Anselm's Other Argument

A. D. Smith

• Publisher: Harvard University Press
• Year: 2014
• ISBN:
  9780674726857
• Topic: Filosofía
• Subtopic: Filosofía de la religión

Anselm of Canterbury (1033–1109 CE), in his work Proslogion, originated the "ontological argument" for God's existence, famously arguing that "something than which nothing greater can be conceived, " which he identifies with God, must actually exist, for otherwise something greater could indeed be conceived. Some commentators have claimed that although Anselm may not have been conscious of the fact, the Proslogion as well as his Reply to Gaunilo contains passages that constitute a second independent proof: a "modal ontological argument" that concerns the supposed logical necessity of God's existence. Other commentators disagree, countering that the alleged second argument does not stand on its own but presupposes the conclusion of the first. Anselm's Other Argument stakes an original claim in this debate, and takes it further. There is a second a priori argument in Anselm (specifically in the Reply ), A. D. Smith contends, but it is not the modal argument past scholars have identified. This second argument surfaces in a number of forms, though always turning on certain deep, interrelated metaphysical issues. It is this form of argument that in fact underlies several of the passages which have been misconstrued as statements of the modal argument. In a book that combines historical research with rigorous philosophical analysis, Smith discusses this argument in detail, finally defending a modification of it that is implicit in Anselm. This "other argument" bears a striking resemblance to one that Duns Scotus would later employ.

1

THE MODAL ONTOLOGICAL ARGUMENT

I propose to begin our investigation of the Modal Ontological Argument with Norman Malcolm, since, as I mentioned in the Introduction, it was he who brought this form of argument for God’s existence to the general attention of the contemporary philosophical world. Like all versions of the modal form of the Ontological Argument, Malcolm’s hinges on the claim that God could only exist non-contingently: that is to say, with logical (or “metaphysical”: i.e., absolute) necessity.¹ Malcolm, of course, based his own argument on Anselm, and he characterizes Anselm as making two claims: “First, that a being whose nonexistence is logically impossible is ‘greater’ than a being whose nonexistence is logically possible …; second, that God is a being than which a greater cannot be conceived” (Malcolm 1960: 45). Malcolm endorses both of these claims, and therefore concludes that non-contingent existence must be ascribed to God—on the grounds of the Anselmian principle that, since nothing greater than God can be conceived, we must attribute to Him everything that it is better or greater to be than not to be (P 5).² Believers in God, in any case, generally do not believe that He merely “happens” to exist. Moreover, the sense of necessity implied looks as if it is not mere causal necessity, for then God’s existence would be dependent upon something else: upon at least certain causal laws, perhaps. Suppose we accepted this. Where would that get us? At one point Malcolm sums up his argument as follows:

What Anselm has proved is that the notion of contingent existence or of contingent non-existence cannot have any application to God. His existence must either be logically necessary or logically impossible. The only intelligible way of rejecting Anselm’s claim that God’s existence is necessary is to maintain that the concept of God, as a being a greater than which cannot be conceived, is self-contradictory or nonsensical. Supposing that this is false, Anselm is right to deduce God’s necessary existence from his characterization of Him as a being a greater than which cannot be conceived (Malcolm 1960: 49).

The correctness of the inference made in the first two sentences of this passage may not be immediately apparent. If God cannot exist contingently, it may be thought, all that follows is that if God did exist, He would exist necessarily—not that He actually does. In fact, however, given certain qualifications to be noted shortly, Malcolm’s inference is sound. This is perhaps best shown, in a way that is now standard, by presenting the Modal Ontological Argument as a formally valid argument in modal logic—an approach first presented by Charles Hartshorne (1962: 50–1).³

The simplest presentation of the argument in this style has two premises. The first concerns the non-contingency of divine existence. As we saw in the Introduction, the best way to avoid the suspicion that in proposing such non-contingency one is bizarrely writing God into existence is to express the claim in a Kantian, conditional form: If God were to exist, He would exist non-contingently, or necessarily.⁴ For the time being, let us accept this as a partial spelling out of the concept of God.⁵ If it is, it is an a priori necessary truth. So let us explicitly signal this fact, and take the following as our first premise: Necessarily, if God exists, He exists necessarily.⁶ The second premise is to the effect that it is possible that God, so understood, should exist. From these two premises it is, with certain qualifications to be noted soon, possible to prove that God actually exists. Here is an informal presentation of the matter.⁷

The most intuitive way of getting a grip on modal arguments is to understand them in terms of “possible worlds”: all the ways things could possibly have been together with the actual world (as the way things actually are).⁸ On this approach a proposition’s being necessarily true is thought of as its being true at all possible worlds. A proposition’s being possibly true is thought of as its being true at one possible world (at least). A proposition is contingently true just in case it is actually true, but false at some possible world. A proposition is contingent simpliciter just in case it is true at some possible world (perhaps not the actual one) and false at some possible world. The analogous glosses for false propositions are obvious. On this approach the claim that God exists necessarily is construed as the claim that the proposition God exists is true at every possible world. Similarly, the claim that God possibly exists is construed as the claim that the proposition that God exists is true at some possible world or other.

The first premise of the argument states that it is necessary that if God exists, He exists necessarily: that is, that this conditional is true at every possible world. So, if God does exist in some possible world, He exists necessarily in that possible world: that is, the proposition that He exists necessarily is true at that possible world. The second premise has it that God’s existence is at least possible: in other words, He exists in at least one possible world. So, from the previous consideration, it follows that the proposition that God exists necessarily is true in at least some possible world. But if in that possible world God exists necessarily, He exists in the actual world—since to exist necessarily is to exist in all possible worlds, the actual one included. Moreover, God exists necessarily in the actual world, since, as we have just seen, in virtue of existing necessarily in some possible world He exists in all possible worlds.

Some will find the above argument objectionable because of the way in which it treats “God” as a proper name or singular term. An argument for the existence of God cannot, of course, simply assume that the term “God” actually refers to anything; and many object to the employment of possibly empty singular terms in serious arguments. One way to avoid this problem is to replace reference to God with reference to a certain (possible, or possibly instantiated) kind of being. Hartshorne’s choice is a perfect being.⁹ His argument has as its first premise the claim that necessarily, if a perfect being exists, it is necessary that a perfect being exists: something that he dubs “Anselm’s Principle” (Hartshorne 1962: 51). At first sight this Principle may seem not to capture properly what Hartshorne takes to have been Anselm’s insight: namely, that a perfect being cannot exist contingently. All that his Principle explicitly states is that, necessarily, if a perfect being exists, then, necessarily, some perfect being or other exists. This does not capture the idea that if there is a perfect being in some possible world, it exists necessarily (in virtue of being perfect). All that the Modal Ontological Argument with Hartshorne’s premise may seem to allow us to infer is that there is some perfect being or other in every possible world—though perhaps a different one in each. The genuine Anselmian insight, if that is what it is, certainly entails Hartshorne’s premise; and the argument with his premise validly leads to the existence of a perfect being. It would, however, be much better to track the modal and metaphysical facts more accurately by expressing Anselm’s “insight” more faithfully.

In fact, Hartshorne’s procedure is not open to the foregoing criticism, because of a further claim he makes. He claims that “perfection characterizes a unique individual, rather than a class of possible perfect beings” (1962: 62). What he means by this is not merely that at most one divine being can exist, but that if in any two possible worlds there is a perfect being, it is the same perfect being that exists in them.¹⁰ Hartshorne may be right about this; indeed, I believe he is. In order to show this, however, one must appeal to some highly controversial metaphysical principles. In order to keep things relatively straightforward at this stage, I shall for the sake of argument allow that there could be more than one perfect being in a single possible world. In order to retrieve Anselm’s “insight,” I propose to modify “Anselm’s Principle” so that it reads: Necessarily, if a perfect being exists, it necessarily exists. Finally, since we all know that the Modal Ontological Argument is supposed to be a proof of God’s existence, I shall replace Hartshorne’s “perfect” explicitly with “divine.”

When we move from talking about “God” to talking about “a divine being” a certain complication arises. We cannot deduce that a divine being actually exists from the following two premises: necessarily, if a divine being exists, it exists necessarily, and it is possible that a divine being should exist. From these premises we can prove that the possible divine being actually exists, but we cannot prove that this being is actually divine. In other words, the proof will leave open the possibility of a being that is divine and yet not essentially so.¹¹ This supposed possibility is no doubt absurd: for it amounts to the idea that something non-divine could have been divine. Nevertheless, this “possibility” needs to be excluded if our argument is to be logically cogent. We can do this by explicitly writing into our first premise the traditional thesis that God, or a divine being, is essentially divine. We then get the following: Necessarily, if a divine being exists, it exists necessarily and is necessarily divine. This, together with the premise that it is possible for a divine being to exist, allows us to prove that a divine being actually exists. For the reasons indicated, it will not allow us to prove that only one divine being exists. The traditional literature is, however, replete with arguments to the effect that at most one divine being is possible—not only within any world but across all worlds. We could subsequently appeal to such arguments to attempt to remedy this shortcoming of the present argument, if that is what it is. For the time being a proof that a divine being exists will be proof enough.¹²

Here is an informal proof of the argument.¹³ The first premise tells us that if there is a divine being in any possible world, the proposition that that being exists is necessarily true at that world. By the second premise we know that there is a divine being in at least one possible world. Hence, we can conclude that the proposition that this divine being exists is necessarily true at this world. If there are two or more divine beings in this world, the propositions that assert of each that it exists are both or all necessarily true—as are the corresponding propositions at other worlds that may contain other possible divine beings. Consider just one divine being in the world in question. Since the proposition that asserts the existence of this being is necessarily true at that world, this divine being exists in the actual world—and, indeed, in all possible worlds. Moreover, this being will be divine in the actual world, since, by the first premise, it is necessarily divine. If it is possible for more than one divine being to exist, either in the same world or in different worlds, then they all exist, exist necessarily, and are necessarily (and, hence, actually) divine.

I said above that, with qualifications, it is possible in modal logic to prove that God (or a divine being) exists. We have now seen the proofs. It is time for the qualifications. They arise from the fact that there are various systems of modal logic. The system that I have tacitly employed above is the strongest modal system there is. It is known as S5. This system has as an axiom the claim that if something is possible, it is necessarily possible: or, equivalently, that if something is possibly necessary, it is necessary. It is this, and this alone, that allows us immediately to infer from the fact that a divine being exists necessarily in some possible world (i.e., that it is possible that such a being should exist necessarily) that it actually does exist necessarily.¹⁴ Now, the fact that S5 is such a strong system may not by itself be a matter of concern, since the vast majority of philosophers regard S5 as enshrining our understanding of absolute possibility and necessity. Nathan Salmon (1982: 230–252 and 1989), however, developing ideas in Hugh Chandler (1976), has presented an argument to the effect that S5 (and even the weaker modal system S4) are so strong that they misrepresent our understanding of metaphysical modality. The argument in question presupposes the truth of the doctrine of the necessity of origin, as famously propounded by Saul Kripke (1972)—a doctrine that I do not propose to contest. To illustrate the argument, suppose I make a table top, T, by cutting it out of a much larger piece of wood. Most people believe that I could not have made that very table top from a completely different piece of wood—even from a completely different section of the larger piece of wood in question. There is, however, a certain tolerance. Surely I could have made T from a slightly different portion of the larger piece of wood. Suppose that I actually make T by sawing across the large piece of wood at two places, producing a chunk of wood W₀ that constitutes T. Surely it would have been T that I made if I had made the two cuts just an inch to the left, resulting in a slightly different chunk of wood W_1. For the sake of argument, let an inch be the limit of tolerance.¹⁵ In other words, if the cuts had been made more than an inch up or down the larger piece of wood, it would (necessarily) not have been T that was made.¹⁶ Now suppose that I had made T out of W_1. If so, I then could have made it from a yet slightly different chunk of wood W₂ that lies another inch up to the left: that is, within the limits of tolerance as it applies in that situation. W₂, however, will exceed the limits of tolerance for T given how it was actually made, for it will be more than an inch different from W₀. This invalidates S4. The “char...