Sunday, May 20, 2012

Omnipotence, Creating an Immovable Stone, and YouTube

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I was thinking of having the title be “Omnipotence, Creating an Immovable Stone, YouTube, and Logic” (as we’ll see, logic plays an important but ironically overlooked role in the YouTube video being discussed) but the title was long enough already. This entry is inspired from a YouTube video I saw. Warning: the YouTube video contains strong language and violence (this article will itself contain some PG-13 level language, though I’ll limit myself) that is unsuitable for children, socially conservative non-maverick Christian old ladies, and bosses peering over your shoulder. If you decide not to see the YouTube video, I’ll just describe one part that I found annoying. The video:

If you didn’t see it, here’s the aforementioned part that annoyed me: At an atheist rally God shows up, violently killing atheists. One atheist and God (the Father) have the following conversation.

Atheist: If you’re all-powerful, could you make a rock so big that even you couldn’t lift it?

God: You idiot, of course I could!

Atheist: Aha! But then you wouldn’t be all-powerful!

God swears, begins to bleed, and turns translucent as if he is beginning to cease to exist.

Atheist: You see? Omnipotence is impossible!

Later in the video God eats a hundred dollar bill to fully materialize and before shooting the atheist dead he says, “You forgot one thing: logic is for pussies.”
The “logic is for pussies” remark was annoyingly ironic. To emphasize the irony I’ll use a bit of symbolic logic in this post:
  • ◊ symbolizes the possibility operator, e.g. ◊P means proposition P is possibly true, i.e. P is true in some possible world.
  • → symbolizes implication, i.e. “P → Q” represents “If P, then Q.”
  • ¬ represents the not operator, e.g. ¬P means “not-P” or “P is false.”
A handy english-to-symbolic-logic table:

EnglishSymbolic Logic
P is possible◊P
If P, then QP → Q

Symbolic logic is handy for showing that a conclusion follows from the premises by certain rules of logic. For example, the following rule of logic is called hypothetical syllogism:
  1. P → Q
  2. Q → R
  3. Therefore, P → R
If you wanted to show that a proposition P is false, premises like these would be great:
  1. P → Q
  2. Q → ¬P
  3. P → ¬P 1, 2, hypothetical syllogism
Someone who grants premises 1 and 2 would have to reject P as false (a little more symbolic logic would be needed to rigorously conclude that, but you get the idea).

Now let’s consider the following argument against omnipotence.

In this case, “omnipotence” is defined as the ability to do anything logically possible. If an omnipotent being exists, it is logically possible for him to create an immovable stone. Yet if there is an immovable stone, then an omnipotent being does not exist (for an omnipotent being could move anything). Therefore, an omnipotent being does not exist.

Now watch what happens when we use some symbolic logic. Using the following letters to represent statements:

O: An Omnipotent being exists.
S: An omnipotent being creates an immovable Stone.

Then we take the following argument...
  1. If an omnipotent being exists, then it’s possible for an omnipotent being to create an immovable stone.
  2. But if an omnipotent being creates an immovable stone, then an omnipotent being doesn’t exist.
  3. Therefore, an omnipotent being doesn’t exist.
…and translate it into symbolic logic:
  1. O → ◊S
  2. S → ¬O
  3. Therefore, ¬O
The argument is invalid, i.e. the conclusion doesn’t follow from the premises. Why? Here’s one reason: just because an omnipotent being could give up his omnipotence (as by creating an immovable stone) it doesn’t follow that the omnipotent being has in fact done so. Inferring O → ¬O from premises 1 and 2 breaks the rules of logic. The “Could an omnipotent being create an immovable stone” argument is hopelessly invalid; so says logic.

But maybe some atheists think logic is for pussies.