God and Rocks

This post is a short aside in which to put a necessary part of an argument I’m making in its own place.  I’ve discussed what I’m going to talk about in other posts, in bits and pieces; but this way it’ll be a one-stop shop that I can always link back to.

God is typically defined as being omnipotent–Almighty or All-Powerful.  This is conventionally understood to mean that He can do anything.  Of course, when it comes to philosophy or theology, sooner or later someone will toss out a question such as this:  Can God make a married bachelor?  Can he make it so that 2 + 2 = 5?  Of course, the classic question of this type is, “Can God make a rock so big even He can’t lift it?”  In classical theism, the answer to all these questions is “No.”  What I want to do in this post is to show why.

Let’s consider the first question.  Some statements, by the nature of language, seem to convey information when they actually don’t.  “Bachelor”  means “unmarried man”.  Thus, “married bachelor” means “married unmarried man”, which is clearly a contradiction.  No information is actually given; a married bachelor, by definition not only can’t exist but doesn’t even make sense.  This is what is called a logical impossibility.  Other examples of logical impossibility would be a finite whole with parts bigger than itself or a statement that is both true and false at the same time in the same manner.

It’s important to point out that logical impossibilities are a priori and are based on the structure of the situation and not on the specifics.  As long as you know that “bachelor” means “unmarried  man”, the term “married bachelor” is a logical impossibility even if you don’t know what “bachelor”, “man”, and “married” mean, even if none of these things exist.  For example, suppose I define “gostak” as “a dosh that has never been distimmed” or “an undistimmed dosh”.  Then, “distimmed gostak” is equivalent to “distimmed undistimmed dosh”, which is obviously impossible, no matter what “gostak”, “dosh”, and “distim” mean.  All this derives from the classic laws of thought, according to which something can not be in two opposite states (married/unmarried, alive/dead, distimmed/undistimmed) at the same time, and in the case of opposite states, there is no middle ground (you’re either married or unmarried, with no in-between).

Another way to look at it is to say that while a logical possibility, no matter how exotic, exists in some possible universe (e.g. there could be a parallel universe where unicorns and flying horses exist), a logical impossibility exists in no possible universe (there is no universe with married bachelors or finite wholes smaller than their parts).

Now, let’s consider omnipotence.  The very word has a subtle nuance often missed.  In English, we say God is “Almighty”–He has all might and strength.  The “omni-” of “omnipotent” means “all”; but “potent” does not mean “mighty”.  Rather, it derives from posse, the Latin verb meaning “to be able to” or “can”.  If I said in Latin, for example, “Legere possum,” this means “I can read,” or “I am able to read.”  The English word “power” comes from potentia (the noun derivative of posse), so “omnipotent” could be translated “all-powerful”; but it’s important to remember that “power” in this context doesn’t mean “power” as in strength or might, but the “power”–that is, ability–to do something.  “Omnipotent”, then, could be translated as “all-able”.  To put it at greater length, one might say it means “Able to do all things that it’s possible to do.”  This is how philosophers define it.

Thus, to say that God is omnipotent means He can do all that can be done or that is able to be done.  By definition, logical impossibilities can’t be done or are unable to be done, even in principle.  Thus, to say that God cannot do the logically impossible–e.g. to make a married bachelor or a finite whole with parts larger than itself–does not diminish Him.  Everything that can be done, He can do.  Things that logically can’t be done are impossible even to Him.  Thus, no matter how many universes God may have made, we can confidently say that none of them contain married bachelors (or distimmed gostaks!); and despite this, God is still omnipotent.

The second question–can God make 2 + 2 = 5–is a little more problematic.  It doesn’t seem to be a logical contradiction in the same way that “married bachelor” is; but it seems to be obviously impossible.  If one understands what “2” and “4” mean, and the concepts of addition and equality, it seems that 2 + 2 = 4 is a necessary truth.  Necessary (or logical) truths are the opposite of logical impossibilities (or contradictions).  Logical impossibilities are true in no universes; necessary truths are true in all universes.  Thus, “all bachelors are unmarried”, given the definition of “bachelor” as “unmarried man”, is true in all possible universes, even if there are no bachelors and no marriage in them.  Necessary truths are obviously true and true a priori–that is, they can’t be “proved”.  They just are.  You can’t be married and unmarried at the same time; a part can’t be bigger than its finite whole.  If one understands the words, the statements are self-evidently true.  A person might still deny a self-evident truth, just as someone might deny the reality of the room he’s in; but that doesn’t make it any less true (or the room any less there).

It seems to me (and many mathematicians and philosophers would agree) that 2 + 2 = 4 is a necessary truth.  It doesn’t seem possible that it could be otherwise, and denial of it would seem to be madness.  Just as God can’t create logical impossibilities, so also He cannot violate necessary truths.  Thus, it would  seem that God is also unable to make 2 + 2 be anything other than 4, without his omnipotence being thereby compromised.  Since all the rest of mathematics is based upon the lower level postulates and necessary truths of addition and such, it would seem that mathematics in general must be as it is, and that no universe could exist in which mathematical truth would be different from what it is here (e.g. in no universe would addition be non-commutative).

So now how about the rock?  This is usually construed as a paradox:  If God can do anything, He could make a rock so big even He couldn’t lift it; but once He’s done that, there is now something He can’t do (lift the rock), so He’s not omnipotent.  However, if He can’t make such a rock, then there’s still something He can’t do; so He’s still not omnipotent.

This is, simply put, the wrong way to analyze it.  As we’ve seen, God can’t do anything at all; just anything that can be done.  Let’s look at it like this:

1.  To say “God can do anything that can be done” seems logically to imply “God has infinite abilities.”  After all, “anything” covers a lot of ground–infinite ground, in fact.

2.  To say “God has infinite abilities” seems logically to imply “God has infinite strength.”  Strength is an ability.

3.  To say “God has infinite strength” seems logically to imply “God can lift an infinite weight.”  The weight can be a rock, for our purposes here.

4.  We’ll take “infinite” here to mean “the highest level of infinity below God Himself” in order to avoid transfinite numbers.  In short, an “infinitely heavy rock” means “a rock of a weight greater than which nothing can be heavier.”

5.  From 3 and 4, we get, “God can lift an infinitely heavy rock.”

6.  If we say “God makes a rock so heavy even He can’t lift it,” by our definition of “infinitely heavy”, this must mean, “God makes an infinitely heavy rock.”

7.  From 6, it follows that “God can not lift an infinitely  heavy rock.”  However, this contradicts 5.

8.  Therefore, it is not possible for God to make a rock so big even He can’t lift it; and since this is a matter of logical impossibility, this inability does not mean God is not omnipotent.

Thus, to sum up, God can not

• make a married bachelor
• make 2 + 2 equal anything but 4
• make a rock so big He can’t lift it

Nevertheless, He is still omnipotent, all-powerful.

As a brief coda, the same would apply to omniscience–knowing everything.  To say God is omniscient means not that He knows everything absolutely, but that He knows everything that can be known.  Thus in some formulations of free will, even God doesn’t know with 100% certainty what a truly free being will do ahead of time, since this would be a logical contradiction.  Whether this is a correct definition of free will or not is something I’m not going to get into here; and whether there are, in fact, things that are logically unknowable is also something I’m not arguing here.  I’m merely stating that if there are intrinsically unknowable things, then the fact that God doesn’t know them does not compromise His omniscience.

Therefore, the seeming paradox that God can’t do some things and yet is still omnipotent is not a paradox at all.

Part of the series “Religious Miscellany”