Four Sides Do Not a Square Make

There are many forms of the ontological argument, most so apparently mistaken that to comment on them extensively would be a waste of time.  But a remarkably clear headed philosopher named Norman Malcolm, restated and expanded a portion of Anselm’s argument so that it is almost an entirely new one, and it deserves some note.  We’ll start with Anselm.

“If it [the thing a greater than which cannot be conceived] can be conceived at all, it must exist.  For no one who denies or doubts the existence of a being a greater than which is inconceivable, denies or doubts that if it did exist its non-existence, either in reality or in the understanding, would be impossible.  For otherwise it would not be a being a greater than which cannot be conceived.  But as to whatever can be conceived but does not exist: if it were to exist its non-existence either in the reality or in the understanding would be possible.  Therefore if a being greater than which cannot be conceived, can even be conceived, it must exist.”

Responsio 1

According to Norman Malcolm, this means that God is “a necessary being”.  So then, in a universe where God exists, His non-existence would be logically impossible (this is subtly different from ‘unthinkable’).  Now, following Anselm’s logic, if we imagine a universal set of everything conceivable we can divide the set in two: (A) conceivable but non-existent and (B) conceivable and existing.  Now then, for everything in subset A even if they could exist, it would be logically possible to think of them as non-existent.  For example, elves; if we pretend that elves are real, it still isn’t logically impossible to think that they do not exist, or that there was a time when they did not exist, or that there is a time when they will not exist.  If God, on the other hand exists, it would be illogical to say the same of Him, therefore God must not belong to subset A, which only leaves subset B, that is to say, God exists.

            Malcolm expands this argument in two ways. 

First he notes that since God is thought of as a necessary being, in a universe where He exists, He must exist; in a world where He does not exist, He cannot exist.  Therefore, God’s existence is either necessary or impossible.  It is impossible only “if the concept of such a being is self-contradictory or in some way logically absurd”.  If that is not so, he says, then God must exist.

Second, Malcolm notes that the proposition “if God exists, then He necessarily exists, [as opposed to God just happening to exist]” is a contradiction.  The antecedent “if God exists,” assumes the possibility of the opposite; Malcolm makes the meaning explicit in this way, “if God exists (and it is possible that He does not) then He necessarily exists”.  Malcolm says that (because necessary existence, like necessary omnipotence, is bundled with our definition of the word God) this proposition is as self-contradictory as “a square necessarily has four sides but it is possible for a square not to have four sides”.

So once again the ontological argument has obviated the debate.  If we were to admit to the validity of Malcolm’s reasoning—and, as will be shown later, we do not—his second point could not fairly be called a proof of God’s existence.  A proof requires a progression from the first premise down to the final one and onto the conclusion.  Malcolm’s second point does not have such a progression unless we take it to mean that ‘God is defined as a being that exists necessarily, therefore God exists.’  Malcolm actually seems to think this is so.  God’s existence, he seems to say, has as much a priori footing as a square’s four sides.  He writes as if the previous statement were as true as saying ‘a triangle necessarily has three sides, therefore a triangle has three sides.’ Adding, contrary to Kant’s opinion, that while the triangle’s existence may be questioned by the conditional assertion “if a triangle exists,” no corresponding conditional assertion can be made of God without contradiction.

Again, I do not take this to be proof.  All he is saying is that we cannot logically say “if God exists, and He may not, then He necessarily exists,” this merely implies a linguistic failure: we haven’t the words to speak about this coherently.  This isn’t surprising since we’re talking about a theoretical mode of existence so far removed from our own.  That is not the same as saying that no debate exists.

After all, let us assume that there exists a necessary thing.  If we had certain knowledge of this necessary thing it really would be nonsensical to speak of it in terms of possibility.  “If a necessary thing exists” becomes a meaningless phrase because where it is possible, it must exist—it cannot happen to exist, nor happen not to exist, it is necessary!  But where we do not know if it is possible or not—or rather, real or impossible—it cannot be illogical for us (who do not know) to speak as if a necessary being might not exist.  Aquinas made a similar point in the first article of his Summa Theologica.

Which is why, in spite of the apparent contradiction, all of us understand what is meant by the proposition; and it brings us back to Malcolm’s first point.  We do not actually know whether a necessary being is impossible or not.  But the real flaw in Malcolm’s reasoning, the one that he inherited from Anselm, is that he assumes that if a necessary thing exists, it must be God.  But just because God is a necessary thing, it does not follow that a necessary thing is God.

What Anselm has really said is:

Premise 1: God is a necessary thing. (A necessary thing is defined as something whose nonexistence is logically impossible.)

Premise 2: “whatever can be conceived but does not exist: if it were to exist its non-existence either in the reality or in the understanding would be possible.”

Conclusion: God does not, not exist—i.e. He exists.

But this is a non sequitur.  The correct conclusion is that a necessary thing exists! (unless it can be proved that a necessary thing is impossible)  But just because a necessary thing exists does not mean that it is omnipotent, omniscient, or benevolent—unless it can be shown that the only possible necessary thing is “a thing greater than which is inconceivable”.  Consider this: it seems that matter/energy can neither be created nor destroyed.  That is to say that it depends on nothing for its existence—which is precisely Norman Malcolm’s definition of a necessary being.

            The ontological argument is so traditionally convoluted in its phrasing that even a philosopher like Norman Malcolm could miss what in plain English should have been so obvious.  Once this is taken into account, all of his deductions become irrelevant to the question of God’s existence.