The Big Rock Conundrum

Can God create a rock so heavy that he cannot lift it?

This is known as the Big Rock conundrum. It is often used by atheists seeking to disprove the possibility of the Christian god, and any other purportedly omnipotent god. Sadly, it is logically flawed.

Remember that omnipotence means the ability perform all tasks. However, tasks that are logically impossible, such as creating square circles, are not really tasks at all; they are nonexistent, the null set. Thus they are not real actions for an omnipotent entity to perform. The Big Rock conundrum disappears when you consider this. In argument form:

Given:

  1. U: The Universal set of tasks
  2. A: A proposed task
  3. B: A proposed omnipotent entity
  4. r: A rock
  5. Cx: Proposed task of creating object x
  6. Mx: Proposed task of moving object x

Assuming:

  1. Omnipotence is the ability to perform all tasks. (All members of U)
  2. If the definition of proposed task A is self-contradictory, then A is not a member of U.
  3. If A is not a member of U, then A is not a task.
  4. Any entity X can only perform real tasks (elements of U)

One can infer that:

  1. If A is logically impossible, then A is not a task (prem. 2-3)
  2. B has the ability to perform all tasks (prem 1)
  3. B only has the ability to perform real tasks (prem 4)
  4. B does not have the ability to perform nontasks (inf 3)
  5. B has the ability to perform all members of U (prem 1)
  6. If B performed Cr such that Mr is a nontask, B could not perform Mr (inf 4)
  7. If B can perform all Mr, then B cannot perform Cr such that Mr is a nontask (inf 4)

In conclusion:

  1. Either B can perform Mr for all r xor B can perform Cr such that Mr is a nontask.

The argument leads to the conclusion that an omnipotent being could rationally be able to do one xor the other and still be omnipotent. The conclusion to this argument is (A xor ~A), which simplifies to TRUE. IOW, this is a tautology. And proves the argument to be valid rather than contradictory (in which case it would end in a direct contradiction, (A and not-A), or a paradox of self-reference, (A implies not-A).

The obvious points of attack are premises 1 and 4. However, if you assume that an omnipotent entity is able to perform both tasks and nontasks, you will ALWAYS end up with logical contradictions or paradoces of self-reference. To borrow a phrase from computer science, garbage in, garbage out. So, I submit that such a definition of omnipotence is inherently empty and will not get you anywhere with relatively rational theists. Another avenue of attack to this definition is to analyze it from the perspective of set algebra: from this view, it does not make a jot of difference whether you define omnipotence to include logically impossible or not; nonexistant tasks form the null set (∅), and the union of any set A with ∅ is always that set A (A ∪ ∅ = A). Thus, either way you still end up with the same set U of possible tasks.

If there is a contradictory conclusion of omnipotence, it lies elsewhere.

I’m unsure when this piece first appeared on the web. It was adapted from a post that I made to talk.atheism on 3 March 1997. The Internet Archive’s first record of the web version is from 12 August 1997. —C.J. 2006-07-10.

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