From Gödel to God

An investigation into religious beliefs:

Let’s begin with a question, probably the most important question there is: “Is there a God?” There can be two answers – or we can allow a third, “I don’t know”. But does it mean that to confidently answer, “Yes, there is a God.” or “No, there is no God.” that we have (or even need) indisputable proof? No, and with good reason. In conducting any scientifically valid investigation, we don’t seek to prove, which is impossible for anything; we hypothesize and then try to falsify[1], [2]. If something is falsifiable but can’t be falsified, we can feel that more confident that we’re closer to some kind of truth.

So then, let’s try to hypothesize: There is a God. If there is a God, can we expect certain things? In short, is there any observable phenomenon (or absence of such), which provides falsification of our hypothesis? This is a most difficult sort of enterprise and here’s why: to say that this or that is required for God’s existence means that we can reason out the mind of God. For example, one might say that if God existed, there would be no evil in the world but that is really taking unentitled intellectual liberties, as we can’t say that God does not allow evil for some reason[3] known to him/her.

Accordingly, theism is not falsifiable...directly. However, we need not be stuck in our search for the truth of God's existence, let’s hypothesize the negative: There is no God. If God does not exist, what would we expect to observe? I think we can make much more progress with this approach. If God does not exist, we should be able to find a natural explanation for everything – what physicists call a “Theory of Everything” (TOE). “Well hold on just a minute!”, I could just hear you saying. “Isn’t that taking intellectual liberties as well? To think that we can figure out the entire Universe!” Well, yes and no. It would be rather presumptuous to say that we, at any point in time, know everything there is to know but it’s quite another thing to model how everything came into existence, that is, to show that all of this is quite naturally possible.

So is there a TOE? No. Better question: is one even possible? No! Here’s what a former TOE searcher, the renowned Stephen Hawking, had to say about it:

“Some people will be very disappointed if there is not an ultimate theory, that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind.” – Hawking (2002)[4]

So why not? Why can there be no TOE? Well, as Stephen Hawking discovered, the entire thing is mathematically impossible, a consequence of Kurt Gödel’s Incompleteness Theorems from way back the 1930’s[5]. Gödel, perhaps the greatest mathematician of the 20th century, one of the greatest logicians in history and a committed believer in God, provides the proof that our Universe cannot wholly be described through science, that is, no one can give a natural explanation for it all and thereby, make God unnecessary[6]. But given the impossibility of a TOE, does that mean that God is necessary and atheism falsified? We're not quite there yet. To see how mathematical incompleteness which leads to the impossibility of a TOE also leads to God being necessary consider the following from footnote 48a of Gödel’s Second Incompleteness Theorem:

"...the true reason for the incompleteness inherent in all formal systems of mathematics is that the formation of higher types can be continued into the transfinite."

Therefore, imagine our explanations for the Universe being like a very, very large onion. As we peel away the outer layers, we move to higher type explanations. We can continue peeling away forever and ever, discovering even higher but still incomplete explanations. There comes a theoretical point where our formal systems necessarily progress toward the highest type explanation imaginable, God. He/she must exist as the only ultimate explanation which will suffice[7].

To clarify, it's not so much that a TOE is not had right now that falsifies atheism - that’s understandable given our level of scientific understanding – it’s that it can never exist and what that logically implies that falsifies atheism. The rather fiercely atheistic position taken by some under the guise of “science” is then clearly ignorant.

So now that we’ve falsified[8] that there isn’t a God[9], what’s left is that there is a God or we just don’t know[10]. Let’s deal with the latter first.

Blaise Pascal in the 17th century presented a logical argument which examined the payoffs associated with agnosticism. An agnostic can bet that there is no God or he can bet that there is a God. Pascal argued that to live as though there is a God is a better bet for the agnostic. Which, when you think about it, makes sense. If there is no God, then by living as though there is, you don’t really lose anything. When you die, you just cease to be and while there’s no reward, there is no punishment either. However, if there is a God and the agnostic lives as though there isn’t any, then when he dies not only does he loses out on a reward but he also faces punishment. So basically, a belief in God wins out.

This logical argument is not without its criticism. One that I think deserves special attention is that the argument only works for the existence of an Abrahamic-type God, that is, the God of the type believed in by Jews, Christians and Muslims. Is this fair? What about other gods, and there are literally thousands! Shouldn’t we examine things in the light of all these other religions as well? To address this criticism we can jump ahead and look at the “There is a God” possibility a little more.

If there is a God, he/she must found within objective truth ideology and here’s why: some religions (such as Eastern religions like Buddhism and Hinduism) take religious truth to be subjective, meaning that truth is based on the perspective of the person and that there are many paths that lead to God (ironically, sometimes called by them as the Absolute Truth). But this can’t be so. Because to say that “truth is subjective”, is itself to make a “true” objective statement. The entire argument is self-defeating, in that it goes: “there’s no other way to look at truth but this way: “there are many ways to look at truth”!” You see the absurdity of the argument? Furthermore, how can these many paths to God teach contradictory things about what appears to be objective reality? For example, the Hindus’ Bhagavad-Gita teaches a cycle of death and rebirth (6:40-45), the Qur'an says that Muslims die once but Kafirs (unbelievers) die twice (40:11) while Christianity teaches that everyone lives and dies only once (Heb. 9:27). Is God saying different things? They cannot all three be right. One can of course say that what’s true for you may not be true for me but we’ve already determined that that’s incorrect. No! Truth is objective and God cannot lie. So if one religion, just one, can show itself to be objectively true, to the exclusion of all other religions or paths, then we need not examine them all[11].

Of the world’s objective religions, the Abrahamic ones (Judaism, Christianity and Islam) make good starting points for our search. Together they provide the vast majority of belief in the world today and even if they don’t pass our truth test, they would at least substantially narrow down our search for God. But which one of the Abrahamic religions to begin with? Well, Christianity is an extension of Judaism and Islam crucially entails a denial of the beliefs of Christianity (that is, the Christian understanding of Jesus) so looking at Christianity provides a natural starting point.

Christianity is Jesus. Jesus is as essential to Christianity as the sun is to our solar system. Can anything be shown about Jesus that would establish the Christian God as the One True God? Yes, actually quite a lot![12] Though, only one thing I shall focus on but it’s a powerful one. You see, Jesus is unique among religion founders. Sure he made some bold claims like the rest of them but he is the only religious figure with actual, hard and fast, in-your-face, verifiable, prophecy to back those claims up!

If someone says, that tomorrow it’s going to rain and it does, you’re likely to say, “lucky guess”. But if that same person accurately predicts the weather for a whole year and tells you you’re going to trip, sneeze, yawn, get a cold, a promotion and have an accident before you do for that entire year, then you’re likely to sit up and take notice. Well, that’s essentially what Jesus did. Jesus fulfilled nearly 300 prophecies written hundreds of years before his birth[13]!

Peter Stoner in his book “Science Speaks” calculated the statistical probability of Jesus fulfilling just 8 of those close to 300 prophecies. Based on those 8 prophecies, there’s only a 1 in 1,700,000,000,000,000,000 (or a 1 in a 1.7 sextillion) chance that Jesus wasn’t who he said he was: God! To visualize that, it’s like covering an area approximately the size of Texas or France completely 2 feet deep in coins about the size of US quarters (a little less than 1 inch in diameter each). Take one of those coins and put a mark on it. Throw in the marked coin, stir it all up and then ask a blind man to randomly walk over the entire area and pick up a coin. He’ll have as much of a chance picking the marked coin as Jesus NOT being God! Wow! Oh, and note we've stopped the calculation at just 8 of Jesus' nearly 300 prophetic fulfilments because adding more makes the probability of Christianity being right astronomically more certain and thus more difficult to conceptualize; instead of coins we'll need to talk in atoms and instead of countries we'll need galaxies, and even then that won't be enough!

But what does all this prove? Does it prove that Jesus is God? That God exists? …perhaps not[14]. But it does make the task of dismissing the Christian claim a WHOLE LOT harder! If Christianity is right[15], which it most certainly looks like, then ALL the others are wrong[16]. Atheism: wrong! Islam: wrong! Hinduism: wrong! Buddhism: wrong! But the beauty of Christianity is that it does not dwell on who’s wrong but shows how Jesus made it possible for everything to be made right. God wants a loving, personal, eternal relationship with you. He’ll be a father to you; you’ll become a child of God! (John 1:12) That’s what’s on offer! Friend, I urge you not to wait! We have all sinned (Rom. 3:23) and without coming to believe in Jesus, we are all heading to hell (Rom. 6:23)! Forgiveness through Jesus is our only hope (John 14:6). Don’t wait until it’s too late; tomorrow is promised to no one; Jesus calls you today (Rev. 3:20)! Will you not answer?

Note: I have crudely summarized many deep apologetic discussions. What’s worse is that I’ve omitted quite a lot of others! I invite anyone so interested to do more research, as well as to independently verify my facts, especially where they seem most curious. I am confident that the conclusions drawn would become only more obvious.

Quick References:

Gödel, K. 2001. "Collected Works: Volumes 1-3: Publications 1929-1936". Oxford University Press

Hawking, S. 2002. "Gödel and the end of physics". http://www.hawking.org.uk/godel-and-the-end-of-physics.html

Lennox, J. 2009. “God’s Undertaker – Has Science Buried God?”. Lion Hudson plc.: Oxford, England

Lennox, J. 2011. “God and Stephen Hawking”. Lion Hudson plc.: Oxford, England

McDowell, J. 1999. "The New Evidence That Demands A Verdict Fully Updated To Answer The Questions Challenging Christians Today". Thomas Nelson; Rev Upd edition

Pascal, B. 1669. “Pensées”. Translated by W.F. Trotter. [With an introduction by T.S. Eliot.]. J.M. Dent & Sons: London & Toronto; E.P. Dutton & Co.: New York, 1931

Popper, K. 2002. "Conjectures and Refutations: The Growth of Scientific Knowledge". Routledge; 2nd edition

Plantinga, A. 1967. "God and Other Minds: A Study of the Rational Justification of Belief in God". Cornell University Press

Stoner, P. 1963. "Science Speaks: An Evaluation of Certain Christian Evidences". Moody Press

Strobel, L. 1998. "The Case for Christ". Zondervan

FOOTNOTES:

[1] This is the hypothetico-deductive scientific model; Popper (2002).

[2] Proofs are possible through deduction within mathematics and philosophy given true premises. 

[3] There are actually several theories put forward for why God may allow evil in the world. These are called theodicies.

[4] Previously, Hawking in a “Brief History of Time” claimed that to find a TOE would be to know “The Mind of God”, i.e. to make God unnecessary.

[5] Someone should pass the memo on to Richard Dawkins et al. who naïvely seem to think that they can disprove the existence of God by simply asserting evolution. By the way, many theists don’t deny evolution. See Lennox’s (2009) exploration of evolution and other scientific issues within a theistic framework.

[6] Referring here to the implications of his Incompleteness Theorem. Gödel did in fact also create a proof of God’s existence which was confirmed in 2013; this is not the proof presented here. Other arguments for God’s existence are the traditional Cosmological, Ontological and Teleological arguments, and Alvin Plantinga’s Reasonable Minds argument.

[7] See Proof.

[8] If logical arguments do not convince you and you're more of the empirical type, there's loads of evidentiary support for theism (See Lennox (2009) to get started).

[9] An atheist may attempt to dismiss this conclusion by offering a God-of-the-gap defense but that is unsustainable as the conclusion isn't based on a gap in scientific knowledge but rather on an inescapable construct of science itself; a completely natural explanation for the universe is impossible.  Consequently, an atheist may then attempt an appeal to ridicule by claiming a “Flying Spaghetti Monster” type can fulfill the explanatory deficiency resultant from Gödel’s Theorem. However, as illustrated, formal systems progress to the point of having the characteristics of God as commonly understood, irrespective of the semantic-disparagement meant to be conveyed by the atheist's criticism (See Proof). Finally, the atheist may choose to retain his/her worldview, believing that the rules of logic would one day be revised to render Gödel’s Theorem incorrect but this really requires an absurdly immense (and ironic) amount of faith.

[10] Actually, the removal of the “there is no God” choice makes the “there is a God” alternative true. There is no argument to moderation with existence. However, we’ll allow agnosticism to remain for completeness, especially if one remains not yet convinced by the preceding arguments.

[11] If any doubt remains, a Pascal Wager could be applied to the matter: it is better to adhere to an objective position on religious truth than a subjective position because subjective truth allows objective truth to be right but the reverse is not true.

[12] Here, I urge the reader to please delve deeper into Christian apologetics. Strobel (1998) and McDowell (1999) make good introductions.

[13] Even our earliest surviving copies of these prophecies pre-date Jesus. For example, the Dead Sea Scroll’s copy of the Book of Isaiah has been carbon dated to between 351 – 41 BC. See Defense of Prophecies.

[14] Deductively, based on arguments in put forward here, the latter claim (“There is a God”) is proven while the former (“Jesus is God”) is statistically “proven” to a highly significant degree.

[15] You may have other questions like “What about dinosaurs?” or, “Did Noah really build a boat for all those animals?” or, “How could a fish swallow Jonah?”. That’s fine. There are theological debates like these among believing members of Christianity all the time.

[16] Please don't take offense. These religions aren't necessarily bad and there are a lot of good people who adhere to them; however, they simply do not pass our truth test.