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)

24 comments:

Steve Newell said...

This is a very good example of why we cannot and must not apply a human logical system on Holy Scripture to create a "doctrine". What I find interesting is that many place more "trust" in the human logical system than they do what God has stated.

L P Cruz said...

Steve,

Thanks.

I notice that our RC and Reformed friends are quite into logical conclusions that may be derived from Scripture.

It is not safe to make deductions apart from explicit statements from scripture, it is even dangerous.

I notice that in Lutheran theology there is less of this. I do not think there is none of this, but there is less of this. And even if there are some, Lutherans tend to be skeptical of such conclusions.


Lito


Lito

Matthew said...

The classic argument from Silence. I'm wondering now if anyone of Godel's coleages noticed that one can fall off the horse on either side if you aren't careful with this "incompleteness" theorum.

You are right about Lutherans not reading to much between the lines, but there's ultimately a different reason than you'd expect. We tend to emphasize the promises of God and view any attempt at eisegesis to be mitigating to the recorded promises. Like if someone can mitigate say, the doctrine of total depravity, one can easily mitigate the doctrine of Justification, and there goes any basis for salvation that you could find spoken in the bible. We stick close to the text because picking and choosing ultimately leaves us with nothing at all.

Glad I added you to my blog roll. I'm enjoying your blog alot.

The Scylding said...

My own use of Godel has been centred in its implications for epistemology - somewhere there is going to be something we cannot prove (http://scyldingsinthemeadhall.blogspot.com/2007/06/augustinian-argument.html). Granted, I have yet to make that argument watertight, but there are some good things down that lane.

Phil Walker said...

Of course, the catch about Goedel's proof is that the Goedel statement is obviously true, it's just not provably so. And the other thing about it is that it's quite specific, along the lines of "This statement cannot be proved true." There's no guarantee that any other statement is non-provable.

As for Lutherans using only Scripture's explicit statements... may I humbly say that when I read Lutherans claim that Psalm 51:7 is about baptism, I get a little suspicious about this "we jus' read the Bible" line? Or again, needle you on how this fits in with the normative principle of worship? ; )

L P Cruz said...

Matt,

Thanks bro, I hope this blog becomes a source of help and edification if it is not proving to be so, I might as well go home and let the experts do it.

L P Cruz said...

Scylding,

Thanks for stopping over.

I am amused. Godel's Theorems are meant for formal systems. Specifically in number theory, it is basically the self referent statements that are syntactically valid but has no proof for it akin to liar paradox.

In other words if you want to say that statement A follows the 1st Incompleteness theorem, A has to be a self referent statement.

Have you looked at intuitionistic logic? In that logic, something is true only if you have a proof of it and as a Lutheran I would be constructivist in that respect.

Also you said consistent systems cannot be complete. This is not true ! For in propositional logic, it is complete! Remember that Godel was dealing with First Order Logic not PL and FOL has enough rope to hang yourself.

Lito

L P Cruz said...

Phil,

Mate, thanks for visiting.

Absolutely correct, G-Statements are self-referent statements like - 'this statement is a lie'.

Hahaha,(LOL) I did admit that we do deductions too like scholastics do!

You got us on that one bro, but we have other bullets on baptism hanging on our holster!

Lito

Augustinian Successor said...

If I may add, the Roman 'inference' or logical sense is different in kind from the Reformed.

The Reformed could never have deduced the Bodily Assumption of the BVM because this presupposes the existence of PROPOSITIONS in the form of AXIOMS in Scripture, which of course is lacking or ont supplied Therein. This may sound 'reductionistic' but is the Reformed method of establishing doctrine by good and necessary consequence (as per the WCF). In other words, the PERSON of the BVM cannot be abstracted FROM Scripture and or PLACED in the context of Tradition. Divine Revelation is circumscribed by Scripture alone (sola Scriptura). For the Romans, the source of Divine Revelation is acknowledged to be Scripture, but it contra sola Scriptura, it is formally insufficient.

The formal boundary of Divine Revelation is both Scripture and Tradition, hence the Roman understanding of the development of dogma vis-a-vis dogmatisation.

The Reformed and Lutheran avowedly holds that the confessional principle articulates the material and formal principle of Divine Revelation to coincide with Holy Scripture, the alone Word of God, i.e. EXTERNAL Voice of the Logos (Logic) made Flesh.

So, the Reformed and Lutheran traditions within the greater Reformation tradition do hereby repudiate the Roman view of development of dogma as extra-biblical and therefore, pertaining to its dogmatisation of pious opinions on the basis of papal infallibility as ANTI-SCRIPTURAL, and ANTI-CHRIST.

Jason

L P Cruz said...

Bro. Jason,

Scriptural statements are AXIOMS, that is a perfect way of describing Scriptural statements. You are a bit more rigorous than I am in your exposition, well done.

Scripture is operating in a logic (the average layman not familiar may find this strange) but it is a higher and more sublime one above us, ie super logic.

Building doctrine from direct assertions are safer rather than doctrines from deductions.

We do share that procedure in common though the BoC does not have a statement concerning the use of reason, unlike WCF does.

Lito

Augustinian Successor said...

Dear Bro. Lito,

I've just got my copy of the BoC! I'm in the midst of joining a Lutheran church in Kuala Lumpur, which belongs to the Lutheran Church in Malaysia and Singapore (LCMS), but no connections with LCMS (USA) rather planted by missionaries from the ELCA. However, it is a non-confessional and broad Lutheran denomination which allows for ordination of women. But what to do? Confessional Lutheranism is virtually non-existent in Malaysia.

In fact, Lutheran identity is almost obscured were it not for the insistence on the True and Real Presence of Jesus in the Bread and Wine. Sacramental symbolisms such as the font and altar with the cross above as the constant and perpetual sign of Objective Justification prevent the further erosion of Lutheran identity and distinctiveness, as are the essentials of the Divine Service including ministerial absolution and robes.

But Our Lord, in His grace alone, has given me the privilege to be in the Presbyterian, Reformed, Anglican and now Lutheran traditions = the Reformation Tradition.

Yes, even though I do not necessarily agree with Lutheran Scholasticism (Orthodoxy) but I admire and support Lutheran Orthodoxy and am thoroughly sympathetic to Lutheran Orthodoxy. I personally do not regard the Pietists as true Lutherans.

Bro. Lito, have you read Robert Kolb's "Bound Choice, Election and the Wittenberg Theological Method", publ. by Lutheran Quarterly Books? I've got my copy, and it's a fascinating account of the predestinarian controversies in the Lutheran tradition up until the FoC.

TQ

L P Cruz said...

Hey God bless you Bro. Jason,

You can be confessional in your own heart maybe you can one day start a work that is confessional!

My denom is LC(Australia). There are 3 varieties of Lutheranism, there is the strict (LCMS/WELS/ELS), there is center(my denom, AALC etc) and there is loose (ELCA and other LWF subscribers). My denom was founded by orthodox and pietist strains and some are a bit liberal now. Some are crypto-Romanists which I observe are present in LCMS. The confessional guys here are not that strict compared, they are German migrants and not Americans that is the reason why. They show respect treating our differences as intramural. Yet we have produced orthodox guys which got associated with LCMS for example eg Nagel, Marquart they used to be from Australia. The late Hermann Sasse was from Australia.

Over here we are fighting other issues, and we can easily divide if we wanted to, we are not that hot on Reformed and Lutheran quarrel, we are a bit beyond that. Our ministers participate in ministerial projects and fellowships. We are all minorities here because Australia is more pagan than Christian and with the flow of Muslim migrations we who name the Gospel - Reformed and Lutheran would have to show where we are together more than where we are apart. We can have our quarrel again when things are already different but right now the pagan world has no label it recognizes except the word Christian. All brands are treated the same, in ridicule and indifference.


There are no denoms that do not have a problem all of them do! The saying of Jesus on speck on your brothers eye but a log in yours is so appropriate!

I was Calvinistic too but I could never without hesitation subscribe to the WCF, so even when I was worshiping in a Presby church and the people there were good and gracious ie very Christian and more hospitable, I could not get myself into membership.

I was looking for a confession I can agree with without mental reservations so far the BoC is where I find myself at home with.

I am aware of the controversy prior to FoC, I do not have Kolb's article but I have heard of him. The truth was that when Luther passed away his shoes was hard to fill, and the Reformation world was looking for Lutheran leadership but they provided none, hence the controversy arouse. It took a while, but that is the historical fatc - they failed at the right moment to give leadership.

I hope that is changing now.


Lito

The Scylding said...

Lito -

You're right. As I said, the argument wasn't complete - or maybe a bit tatty? However, it might still serve well as a buffer against Dawkins-like atheism, as the latter is absolutely scientific-dependant - which implies it rests on (amongst others) arithmetical systems - which Godel demonstrates cannot be complete.

Intuitional logic (not that I'm very knowledgeable) seems to me akin to what Lewis used in the Pilgrim's Regress: The figure Reason could tell you what is in your mind, not what is the truth. IOW, it was about relational truth, not absolute truth.
And that is just it - my argument was originally in dealing with individualism (as per character "J"), and subsequently evolved into an argument with "scientific" calvinsim (Doug Woukoun) and classic RC'sm (Bryan). Thus the argument was in fact a first order argument, but I need to flesh it out, I agree.

L P Cruz said...

Scylding,

Please let me know if you have made some revisions of your exposition. I will be interested.

Now admittedly 1st Theorem can be used to believe in God.

But the tack is again, not to employ it for we have proof that God exists per axiom from the Bible - he reveals himself, he acts and he creates and Jesus is that action of God.

The idea is to appeal to another source outside our assertions. The atheist would have to deal with the notion of axioms and why there as systems that work which axioms may have no proof.

Now in intuitionistic logic, which I think is akin to our Protestant philosophy of sola scriptura, something is true iff you have a proof of it.

For example, a unicorn exists, OK, show me where it is and bring it to my face.

God exists, my proof - the axiom of Scripture.

I think we will have fun on this next up on my list is "defining truth need not solve the lie paradox".

What do you think?

Lito

jim cronfel said...

Dear Lito,
sorry about my outburst but I need a review!

Logos means logical means axioms:


http://www.sermonaudio.com/sermoninfo.asp?SID=11180514494

In Christ,
your old buddy,
Jim Cronfel

L P Cruz said...

Actually, Jim, I am sorry too for the delay. Righty-oh, comments coming up over the week end.

Lito

The Scylding said...

Lito,

I answered you yesterday, but the post disapeared! No, I haven't updated it yet, what with moving into a house with a garden that had no attention for 10 years, unpacking stuff I haven't seen for 13 months etc. So my proper thinking time is somewhat limited of now - and I really need to consider that argument carefully. I do have some ideas though....

L P Cruz said...

First things first Scylding, go back to your blogging !

Safe move...

Lito

Mark said...

Lito,
Sorry, this is a little off thread, but further to your remarks about strict, centrist & loose Lutheran church bodies, the
LC-MS & AALC are now in fellowship as of the recent LC-MS Convention.
It's an interesting move. Also, within the Missouri Synod itself there is a continuum from the right to the centre, and even a few marginals on the left, much as in our LCA.

L P Cruz said...

Pr. Mark,

I have spoken with quite a few LCA pastors and they describe our LCA as centrist which I believe I am at home with. Having lived this long I am under no illusion that there is a perfect Synod/Denomination. What matters is what happens on the ground I am in.

What is the point isn't it, of me (say as a pastor) correcting the Synod if my parish is in disarray? What is the point of that if I don't get my sermon right, I fail to show Jesus' Law/Gospel in my sermon, my people are still starving and are considering going to where food is found?

Synod politics and controversies sometimes provide a good foil for me to excuse my daily duties as pastor.

My $0.02 of my thoughts should I be a pastor in our LCA.


Lito

Mark said...

Lito,
Yes, we certainly must first tend to our own patch and only deal in other matters as the Lord sees fit to involve us, which please God will be as little as possible.
As Dr Sasse used to say, one good sermon works more for the advancement of the Gospel than all the synods and councils put together.

And, perhaps, one day you *will* be a pastor in the LCA!?

L P Cruz said...

Amen Pr. Mark.

Do pray for guidance, I got this energy/enthusiam and I want to do somework promote the very very good news!

Blessings,

Lito

Mark said...

And our church needs good men who love the Gospel to consider the ordained ministry, Lito. I will certainly pray on this matter for you. In the meantime, blessings on your current studies.

L P Cruz said...

Pr. Mark,

Blessings I will let you know what happens.

Lito