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