Comments on Oppenheimer and Zalta's "On the Logic of the Ontological Argument"


This paper is Dr. Willard’s response to Paul E. Oppenheimer’s and Edward N. Zalta’s “On the Logic of the Ontological Argument.” Presented at the APA Pacific Division Meetings, Los Angeles, CA., March 29, 1990.


In this paper Oppenheimer and Zalta provide a novel and highly elegant reconstruction of an Anselmian argument for the existence of the greatest conceivable being—or God, for short. Anselm contrasted existence in the understanding or mind with existence in reality or in the "external world." The greatest conceivable being exists in the understanding of anyone who conceives of or thinks of him. But, Anselm holds, any thought of any being as non-existent cannot be a thought (conception) of the greatest conceivable being, for then you could think of a being greater than the one you thought of: namely, one just like it, but also existing in reality. So one must think of (conceive of) God as existing in reality, or else not think of him at all—and hence not even be able to deny his existence, since in thinking of him as non-existing you would always be thinking of something other than him. So the non-existence of God would be inconceivable.

Unfortunately, in my view, all of this never really gets us beyond how we must think if we are to succeed in thinking of God. It does not imply anything about what must be the case given that we do think of God, much less whether we think of God or not. This is why there is such a strong tendency to give modal interpretations of Anselm's argument(s?). But I strongly agree with Oppenheimer and Zalta that his argument is not modal. My own view is that it is a non-modal argument that is invalid as well as unsound.

The great difficulty with regard to this argument has always been to provide an interpretation of existence in the understanding under which that "existence" will necessitate existence of the "same" object in reality for, precisely, the case of that particular object which is such that one cannot think of an object greater than it is thought to be. From Aristotle on through early Modern philosophy there is a philosophically rich story, with numerous variations, about what it is for something to be an object of a thought. Generally speaking, the "thought" must significantly take on the nature of its object, and this is what is supposed to justify speaking of the object, or of what it is, "existing-in" the mind.

Oppenheimer and Zalta, interestingly enough, stand entirely outside of this tradition, saying nothing at all about what it is for something to be an object of a thought. They try to reconstruct "the" argument entirely within the nomenclature of contemporary logical formalisms. Their view is that it is "the quantification that is doing the real work" in Anselm's argument. I cannot pass by this without noting the extreme unlikelihood that it should be so, once you stop to think about it. I suppose the authors regard the action of quantifiers as being what Anselm, unbeknownst to him, was trying to talk about in speaking of objects existing-in the understanding. But they do not really discuss whatever it is that quantifiers do in accessing objects and what that might or might not have to do with those objects having or having to have the "property" of existence.

Instead, their strategy is to distinguish between saying that a thing x has being (or "saying there is such a thing as x") and saying that x exists (or "saying that x has the property of existence"). (p. 1) The former is done in their formalism, as is increasingly common today, by using the expression " y(y=x)," while the latter employs the expression "E!x." The expression " y(y=x)" has been used in recent years to construct formalized languages "in which one can talk about and refer to objects even though they may not exist in reality." (p. 1) The authors assure us that we "need not accept any theory asserting that there are nonexistent objects to appreciate our version of the ontological argument—only the viability of the distinction between being and existence." (p. 1) Unfortunately, they give us no idea of what this distinction is or what its "viability" amounts to or how it relates to Anselm's two ways in which the same thing might "be." They simply rely upon its current employment.

The way the authors set up the formalism for their version of the ontological argument (pp. 2-5) appears to me to be beyond reproach—as, indeed, does the formal structure of the demonstration, "The Ontological Argument," on p. 9, which gives us the conclusion "God exists." However, I do have some concerns about the non-logical predicates they have chosen, and about the manner in which they attempt to symbolize Anselm's premises. They attempt to formulate the argument utilizing only the two predicates "x can be conceived" and "x is greater than y." Obviously lacking is a predicate for being conceived to be greater than. This idea, which is the core of Anselm's argument, is to be captured by the sentence structure in which the two predicates are placed. But can it really be done that way? The first premise of Anselm's argument is acknowledged to be: "There is (in the understanding) something than which nothing greater can be conceived." (p. 5) The authors read this into their formalism as:

Premise 1: x(Cx & - y(Gyx & Cy)).

Which, they say, "simply asserts that there is a conceivable thing which is such that nothing greater can be conceived." (p. 5) And it should say that. But does it? I don't think it does.

What it really says is that there is something that can be thought of ("conceived") and everything either is not greater than that thing or cannot be thought of. Is this Anselm's premise? I don't really see how it could be. For if a is greater than b and a is conceived of, it does not follow that a is conceived of as greater than b or not. No conjunction of being-greater than and being-conceived-of can give you being conceived of as greater than. Surely it is this latter which is the heart of Anselm's premise. He wants to argue from the (alleged) fact that you cannot conceive of anything greater than x to its existence, not from the conjunctive "fact" that there is nothing both greater than x and thought of (conceived). Indeed, this latter looks awfully close to just begging the question at issue, once we know that existence is a greater-making trait and so must be analytically included in "greater."

I have similar misgivings about the other premise in the reconstructed argument: x(-E!x -- y(Gyx & Cy)). This is supposed to capture Anselm's claim that, for any given thing, "if it were only in the understanding, it could be thought to exist also in reality - which is greater." (quoted on p. 8) But the formalized sentence doesn't seem to me to say this at all. Rather, it seems to me to say: Everything is such that if it does not exist in reality, then there is something greater than it and conceivable. This does not require that the "something greater" be the same thing as failed to exist in reality, nor does it capture the basic point that something conceived of as existing in reality is greater than the same thing conceived of as not existing in reality—all of which is, I take it, essential to Anselm's argument.

Possibly the authors will say: Precisely our point! All of that stuff really has nothing to do with the argument. It has only to do with quantification, and with how definite descriptions can be introduced in free logic, where being is a mere matter of quantification, to yield an E! from and x. They conclude their paper by saying: "We show how simple are the logical mechanisms and metaphysical assumptions of Anselm's Proslogium II argument." Perhaps I have not understood, but I am not yet convinced they do. And it is not just the historical point concerning what all this has to do with Anselm. There are the systematic issues, having to do with the difference between being (quantification) and not being (not quantification?), the difference between existing and not existing, and how being and existing relate to each other. The mere suitability of distinguishing being from existing within formalisms associated with certain logical theories does not seem to me enough to bear the weight of a derivation of the reality of God from our capacity to refer to him. What is yet lacking is an ontological analysis of quantification itself, in free and in non-free logics—that is, a clarification of exactly in what sense a quantifier in free logic lays hold of an (existing or non-existing) object, and of exactly how the object's being (as quantification [top p. 10]) is, in a certain special case, enough to require the actual existence of the object.


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