The essence of ontological argumentation is the inferential move from the concept/essence of F to the existence/nonexistence of F. We are all familiar with ontological arguments for the existence of God. They have been a staple of philosophy of religion discussions from Anselm to Plantinga. But there is nothing in the nature of ontological argumentation to require that God be the subject matter, or that the argument conclude to the existence of something. There are nontheistic ontological arguments as well as ontological disproofs. Thus there are four possible combinations.
1. Ontological Disproofs of Nondivine Items. Some people think that conceptual analysis is irrelevant to questions of real existence: They think that what exists and what does not can only be determined empirically. But this is not the case. By sheer analysis of the concept round square I can know, and know a priori, that there cannot exist a round square. Round squares and the like can be ruled out on conceptual grounds alone. Even if nothing can be ruled in by conceptual analysis, surely some things can be ruled out. By sheer thinking one can know something, albeit something negative, about reality.
2. Ontological Disproofs of God. Nothing could count as God that did not have the property of aseity, or in plain English, from-itself-ness. The concept of God is the concept of something that by its very nature cannot be dependent on anything else for its nature or existence, and this holds whether or not anything in reality instantiates the concept. Given that nothing could be a se that was not self-existent or a necessary being, this is equivalent to the assertion that God exists necessarily if he exists at all. But if everything that exists exists contingently, as philosophers of an empiricist bent are likely to maintain, then we have the makings of an ontological disproof of God. In a 1948 Mind article, J. N. Findlay gave essentially the following argument:
a. God cannot be thought of as existing contingently.
b. Everything that exists can only be thought of as existing contingently.
Therefore
c. God does not exist.
This ontological disproof of God turns Anselm on his head while retaining the Anselmian insight that God is “that than which no greater can be conceived.” Precisely because God is maximally great, supremely perfect, id quo maius cogitari non posse, he cannot exist. For if everything that exists exists contingently, then nothing exists necessarily. Necessary existence, however, is a divine perfection. Ergo, God does not exist.
The trouble with Findlay’s 1948 argument, an argument which the older and wiser Findlay renounced, is that premise (b) is by no means obviously true, even if we replace ‘everything’ with ‘every concrete thing.’ So, while the argument is valid in point of logical form, it is not obviously sound. A sound argument is standardly defined as a deductive argument the logical form of which is valid but which has one or more false premises. Since we do not know whether premise (b) is true or false, we do not know whether the argument is sound. And since we do not know whether the argument is sound, we cannot legitimately call the argument a proof, sensu stricto. For an argument to be a proof, it does not suffice for its premises to be all true; they must also all be known to be true.
3. Ontological Proofs of God. Here is an example. God, by definition, is ens perfectissimum, a maximally perfect being. Now a maximally perfect being cannot be modally contingent, but must be modally noncontingent: it must be either impossible (existent in no possible world) or necessary (existent in every possible world). But surely it is possible that there be a maximally perfect being. (There is at least one possible world in which God exists.) Therefore, God exists in every possible world, whence it follows that he exists in the actual world.
Simplified version: if God is possible, then God is actual. God is possible, therefore God is actual. This is the modal ontological argument in a nutshell.
It is a perfectly valid argument. The problem, however, is to provide a compelling reason for thinking that God is possible. The fact that one can conceive of God without contradiction does not establish that God is possible. Conceivability, defined as thinkability without contradiction by minds of our sort, is no sure guide to real, extramental, possibility. At best, conceivability is a defeasible indicator of real possibility.
4. Ontological Proofs of Nondivine Items. Can one establish, by conceptual analysis alone, that something exists even if one cannot establish, by this means, that God exists?
Consider the concept true proposition. We have the concept. Can we show a priori, by sheer analysis of the concept, that is has a real, extraconceptual, instance? The concept is either instantiated, or it is not. If it is not instantiated, then it is true that it is not instantiated, which implies that the concept true proposition IS instantiated. If, on the other hand, the concept in question is instantiated, then of course it is instantiated. Therefore, necessarily, the concept true proposition is instantiated, and there necessarily exists at least one truth, namely, the truth that the concept true proposition is instantiated. (A truth is a true proposition.)
This is a valid ontological argument for the existence of at least one truth using only the concept true proposition, the law of excluded middle, and the unproblematic principle that, for any proposition p, p entails that p is true. By 'proposition' here I simply mean whatever can be appropriately characterized as either true or false. That there are propositions in this innocuous sense cannot be reasonably denied.