hence G is true or God exists.

This is my elaboration of Buridan's Proof of the existence of God.

Thursday, April 28, 2011

To know the man, ask his wife

This is not me. That is the picture of mathematician and logician Kurt Gödel.

What Einstein did for Physics, Gödel did to Mathematics and Logic.

Gödel identified himself as a baptized Lutheran. Many academics are embarrassed to admit that Gödel might have been a true believer.

When people make claims that Gödel was a secret Christian, people in academia are quick to dismiss and make appeal to his biography how he denied this or that. You see, academia does not allow a man with a great mind to be a Christian as well.

Gödel wrote his mathematical proof for the existence of God. I suspect he did not publish it while he was alive for fear of being persecuted. However, it is in God's good providence that it was kept waiting until he passed away.

I pointed out in some Internet discussion of his Christian leanings and right away I was presented with disclaimer etc. etc.

It is funny that his wife Adele testified that her husband, while alive, would read the Bible every Sunday morning. That is why I said to the nay sayers - hey forget what this professor or official biographer wrote, if you want to know the man, ask his wife.

Lastly Gödel's quoted statements presupposed a Christian understanding of reality.

He said... "I only believe in apriori truths".

Well, where do you find apriori truths? How else if not from God who first declares them? Apriori truths are only found when God defines or declares them.

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.



Monday, December 07, 2009

Is self-reference required?

I often read other people's blog. My teachers here taught me that in order to write, you should read. So I read some comments and interactions that take place in other people's blog. Recently I have read of an RC Apologist saying that Scripture does not teach the Reformation principle -Scripture Alone, or sola scriptura. Hence, it is not taught by Scripture.

His objection (I paraphrase).

"There is no Scripture in Scripture, that says Scripture alone is sufficient for faith and practice".


In logic, this is called a self-reference. It is a statement that speaks about the statement itself.

Here is another example:

"This statement is a lie".

Our language is capable of self-reference, but such referencing is not capable of being evaluated. It goes into cycles. So in the above, if that statement is false, then it is true and is not a lie, which it said it is etc etc, you can go crazy at this.

So going back to the requirement of the RC apologist, he seems to be saying that in order for sola scriptura to be true, you should find a statement of it in Scripture. There is one in Scripture such as 2Tim 3:16-17 that matches this but this is dismissed by RC apologists because it is not explicit enough.

There is a fallacy going on in the apologist's requirement. There is no necessity that for a document to be true, it has to state something about its own truthfulness and if it does not, then it is not adequate to inform.

Another point is this, even if there is one such explicit statement, the apologist can come back and say - well self-reference is not valid anyway because you are simply stating your statement is true, does not make it true.

Sophistry is like that, your system is able to prove or refute too much. At first blush they think this is virtue, but as I often say - this is not virtue, instead it is vile. A form of reasoning that is able to prove anything you like is not a good thing because that means you have falsehood also inside it.

Ex falso quodlibet - from a contradiction (falsehood) you can deduce anything. This is the fallacy that sophistry includes and is hidding inside that form of reasoning and for this reason is able to prove anything.

As fallen people, we are capable of sophistry. Even in culture such as the pop culture of young peole, you can observe this happening today.


When people are swimming in their own sophistry, they are not aware of it or fanatical adherence makes them deny it. It is like telling the fish - hey do you know you are swimming in water? Huh, what water?




Wednesday, February 25, 2009

Scientific bias

Laypeople should not think that scientists are unemotional unbiased people. They have biases and as bigoted as some of us. Scientists are into the politics of ideas. They are into band wagon and what is the "flavor of the month theories". They are swayed by popular ideas just like any of us. In fact most of them follow the crowd, or the mainstream, it is good for their career.

Some laypeople think that scientists are active passionate seekers of the TRUTH. You have to laugh because right now, some of them do not have a definition of TRUTH. Most do not even adopt such category in their mental machinery.

What do I mean by politics of ideas? I mean, scientists throw their weight on a particular theory not because they have investigated the merits of such a theory but because it is popular, i.e. since lots of people are into this stuff, so they reason, then it must be good and worth their time. This happens so much so that if you present an idea that is even vaguely challenging the popular view, they look at you as a moron, someone not to be taken seriously. They did this to Godel and Einstein.

I come from a traditional mathematical background, I was taught to look for elegance. Even in my programming practice I strive for it. What do we mean by elegance? We mean it is the simplest solution to a problem. However, most scientists are not convinced that the simplest solution is usually the answer to a complex problem. Simplicity is beauty.

Let us remember scientists have presuppositions and biases, they are human beings just like the rest of us; the smartest ones recognize their biases and have learned to be skeptical of themselves.

Tuesday, December 30, 2008

A mathematician speaks about Darwinism



Here is what Dr. David Berlinski, a mathematician, who is not even a Christian, says about Darwinism.

Knowing what the scientific method entails, it is really hard to believe evolutionary theory is a science. It is science only by dictum but not in practice. Here Berlinski argues against from an engineering standpoint.

Evolution plays so much on this thing called "randomness", meaning - accidental. Perhaps this is the best time now for me to assert that randomness in science does not really exists but it is a mathematical construct, a bit bucket to direct our none-knowlege of information we do not yet possess. Philosophically and mathematically there is no such thing as randomness.

Let me explain, take the process of tossing a coin in the air, probability says that it will land 50% heads or 50% tails. Now that is true if we do not have more information than the possibilities of outcome. However, if I know that the landing of heads or tails is influenced by other factors, like wind direction, weight of the coin, material composition, if I know the starting angle my thumb lifts it and the height it goes and the material it lands (it could bounce), I will be able to predict what comes up and not rely on 50-50 chance. The reason why we go by probabilities is only because we do not know these factors, but if we do, we will not calculate what face will land based on it, we will use these information to build a formula and that is what we will use.

Evolution says that information is random but randomness when you go down to the core is none-existent.

As a person trained in mathematics, I have to have more faith to believe that evolution theory is science.

Saturday, December 13, 2008

Godel and Falsifiability of Evolution

Falsifiability in science is a very important concept. For me, a scientific theory deserves serious consideration only if it is falsifiable. Simply put, assume the theory to be false, can we have a method of verifying this physically by experiment or observation? OK, I am Popperian ( Karl Popper another Lutheran) in this regard, I offer no apologies and not ashamed of it because I believe his requirement of falsifiability is common sense.

Example of what is falsifiable: Theory of Gravity: It says what goes up must come down ( spinning wheel ... I won't sing it). Assume this theory is false, is there a way of confirming its falsehood? Yes, throw an object in the air and if it does not land down, you can say - heck Newton was wrong. Ergo: Theory of Gravity is scientific.

Take the case of Theory of Evolution - is this falsifiable? No. There is no physical method of validating its falsehood. Why? You need ions and ions of time and by that time, the experimenter is already dead before he sees evidence of this. So, sorry this is not science. I don't buy it for that reason - it does not meet falsifiability. There is no physical way of observing this phenomenon in action

Aha, but maybe there is!

Enter Kurt Godel (my patron logician - see my picture? another Lutheran , OK you get it I am biased). Godel brought Einstein's Theory of Relativity (ETR) to its final conclusion. Godel calculated that by virtue of ETR, it is possible to do time travel, if you travel at the speed of light.

So how does Godel help falsifiability of Evolution?

Simple, we ask the Evolutionary Theorist when she thought a particular specie evolved to another - she says , this happened according to carbon dating, for the sake of argument, 10Billion years ago.

Easy. We set the time machine to year = -10,000,000,000 years and go there and observe Evolution in action. You can even see that specie giving birth and even die.

Sounds good? Ya with me? No? You think this is nonsense? Well at least deep nonsense.

Monday, December 08, 2008

Consistency, not enough.

Most people are swayed by apologists who claim that their systematic theology is consistent within itself.

Consistency is appealing to many people. Common sense can detect when statements are contradictory. Apologists would point to the Law of Non-Contradiction, that it is not violated by their theology, and so on and thus it must be true. So laymen are easily sucked up by such propaganda.

Do not get me wrong, consistency is very very important and it must exist in a system. However, it is not enough. It is a necessary condition but it is not sufficient; and this is where the unsuspecting Christian gets rounded up. They get rounded up because they look at consistency syntactically, and not semantically.

When it comes to TRUTH, consistency is not enough. Rather you must demonstrate a world wherein your statements are true (in logic, this is called a model).

Example:

All unicorns are horses that have one horn.
Silver is a unicorn.

Ergo: Silver has one horn.

This is good syllogism, and it is consistent, valid reasoning. But this is not yet true. We must demonstrate there are indeed unicorns. We must demonstrate also there is a unicorn named Silver. So where is that world?


The name calling in Calvinism/Hyper-Calvinism or Arminianism/Hyper-Arminianism etc happening in the Evangelical world hinges on the concept of consistency, but consistency is not enough.

Consistency is good, and it is mandatory, we will not accept any less, but the question with consistency is this - consistent with what? With philosophy or the Bible?


This is where I find Lutheranism different. It has no shame, no insecurity and no sense of guilt when it is not able to answer certain questions. Faith does not always have the answers, it believes what the Scripture promises even when the senses say otherwise.

Monday, October 15, 2007

Did not mean to

...cause quite a stir in this blog. Mine was an honest innocent question...I was just asking why is it that Calvinists who believe in baptismal regeneration can quote Calvin on their side, and at the same time Calvinists who reject it, can also quote Calvin on their side too?! It seems to me that Calvin and Melanchton (who were friends) tended to revise some thoughts they had and they kept on re-writing, this does not seem to happen with Luther at least in vital issues like Word and Sacrament. What I mean is that no baptismal regeneration denier can quote Luther on his side. It will never happen.

At any rate, it appears that Calvin believed that baptism conveyed regeneration...to the elect only. That means, some babies and adults are just getting wet. The reasoning seems to be that since the Jewish nation got circumcised and yet not all who were circumcised believed in the Messiah then that meant ( for the church father - Calvin), it is happening only to the elect.

Putting aside the other issues that go with regeneration, let me go back on that reasoning. The question I would have asked next is this - the fact that someone got circumcised during OT times and yet did not believe, did that mean that nothing was given? OK, now look at these baptized folks living like the devil and even denying Christ, so does it prove that they have never been regenerated at their baptism?

I know, it is funny for me to argue this way since I was a credo-bapti-costal.

There is some connection being made by Calvin on a regenerated man and his faith i.e. the regenerate will never abandon faith. This needs some further quizzing. If the baptized individual denies faith does that mean nothing was given to him? Anyway, the more pressing idea is on the elect. In other words, baptismal promises of God are only to the elect as far as this idea of Calvin goes. Since we do not know who are the elect, we may baptize everyone anyway and yet not hold on to the promise of God attached to it. Of course, we will never know who the elect are, besides baptism is effective only for them. So what to do? Believe and not believe baptism does something.

To say that God only regenerates the elect in baptism is to make a tautological statement. In my view it fails to add meaning to the pool of data. From my training, tautologies are helpful only if they add or advance information to the existing knowledge we have. You can forever repeat true statements and yet not terminate your reasoning process with new knowledge. I can prove this; say you have A-->B, B-->C and we want to prove A-->C. You can start by assuming A. Yet you can keep on asserting A-->A again and again, a tautology, you can do this infinitely without terminating the proof. The step is still valid but does not help. See what I mean?

I hope my Calvinistic brothers/sisters see that with those caveats or qualifications on baptism the practice itself looses its sense of meaning, at least that is true in the Reformed camp, of all varieties too. I think this accounts for why there are heated exchanges from within Calvinism in various sectors, between non-regenerative and regenerative, between paedo and credo baptizers etc. This type of squabble does not happen amongst Concordians (I mean at least in this area of baptism). I am a bit sad though, I wish Calvin did not have to modify or re-qualify his statements. There would have been a lot less people becoming upset at each other.

Saturday, September 01, 2007

Another Proof - all numbers are the same

I found another proof for this theorem--

Theorem:
All numbers are the same.

Proof:

We prove by induction on any number n. For initial case, we now that 1 = 1. Now for inductive hypothesis: assume it is true for any number n and now show it is true for n+1. We know that n+1 = n+1, hence it is also true for the case n+1.

QED. (I think it should be replaced by LOL)

Want another even shorter proof?

Proof:
We use proof by contradiction. Assume it not true that all numbers are the same. We know that 1 = 1,hence a contradiction, thus all numbers are the same.

LOL.

Want another even really shorter proof?

Proof:
Trivial (the mathematicians favorite word).

LOL.

What is the moral of the story? If sophistry can be done in maths, the more it can be done in theology.

The Book of Concord in the Apology charges their adversary with sophistry. A sample is in Article 6 verse 26

26] May God put to confusion these godless sophists who so wickedly distort God's Word to their own most vain dreams! What good man is there who is not moved by such indignity? "Christ says, Repent, the apostles preach repentance; therefore eternal punishments are compensated by the punishments of purgatory; therefore the keys have the power to remit part of the punishments of purgatory; therefore satisfactions redeem the punishments of purgatory"! Who has taught these asses such logic? Yet this is neither logic nor sophistry, but cunning trickery. Accordingly, they appeal to the expression repent in such a way that, when the inexperienced hear such a passage cited against us, they may derive the opinion that we deny the entire repentance. By these arts they endeavor to alienate minds and to enkindle hatred, so that the inexperienced may cry out against us [Crucify! crucify!], that such pestilent heretics as disapprove of repentance should he removed from their midst. [Thus they are publicly convicted of being liars in this matter.]

Thursday, August 23, 2007

Ahh, that's a negative, over...

My Professor and I were discussing over lunch and in passing the notion of negation. What happens when we negate a proposition? For example NOT P. If it is NOT NOT P, does this mean P? In classical logic, yes, but that is an axiom (depending on how you structure, it can also be a theorem). We have a thing called "negation as failure". For example if I can not prove NOT P, we conclude it is P. Yet that is because we assume that NOT NOT P ->P, i.e. implies P. In general this is not true, I know this is hard to believe, I still get mental on this.

Now what does this have anything to do with theological ideas? Well, a plenty. Notice that when we say NOT P, we are not saying what it IS. We are saying what it is NOT, and not what it IS. For example, if I say "this is not a pen", I am saying what it is not, but what it IS has a myriad if not infinite of possibilities. Using your eyes and looking to where I point my finger to the thing I am referring to, well, you can infer what it might be. Now if we are only communicating non-visually, like conversing like this, via blog, then nothing helps to clarify when I state a negation to you.

My concrete example then is found in the Chalcedonian Formula. There we read this words in reference to the Lord Jesus being God-Man...
inconfusedly, unchangeably, indivisibly, inseparably
The above is what we are not to do with his God and Human natures. That is, NOT confuse them, NOT change them, NOT divide them, NOT separate them.

Whatever we do, we are not to do the above. You can do plenty of reflecting on it but see to it that you do not fall on the negation's edge. Because, if you do, you get into error and that can be fatal spiritually.

As you notice, the mathematical-logician's downfall is negation. For the theologian, well, he gets into trouble when he crosses "negation" too.

Wednesday, July 25, 2007

Jimbo's Book



One of the greatest delights of this internet world is that you meet new friends, brothers and sisters in Christ. My buddy Jim Cronfel, a Reformed guy (one day he will come to the light ;-)), sent me a copy of his first book. The subject is the idea of annihilationism, and Jim does the job of critiquing this concept with a passion. Congratulations to Jim, it is not often that one writes a book that the masses can read and it is about Christian faith too. I know of only a few in Evangelical world that believes this, one is Dr Stott mentioned in the book and I think the Adventists believe in this concept too. He would appreciate a comment or two.

Speaking of books, I think it is a privilege to have written a book. Perhaps also, I can turn my thesis into a book one day, when it is finished. Its tentative title is "Contextualizing Description Logics" or something like that. My wife is looking forward to it as she thinks it would be a wonderful gift idea. She says it has lots of uses for every day folk like her. She says, it can be used as a door stopper, paper weight, or a decorative item. She is a very perceptive and clever girl.

Thursday, July 19, 2007

Godel's Theorem and Religious Assertions



If you are not a geek, you may be intimidated by this post, please don't be. What I am posting here may sound way above your head but hang on a bit, you may find this post interesting if not intriguing as it is related to Christianity in an indirect way.

You must have heard of Albert Einstein (you haven't? you must be gen X), but very likely you may have not heard of of Kurt Godel (see my picture? That's his photo). If Einstein is to Physics, then Godel is to Mathematics. Both of these figures discovered major results that revolutionized their fields. In one way or another, you must have heard of Einstein's Theory of Relativity, remember your high school physics? I doubt if you have heard of Godel while you were doing your high school algebra. You encounter him only if you are taking logic or number theory subjects, that is quite true but let me reduce in a nutshell the point I am about to make.

Godel is known for his Completeness and Incompleteness Theorems. Skip the first one, but let us focus on what his 1st Incompleteness Theorem because this has a relationship to theology.

In a nutshell, Godel's 1st Incompleteness Theorem may be stated this way on a popular level - there are some true things or statements that can not be proven. Remember this is my popularizing of it but technically what he stated was in the realm of arithmetic about arithmetic truths (about numbers and their properties). Since our language includes arithmetic (human language does) then simplistically, there are some true statements that have no proof in our world. This line of reasoning sounds reasonable but let us for the sake of argument, agree to this even though such popular notions is just an analogue of Godel's.

Now this has plenty of implications for the people of faith. For the one committed to sola scriptura, beliefs must be gathered from assertions made by Scripture. For those who are not committed to sola scriptura, then they may employ this theorem to their advantage. They can assert a statement of belief with nothing to back it up.

Let me give an example, take the RC belief in the bodily assumption of Mary. There is no direct support of this from Scripture and no matter how one tries, the Scripture just does not give even a suggestion that this has happened. Try as one may, it only winds up in frustration, making hard for Protestants to be convinced. Now to an RC apologist who is quite an expert when it comes to Philosophy ( they really are philosophically savvy and sophisticated), Godel's 1st Incompleteness Theorem may be appealed to for support - they can say "Mary was assumbed bodily into heaven" is one of these true statements that have no proof!. Let as call this statement - M.

There is a catch though, it won't work. The reason is that in order for them to say that M is true, they are still left with work to do, they still have to prove that M is a G Statement ie it satisfies the Theorem's properties. Hence, they must demonstrate that M is one of those statements that the 1st Theorem speaks about. Where do you go to prove M has the property of Godel's Incompleteness Theorem? You wind up showing a proof which is a type of question begging exercise.


(for amusement see here for weird reasonings based on the fact that since the Bible does not speak about all things we may derive many things)