Many arguments have been put forth for the existence of god. Among them is the ontological argument, which was first proposed by St Anselm, and was later used by Descartes in his Meditations on First Philosophy. The ontological argument is notable for three reasons. First is that it is one of the few arguments for god’s existence that attempts to prove its conclusions without relying on evidence from experience. Secondly, many other arguments for god’s existence “lean on” the ontological argument; to show that the ontological argument is invalid would force these other proofs of god’s existence to be discarded (the reliance of other arguments on the ontological argument was shown by Kant). Finally, reasoning about the ontological argument reveals other interesting problems about the logic of existence, which are at least as interesting as the question of god’s existence.
The ontological argument comes in two basic forms, a weak form and a strong form. The weak form of the argument (also the original form of the argument) runs as follows: god is a being with all possible perfections. Existence is a perfection. Therefore god exists. Kant argued that this form of the ontological proof of god’s existence was invalid because existence was not properly speaking a predicate that could be applied to anything. In Kant’s view to state anything is to state that it exists. However we might think that a predicate of “existence” might be reasonable if we define existence more narrowly, say something that has a casual effect on the world (or something else that makes existence more concrete). In this case there might be possible entities that don’t “exist” in this sense (say a particle that never interacts with anything), thus showing that it is reasonable to say that “existence” is a property that can apply to some things and not others. Even if we allow existence as a predicate the argument is still invalid. The problem we now run up against is that to conceive of something as having a property does not guarantee that it actually has that property, unless the object in question is purely mental. For example I might assert: “this table is red”, but that in no way makes the table actually red. Likewise the assertion “god ‘exists’” in no way guarantees that god actually exists. Of course we could use the ontological argument to show that the idea of god exists, but since this is trivially obvious, and in no way guarantees that a god with real power exists, the weak ontological argument seems to be a failure.
Let us then turn to the strong form of the ontological argument. In the strong version the goal is not to show that god simply exists but to show that he/she/it necessarily exists (or has “maximal existence”). If something necessarily exists then it exists in every logically possible world (and thus in our real world as well). The argument runs as follows: Consider a being (god) who necessarily exists. Clearly is possible that such a being exists, which means that this being exists in some possible world. However, due to the meaning of necessary existence, if this being exists in one possible world it exists in all of them. Thus god exists. There are two flaws with the strong version as presented here. One is that to be necessary is an attribute of statements, not of things. It is meaningless to say that something is necessary; what the argument meant to say was that god’s existence was necessary, meaning that the statement E(g) is necessary. The real flaw in the argument however is a confusion concerning the role of necessity and the structure of possible worlds. There are three classifications of sentences that define the structures of possible worlds, necessary, possible, and contradictions. Necessary sentences are true in all possible worlds, possible sentences are true in some and false in others, and contradictions are true in no possible world. These classifications are exclusive, a sentence can only belong to one of them, and it belongs to the same classification no matter what possible world we are considering. The flaw in the argument then is to assume that E(g) is necessary and possible, when it can only be one of the two. If we assume that E(g) is possible, as the argument states, then clearly it is not necessary. One (valid) way to determine when a sentence is necessary is if its negation is false in all possible worlds (its negation is a contraction). However it is extremely easy to imagine very simple worlds (for example those without time, containing only a single particle) where not-E(g) is true, showing that E(g) is not necessary after all. Finally let us consider momentarily the possibility that the argument is correct, and my objections wrong. If this is true we could form an equally valid argument as follows: it is possible that “my desk is red” is necessary. Since it is necessary in some possible world then it must be necessary in all of them. Therefore my desk is red. Since my desk clearly isn’t red this is absurd.
Have I demonstrated the non-existence of god by refuting the ontological argument? No. In fact it is impossible to prove the non-existence of anything unless it is a contradiction. However E(g), while not necessary, isn’t a contradiction either. It is possible to conceive of a world where E(g) is true as well as worlds where E(g) is false. I personally think that E(g) is false based on the available evidence and epistemological grounds, but that doesn’t prove I am correct.