Wednesday, 3 June 2015

Does God Exist? The Pool Table Argument


Does God exist? This question has been around for thousands of years. Many philosophers, theologians, scientists have presented several arguments for and against the existence of God. So who's right? Well, it depends on who you're talking to.

I used to be a militant atheist before converting to Christianity. When I was an atheist, I used to believe in determinism, which is the "philosophical idea that every event or state of affairs, including every human decision and action, is the inevitable and necessary consequence of antecedent states of affairs".

During a conversation with my brother, we were describing a Pool table game. Under determinism, if the balls were hit and we had complete knowledge of physical laws, we argued that we should be able to determine when and where each ball will end up at in the pool table. We should be able to trace all the events back to the beginning because they must have obeyed physical laws. We also argued that no matter how much we go back and forth in time, the result could never change, because other factors can't exist.

But we faced a dilemma. What about the white ball? How could we determine how it was hit? Why was the white ball hit this way, and not in any other way? This what brings me to the Pool Table argument for God's existence.

Pool Table Argument for God's Existence

This argument is very similar to many other arguments such as: Aquinas' "Uncaused first cause" argument, Plato's "Self-originated motion" argument and William Lane Craig's Kalam Cosmological ArgumentThe pool table argument goes like this:

1. Premise A: Every cause was either caused or uncaused (Null Hypothesis)
2. Premise B: There is a finite number of past causes.
3. Let n be the number of past causes and let C be the set of all causes that ever existed: c1, c2, c3 ... cn
4. Now choose any cause cx from the set of causes C.

Using Recursive process

5. Does cause cx have at least one preceding cause causing it?
6. If the answer is no, then cx is an uncaused cause. End of proof
7. If the answer is yes, then cx has at least one preceding cause causing it
8. Let cy be any of the causes that caused cx
9. Remove cx from the set of all causes C. Now the size of C will be reduced by 1
10. Now make cx = cy and repeat steps 5 to 10

The recursive process will loop until either:

a. An uncaused cause is found in step 5; or 

b. After a maximum of n-1 iterations, the size of set C will become 1. At that point, there's only one cause left in the set. There are absolutely no other causes available that can cause it. Therefore, this single cause must be an uncaused causeEnd of proof.

Conclusion: The logic above, if the premises are true, concludes that there must exist at least 1 uncaused cause.

Implications of an uncaused cause

Now that I've demonstrated the necessity of at least 1 uncaused cause, let's examine some of the properties of an uncaused cause:

1.  An uncaused cause must have behaved in a certain way that's not predetermined.

2. This cause couldn't have been naturally caused.

3. The cause must have acted freely. If it wasn't free, then what made it act this way?

4. The cause existed before the creation of the universe, and therefore it can be deduced that it's the main cause for the creation of the universe.

Therefore the first uncaused cause is unnatural, free, not predetermined and created (or was the first cause) of the universe. If this doesn't sound like God... Then I really don't know what does?

Supporting arguments from Science

The Big Bang theory is a well accepted theory that confirms that the universe has a beginning. The Borde-Guth-Valenkin theorem also proves that the universe had a beginning. The BGV theorem also states that any universe with an expansion rate of greater than zero must have a beginning and cannot be past-eternal. Even if you argue that this universe was caused by a previous universe which was caused by another universe, you will eventually have to reach a universe that simply began.

These theories only support the initial claim that there exists at least one uncaused cause which somehow (directly or indirectly) led to the creation of our universe. I argue that these theories support the God hypothesis. When scientists presented evidence that the universe wasn't eternal in Hawking's 70th birthday, Lisa Grossman described it as the "worst birthday presents ever". She argues that "…physicists, including Hawking, tend to shy away from cosmic genesis. A point of creation would be a place where science broke down."

Why is there a finite number of past causes? (Defense of Premise B)

One may argue that my argument fails because there could exist an infinite number of past events. However, Infinity ∞ doesn't actually exist. It's only a potential abstract concept. Many make the mistake that it's a number. Here are some peculiar properties of ∞:

∞ + 1 = ∞
∞ x 765 = ∞
∞ + ∞ = ∞
You can't even say that ∞ = ∞, ∞ ≠ ∞ or ∞ > ∞!

Past events are events that already occurred. David Hilbert explains this with Hilbert's paradox. You will love the video!

Hilbert's paradox goes like this:

Imagine that there is a hotel with an infinite number of rooms. And every room was taken! Someone comes to the hotel and wants a new room. The owner will say "Yes of course!" How? Well, you ask the tenant of room 1 to go to room 2, 2 to 3...etc. Guess what! Room 1 is now vacant.

If an infinite number of new tenants want to enter the hotel, they still can! You ask tenant of room 1 to go to room 2, 2 to 4, 3 to 6…etc. Now all even numbered rooms have been taken, and all odd numbered rooms are available (Infinite of them)! 

Basically, basic laws of math fail with infinities. Because infinities are potential values, but can never be achieved. No matter how much you add to a number, you will never reach infinity.

There's also a scientific way to prove that there can't be an infinite number of past events. (Please excuse the calculus).

Let m = n + 1, where n, m ∈ ℕ
∀n, ∀m ∈ ℕ, m - n = 1
Let n = 
m = n + 1 = ∞ + 1 = 
m - n = ∞ - ∞ ≠ 1
∴  ∉ 

Or in other words, ∞ is not a number.

Since past events actually occurred, then it's impossible that there is an infinite number of past events.

[Update] Aquinas' Argument from Motion

I just stumbled over a book1 that explains Aquinas' "Argument from Motion" with a pool table, so it appears that I am not the first to coin this idea with a pool table.

1 T. M. Renick, "Aquinas for Armchair Theologians", pp. 22


  1. Cantor proved there are different values of infinities, check out the diagonal proof. Which is why you appear to have absurdities like Hilbert's Hotel. It's not because an actual infinite is impossible.

    Also, if your argument was correct, that doesn't mean there cannot be an never ending series of past events. The absurdities appear because guests can be moved, but you cannot simply move past event out and around. It deals with an infinite amount of fungible values coexisting. Not an infinite amount of past events.

    Infinity may not be a number, but that's irrelevant. Infinity is a category that we put numbers in. That doesn't entail a number cannot infinite. Although I'm unsure if that's what you were arguing or just stating the confusion comes form people believing it's a number.

    1. @N7, thanks for reading my blog.

      The idea of moving guests around is only an illustration of why infinity cannot actually exist. In the sense that you can never have an infinite number of guests.

      The thing about past events, is that they have already occurred, and each event is a finite event. Event #1, Event #2....etc. While you can have an unlimited numbers that are greater than 100, but that's because these are abstract things. While events are related to actual things that occurred.

      While Cantor was brilliant, there was an issue with his logic. If you can actually count infinity, then you can easily introduce contradictions into mathematics and then eventually you can prove that everything is true. You could even prove that 1 = 2 and 3 = 7!

      So let me put it this way! If infinity could actually exist, and it is countable as Cantor claim is to be, then it is only logical that 1 = 2 which is clearly absurd. There is a reason why you cannot say that ∞ = ∞. Because in mathematics, you can only refer to ∞ as limits.

    2. That illustration is what gets you to your conclusion. If that illustration doesn't accurately portray the situation in question, then your judgement on that situation is going to be flawed.

      If there was an issue with Cantor's logic, wouldn't that entail there is something wrong with his proof? If so, what is it?

      I also don't see how this would bring up contradictions in mathematics. As you said, infinity isn't a number, but a concept. 1 and 2 are in the category of natural numbers, but this doesn't mean it's a contradiction to state "natural numbers=natural numbers" and state natural numbers have different values. The same is true with infinity.

    3. @N7 - What Cantor attempted to prove is that infinity is countable, and that there is an actual *Absolute Infinite*. According to Cantor, there is an absolute infinite that can be reached (which oddly he equated as God, but that's besides the point). This posed many problems, specifically "can't there be a number larger than infinity", and he simply concludes that all numbers "transcend" from this absolute infinite.

      The reason that I don't agree with Cantor is because his argument breaks a lot of math rules and logic itself. Also, Cantor's argument is not accepted by the scientific community as a fact.

      Now, just for the fun of it, if Cantor was right, then my argument would *still* be valid. Why? Because the iteration will eventually end, according to Cantor!

      There's also another way to show the existence of a first uncaused cause. Since the numbers of all causes that ever existed is only increasing, then if you go backwards, then the number of caused causes will continue to be reduced (convergence theory). So if Cantor was right, then it can be shown that number of caused causes will converge to a single point (basically zero). This would still show that my logic was correct and my argument as valid.

  2. The core assumption of this argument is that the "uncaused cause" must be the cause of the universe. We have no reason to believe that - it can be an uncaused cause of anything, but we have *no* reason to believe this "uncaused cause" caused the universe. Natural laws and the universe could have very well existed prior to the uncaused cause -- they began to exist causelessly.

    1. @Anonymous - thank you for your comments and for reading my blog. I hope you enjoyed the article even though you disagree with it.

      You argue that the natural laws and the universe itself may have existed prior to the first uncaused cause. Well, let's explore this idea further. If the universe did exist forever, and there are no causes, then it's only logical to assume that the universe was not going through any changes of any kind. It would have been relatively static. For example, all the atoms and energy were "just there" since forever, but they weren't interacting or causing any changes. At one point however, all that changed because "some uncaused cause", whatever that it, changed everything. Now you have energy causing particles to move, interact and change… energy became every changing… It caused our universe to begin 13.8 billion years ago. This doesn't refute my argument in any way or form. My argument would only conclude that even if the universe existed forever, there was an initial cause that changed everything.

    2. You entirely misunderstand my point. A universe existing prior to the uncaused cause *does not* imply an eternal universe. It implies either (a) a simultaneously caused universe, as Quentin Smith advocates, or (b) a universe that came into existence ex nihilo.

      The universe began *expanding* 13.8 billion years ago from state of singularity. This does not mean the universe "began to exist" 13.8 billion years ago, since eternalism implies the phrase "began to exist" is incoherent.

      A universe that came into existence ex nihilo is highly plausible, since without physical constraint and time directionality the causal principle breaks down.

      Now, the obvious question follows: WHAT did this uncaused cause cause? The core assumption of this argument is that the uncaused cause caused the *universe*, which is not necessary.

    3. You argue that "a universe existing prior to the uncaused cause *does not* imply an eternal universe". But prior to the uncaused cause there were no other causes. But without any causes, it means it cannot be changed. Whatever state the universe was at before the first uncaused cause would have to be and remain static, and therefore it must be eternal.

      Regarding "a simultaneously caused universe" is a mute point, because prior to the first uncaused cause, there were no causes.

      Regards "a universe coming into existence" is also a mute point because there was no cause to cause it to exist.

      Now you're appealing to Eternalism or the B-theory where everything existed at the same time. So basically, you're arguing that cause and effect is false. Because for causation to exist, the cause must exist prior to the effect. But according to Eternalism, they both exist simultaneously. Why should I ignore a scientific fact for the sake of a disputed theory?

      Now to say that a universe existing ex nihilio (out of nothing) is highly plausible! Now that's not responsible. Why is it highly plausible when it's illogical from something to come out of nothing? You would have to provide strong evidence to to make an illogical claim, and there's highly any evidence for that.

      Now regarding the question - What did this uncaused cause cause? It was the mother of all things that were caused. That's a huge argument for God.

    4. "It's illogical for something to come out of nothing .... provide strong evidence to make [the] claim."

      (1) Appeal to intuition fallacy. Why is it "highly illogical"?
      (2) Fallacy of composition. Just because things within the universe need causes doesn't mean the whole universe needs a cause?
      (3) Shifting BoP fallacy. You're the one asserting the universe was caused, such a claim has to be demonstrated--if you're asking me to demonstrate possibility of ex nihilo, then I ask you to demonstrate possibility of causation sans committing fallacy of composition.
      (4) It *is* possible (ex nihilo). An example would be zero-energy genesis--fluctuations from *absolute* vacuum, i.e. particle-antiparticle annihilations would form, and the two photons go out of existence before replicating in a period of less than 10^-34 seconds, *unless* the fluctuations have zero energy. Universe, for example, has zero-energy, and this is a *possible* explanation. There are multiple other explanations, and I'm agnostic about which explanation.
      (5) I personally remain somewhere between an absolute agnostic and agnostic atheist, so very, very weak atheism, one could say, but that's just because of Occam's razor and nothing else; without Occam's razor existing I'd just be a complete agnostic.

    5. fIt appears that my response wasn't saved. So I'll try to answer your questions to the best of my abilities.

      Why is it "highly illogical" for something to come out of nothing? The answer is simple. Scientists always ask the "how" questions. When Newton saw an apple falling, he asked "how" or "why" did it fall? He didn't settle with the answer "it just fell" The same thing applies to something coming out of nothing *without any cause* or for *no reason whatsoever*. This is not tenable. You would ask "why did it come from nothing in this way and not in any way.

      Now you may argue that I'm shifting the BoP (Burden of Proof). To the reader, shifting the BoP is a tactic where a debater requires the other side to prove that his argument is false, instead of proving his argument is true.

      But in this case, the BoP shift is warranted. What I claimed that Eternalism renders the law causality as being false. But the law of causality is a scientific fact. For someone to believe that a disputed theory is true against a known scientific fact, required the owner of the claim to prove their position.

      Fallacy of composition to the reader is the fallacy that a property of the parts means the whole has the same property. For example of this fallacy would be: All the cells in a lion are tiny, therefore the lion is also tiny. That's clearly fallacious. I didn't claim such a fallacy. I didn't say that everything needs a cause. I actually showed the existence of an uncaused cause. And in any case, I didn't claim because every part of the universe has a cause then then *the universe* must have a cause as a result.

      Now you said that it's *possible* that an ex nihilo universe came to existence, while before you said *plausible*. I respect your agnostic position.

      Finally, you mentioned that you are a weak atheist. I was a very strong atheist, so I respect your position as you are more humble than I was. I doubt that my argument will cause anyone to convert to theism, but I only hope to provide thought provoking arguments.

    6. (1) Oh, I think your argument will get a lot of people to convert to theism. It's very powerful, and it's almost the same as Aquinas' first cause argument, wonderful.

      (2) The law of causality is based on Conservation of Mass/Energy, and the First Law of Thermodynamics, together forming the "causal principle". But outside the universe, we lack time directionality and physical constraint, so the law of causality breaks down - it's not required anymore.

      (3) Fallacy of composition is committed here when you use analogies of objects that *make up* the universe to demonstrate the universe needs a cause.

      (4) I'll provide an example of something uncaused. I'm going for zero-energy universe quantum fluctuation. Now, a quantum fluctuation (as you probably know) is an annihilation of two particles to release two photons from the quantum vacuum. Again, as you probably know, the quantum vacuum *does* have energy, so its not exactly "nothing", but *theoretically*, it is possible for a quantum fluctuation to come out of *absolute* vacuum (not the usual quantum vacuum used by Krauss and other physicists), only to dissipate out of existence in a period less than Planck time, or probably not come at all. In other words, such fluctuations never occur--but there is *one* exceptional case when they would, documented in Tryon (1976). That is when the fluctuation doesn't have energy. It's made of no energy--nothing. The annihilation allows for a vector force to be caused like a "bubble" -- the vector cancels out the scalar and allows the energy to dissipate out of existence. But the vector can split from the scalar to actually have some energy, but the *net* energy would be zero. It's possible the universe is such a vacuum fluctuation, since it's energy is zero.

      (4) Once more, I'm not expressing support for the above model. It's just an example from Hawking and Penrose's singularity theorems and the calculations of NASA's WMAP. I remain relatively agnostic, but a weak atheist.

  3. Your case against actual infinities, at most, shows that actual infinities have *odd* properties, as Michael Martin writes in "Atheism: A Philosophical Justification."

    Actual infinities do exist in gravitational singularities.

    1. Let's argue for the moment that infinity was somehow countable, as the mathematician Cantor argued (and I am being very supportive here). Since the number of causes is only increasing, this would logically and necessarily mean that if we go backwards, the number causes would only be decreasing. And anything that's continuously decreasing would converge into zero or a singularity… that's a known scientific property. Remember, according to your assumption, we should be able to count backwards infinitely, correct? This means that it will definitely converge to zero or a singularity. This is the same property that was used by the BVG theorem to prove that any universe that's expanding must have a beginning. In other words, even if infinity was somehow countable, as the mathematician Cantor claims, we could still show that there was an uncaused cause. The only way to refute my argument would be to show that infinity is uncountable, yet at the same time can actually exist. There isn't even one scientist (that I know of) that supports such a claim, and I've done research on this subject.

      I would like to give a piece of advice here, if you allow me. Your analysis would be considered an ad hoc rescue. An ad hoc rescue occurs when someone introduces a weak argument just to rescue their world view. For someone to accept that infinity could actually exist, you would expect that the majority of mathematicians would agree to such a notion, which is not the case. This type of argumentation is dangerous, because it can lead to biases and world view overriding rational thinking. Do you know that there are people who still believe that the Earth is flat? Don't atheists ridicule those who claim that the universe was created in few days? Or that Earth is not more than 4 billion years old? You could basically argue anything, but that doesn't mean that everything is reasonable. I could argue that the universe is being carried by 4 turtles and 12 chariots. Good luck proving me wrong, because you can't. But does that make it reasonable in any way? I admit that many theists make this same mistake, and it frustrates me… these are classified as "God of the Gaps" arguments. But no one should accept these claims as face value. I liked one of Lawrence Krauss comments in one of his debated (ironically against God) where he said something like "We could all have been created 10 minutes ago, and all our past memories simply exist in our brain. But why should I believe such a thing?" And I agree with him. My brother-in-law said to me that "I'm the most skeptical Christian he's ever met". I don't think he meant it as a compliment, but I did consider it as such. I believe that no faith or belief system (including my own) should be exempted from scrutiny and questioning.

      I am naïve to expect that everyone who reads my argument will fall down on his or her knees and worship God. I thought of this argument for at least 4 years before converting to Christianity, and it was hardly the main reason I converted. My only goal for writing this argument is to make people think and ask the "What if" questions. I argue that my argument is very solid, and I only hope that people think and argue about it. Where will that lead them? That's up to them.

      This turned out to be longer than the article, so I apologize. I might even post it as a separate post. But thank you for making me think.

      "I think, therefore I am" – Paul Sartre

    2. There was an error in my last reply. René Descartes is the one who said "I think, therefore I am", not Paul Sartre.

    3. First, a singularity IS an actual infinity, and you just conceded that singularities exist. Mathematician John D. Barrow writes, "Einstein's theory of general relativity suggests that an expanding Universe (as we observe ours to be) started at a time in the finite past when its density was infinite — this is what we call the Big Bang. Einstein's theory also predicts that if you fell into a black hole, and there are many black holes in our Galaxy and nearby, you would encounter an infinite density at the centre. These infinities, if they do exist, would be actual infinities."

      Your interpretation of the BGV theorem relies on a Presentism ontology of time and a classical interpretation of spacetime physics, the former being dubious in light of special relativity and the latter in light of quantum gravity.

      Furthermore, we have *absolutely no reason to believe* the singularity couldn't have existed forever. While I personally don't support an eternally-existent universe, it's still a plausible hypothesis.

      Mine is not adhoc -- I'm just attacking the bare assertion you made by saying infinity can't exist simply because ∞ +/- x = ∞. Adhoc can only be used in *positive* assertions. I'm saying your a priori arguments, e.g. Hilbert's hotel, merely show differing properties of ∞.

      This *does not* imply actual ∞ can't exist.

  4. I have questions in regards to the pool table argument.

    1. One of the primary attributes of God is *intelligence*--sans intelligence, it's just a force that caused the universe, and a force that caused the universe isn't exactly God. It could just be a singularity that caused the universe, which *would* act as an external cause.

    2. You say actual infinities can't exist, so the universe couldn't have existed eternally. Then how can God exist eternally? If actual infinities are impossible, then eternal existence is impossible, so something must have caused God, which means God can't be the "uncaused cause", so the pool table argument doesn't prove that.

    3. I object to Implication 4 of the existence of an uncaused cause. "The cause existed before the creation of the universe, and therefore it can be deduced that it's the main cause for the creation of the universe." -- this is *not* justified. The universe could have been caused via. quantum entanglement (retro-causality), branes of spacetime (ekpyrotic universe), caused itself (simultaneous causality--though admittedly this is probably dubious sans the retro-causal aspect), or began ex nihilo--"retro-causality" and the ekpyrotic universe model aren't exactly forms of "causality" themselves, since there is no cause. Sans justification this uncaused cause isn't God.

    1. Thank you for reading my blog. I'll try to answer your questions.

      1. My argument concludes that there is an uncaused cause. This uncaused cause (or call it force if you may) created the universe that we live in and did so freely. Now intelligence can mean "cleverness" and it can also mean "having the ability and skills". So my argument doesn't prove "cleverness", but one could argue that giving the outcome of the cause. But I do argue that the cause was intelligent because it had the ability to create the universe.

      2. What I meant, is that an infinite number of things can't exist. This doesn't mean that something can't be always and infinitely full or infinitely empty. Actually my argument proves the existence of an uncaused cause. Therefore this uncaused cause must have existed eternally, because it couldn't have a beginning? Unless it decided to create itself, but how can something create itself if that thing doesn't exist? That's not tenable! An uncaused cause must have existed eternally.

      3. Regarding objection #4, all the examples you provided are actually caused, which means there is a transcendent uncaused cause to it. So if the universe was caused via quantum entanglement, then the uncaused cause must be either the quantum particles or the cause of quantum particles. So this doesn't negate the implication.

  5. This is a different version of the same argument that I heard from my school teacher. It goes like this: If you look at sandwich you eat at lunch, who made it? the cook cooked it from meat... and where did the meat come from? the butcher made it from the cow.. and where did the cow come from? the farmer in the farm..and who made the farmer?.....

  6. Point #1) Duraid's comment is the only comment that makes sense to me.
    Point #2) You clearly dont have enough work to do... would you like some of mine???

  7. Would you mind if I write a critique of this on my blog? That way, we can respond to each other via blog posts.

    1. Feel free to do so. I look forward for your critique.