Ruminations

Is there anything God can’t do?

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Can God make a rock so heavy, not even He can lift it? If yes, then is there something God can’t lift? If no, then is there something God can’t make? This is a classic argument against the logical possibility/existence of omnipotence. It’s so intriguing and popular that even Stephen Hawking mentions it in as unrelated a work as his A Brief History of Time.

At the center of this question lies the implicit conclusion that God can’t be omnipotent and that omnipotence is a fiction. After all, this is a “Yes or No” question; it can’t be both and it can’t be anything else. Imagine a restaurant that says it serves a certain dish only at night, but one of the ingredients in the dish can be prepared only in the morning. The dish has to be served either in the morning or at night depending on the criteria taken into account, and ends up needing to be served during both! Clearly it is, therefore never served, and might as well not even exist. It’s like a restaurant that says it’s open on February 31st (they’re closed on the 30th though).

But how valid is this objection? If something is logically impossible even for God, such as square circles and married bachelors, does that refute the claim of omnipotence? I don’t think so: the conclusion doesn’t follow from the observations at all! The problem with this example, and any such variation of it, is that it pits God’s power against Himself. What the question basically asks is, “Is God more powerful than Himself?” – “Can God destroy Himself?” We can already see this as an absurd postulate for omnipotence or any kind of power. True, something non-omnipotent can willingly destroy itself: suicide for example. The 1st century Roman naturalist, Pliny the Elder, even regarded this as the one “advantage” man possessed over God!:

“God cannot give himself death even if he wishes, but man can do so at any time he chooses.”

But since there are different kinds of strengths, just like an airplane overcomes gravity but a malfunction can certainly overtake it, this obviously means one isn’t omnipotent by being weaker at one of them.

The whole issue can easily be untangled by understanding something very simple. First of all, Immanuel Kant points out that things like power, logic, or existence aren’t predicates. That is, they’re not like a chair that has a physical description and illustration in and of itself. These are relationships to one or more such objects. The same goes for love, hatred, information, etc. A good example is infinity, which is not a number, but is generally spoken of, and often for convenience’s sake treated as one. These are concepts that relate, but we give them a word for convenience’s sake, which we can easily misuse by manipulating as if these ideas are objects if we forget our starting points and definitions: namely, the fallacy of language. This answers the question of whether God created “existence” and if so, how did He Himself exist? Was it simultaneous? If so, existence is as ancient as God, and has an origin other than Him (i.e. God didn’t make “everything,” because He couldn’t, and so again, isn’t omnipotent).

“What’s in a name?” “A rose by any other name would still be a rose.” Quite right! This basic concept can be seen in many places, whether philosophical or theological. Paul masterfully dismembers this kind of abuse regarding the issue of eating food “polluted” by idols (which don’t exist – 1 Cor. 8/10, Romans 14).

So when we say that God “can’t” do something, it’s because this something isn’t a “thing” to be done in the sense we’re talking about at all. Married bachelors can’t exist. Square circles might be possible in non-Euclidean space though, I’m not sure.

But let’s explore whether God could have created logic as Martin Luther and possibly Descartes believed. A simple demonstration to the opposite would be the following. Let’s make a contradiction be true:

“A = not-A” (or ~A in symbolic logic)

Let’s modify this by specifying:

“A exists and A doesn’t exist.”

Could God do this? Sure, why not – He split the Red Sea. Well replace “A” with “God” and what do you get? Now, someone could easily say, “Well this applies to everything but God.” Fair enough, after all we’re not being logical here. And sure, God isn’t necessarily a “thing” to contain, one might argue. But it seems to my mind that we’re using logic to define “illogic” and that in the end the whole argument is either meaningless, or we’re back to the original conclusion that logic simply isn’t a “thing”. After all, we can always go back to the question of “Can God destroy Himself?” to illustrate that this train of thought is simply a dead end.

Vacuous Truth

However, there’s two additional pieces of information that can shake things up here. First of all, there’s a little known property in modal logic known as a Vacuous Truth (good introduction at Wikipedia here). It deals directly with the above issue of “non-logic” and “existence.”

A good example the article uses is, “If there are no cell phones in a room, are all cell phones (in that room) on or off?” The answer is both! You can easily prove this with De Morgan’s Laws and some other simple modal/formal logic rules. The answer is strongly related to the (valid!) concept of premises and conclusions in logic. For example, an argument is invalid only if its premises are true, but its conclusions false (T->F). If an argument has false premises and a true conclusion (or a false one) – (F->T and F->F), it is valid! It isn’t sound (T->T), but it’s valid. How can this be?

Take, for example, a geometric shape “X”. Let’s say that “X” is a circle. Isn’t it true that “If ‘X’ is a square, then ‘X’ has four sides?” But shape “X” is not a square, and doesn’t have four sides. So the logic has a false premise and conclusion (with respect to reality), but it would be true, if “X” were a square, so it’s valid.

The same is true of false premises with true conclusions. Imagine there are two countries at war: Country A and B. A soldier from Country A comes offering information to the other. He sympathizes more with them. Country B then has to decide whether he’s telling the truth or is a spy trying to lead them into a trap. They reason like this: “If what he says is true, we are already prepared as best as we can so he’s of no use, we should send him back. If he’s lying or is trying to trick us, it’s the same result – send him away.” So it’s valid for them to send him away regardless of whether his statements are true or false.

So what does this mean? Just as the vacuous truth’s conclusion is both True and False, so also the original question, “Can God make a rock so heavy, not even He can lift?” has both a “Yes,” and “No,” answer. This means that the question itself is invalid. It’s not that you “can’t” ask the question; it’s that it doesn’t make sense due to the fallacy of language. It’s the difference between asking whether a bucket is full or empty, whereas there simply is no bucket. On the other hand, one might be inclined say, “the answer is both ‘yes’ and ‘no,’ and God is above logic, just like the vacuous truth, which ‘exists’ (?)”

The bottom line is that having a question like this in no way invalidates omnipotence, if it is understood properly, any more than logic and truth are invalidated by asking whether the statement, “This statement is false,” is true or false. There are many similar problems in mathematics as well, whose resolutions are similar, such as Russell’s Paradox.

Set Theory and Cardinality

The second connection to this topic involves math. How many natural numbers are there (1, 2, 3…)? Infinite. How many fractions? Infinite. How many rational numbers? Infinite. How many real numbers (rational and irrational)? More than infinite. There’s actually a way to show that, although there are an infinite number of rational numbers, the number of irrationals outnumbers them! This is Cantor’s Diagonal Proof and an excellent explanation can be seen here (from 1:57-6:04, particularly 2:55-6:04).

If something can exist that’s “bigger than the biggest,” does it mean God could’ve created numbers? And since math is basically logic, logic itself? And how does “bigger than the biggest” relate to omnipotence and our original question, or whether an omnipotent force can destroy itself like a non-omnipotent (finite and non-equivalent(?) to it) one can? I personally don’t have a clue.

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2 thoughts on “Is there anything God can’t do?

  1. Pingback: How is Infinite, eternal punishment for finite sin fair? (and other questions) | Ruminations

  2. Pingback: Looking for answers on the question Is there a God #4 – Questiontime – Vragenuurtje

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