TWO ARGUMENTS of ST. ANSELM 1. in Proslogium II, St. Anselm

APPENDIX TWO ARGUMENTS OF ST. ANSELM 1. In Proslogium II, St. Anselm argues as follows: And assuredly that than which no greater being can be conceived, cannot exist in the understanding alone. For suppose it exists in the understanding alone: then it can be conceived to exist in reality; which is greater. Therefore, if that than which nothing greater can be conceived exists in the understanding alone, the very being than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. Hence, there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality. 1 I shall take "exists in the understanding alone" to mean "is logically possible but not actual", and I shall take "a being than which no greater can be conceived" to mean "a being than which no greater being is logically possible", i.e., "a maximally great being". Moreover, I shall take "[If X] exists in the understanding alone, [then] it can be conceived to exist in reality, which is greater" to mean "If X is merely logically possible, then it would be greater if it were actual"; and I shall take it that the bearer of the predicate "would be greater if it were actual" is, at least, a logically possible object. Given these interpretations, Anselm's argument can be restated as follows: (1) If there were a logically possible object which is a maximally great being and it were merely logically possible (rather than both logically possible and actual), then it would be greater if it were actual. But (2) "X is a logically possible object which is maximally great" entails "X could not (and would not) be greater under any conditions, including its actuality". 141 142 APPENDIX So (3) there is no logically possible object which is both maximally great and merely logically possible. But (4) there is in fact a logically possible object which is maximally great (namely, God). Hence (5) there is a logically possible object (i.e., God) who is not merely logically possible but both logically possible and actual as well. 2. Premisses (1) and (4) of this argument are, of course, contro versial. Premiss (4) is false unless (a) there are logically possible objects and (b) God is among their number. However, I have defended the thesis that there are logically possible objects in 7.5, and I have discussed the question whether God is logically possible in Chapters 6 and 9; so I shall say no more about premiss (4) here. But now what are we to make of premiss (1) - the claim that if there were a merely logically possible object which is maximally great, then it would be greater if it were actual? Isn't that claim suspiciously similar to the claim that, e.g., a merely logically possible glass of beer would, ceteris paribus, contain more beer if it were actual? Reflection will show that the answer is "No". Qua glass of beer, the only difference between a merely logically possible glass of beer and an actual one is just that the former is merely logically possible and the latter is actual. Actuality is not a beer-increasing property and being merely logically possible is not a beer-diminishing property. However, things are otherwise with respect to greatness. Actuality is a greatness-increasing property relative to God, as the following will show. We can say with perfect propriety about some individuals (e.g., St. Francis) that it is better than not that they are (or were) actual. And it is even clearer that it is better than not that God, a maximally great being, be actual. But maximal greatness entails having every property TWO ARGUMENTS OF ST. ANSELM 143 which is such that it is better than not that an omnipotent, omniscient and perfectly good being have it. Hence, even though, for most predicates, it is false that the actuality of the object which bears them increases the amount or degree in which they are possessed, actuality is a greatness-increasing property relative to God (though not relative to, say, Hitler). But now it is surely a necessary truth that if an individual, X, lacks a given greatness-increasing property, G, then, ceteris paribus, it would be greater if it possessed G. It follows that if God is merely logically possible, then he would be greater if he were actual. It is of note that, even if we subscribe to a relativistic interpretation of actuality - even if we hold that "X is actual" always expands into "X is actual relative to a given possible world, W' and that, hence, the possible world, which is actual from our point of view, has no privileged status with respect to actuality, my argument will still hold. For, whatever may be thought of other possible worlds, it is plainly better than not that God exist in the world which is actual from our point of view. And, again, it is a necessary truth that a maximally great being would have every property which is such that it is better than not that he possesses it. But, finally, does God exist, not only in our world, but in every possible world? Anselm's Proslogium II argument does not require this to be the case; but if it is not the case, then God does not exist with SS necessity. And it is not, perhaps, just intuitive that God occupies every possible world. (Aren't there possible worlds in which, e.g., the only non-divine things are mud and rain? And if so, is it really better than not that God occupy those worlds?) But fortunately we need not simply rely on our intuitions here, since Chapter 5 provides us with a demonstration that if God exists in one possible world, then he exists, with SS necessity and qua maximally great, in all possible worlds, including our own. (If it is clear that God would not inhabit worlds in which the only non-divine things were, e.g., mud and rain, then, if God exists in some possible world, so much the worse for 144 APPENDIX mud-and-rain 'worlds'. They are demonstrably not possible.) 3. In Responsio I, Anselm presents the following argument: Furthermore, ifit can be conceived at all, it must exist. For no one who denies or doubts the existence of a being than which a greater is inconceivable [i.e., God] denies or doubts that if it did exist, its non-existence would be impossible. For otherwise it would not be a being than which a greater cannot be conceived. But as to whatever can be conceived but does not exist - if there were such a being, its non-existence ... would be possible. Therefore if a being than which a greater is inconceivable can even be conceived, it cannot be non-existent.2 Norman Malcolm has written as follows about this argument: Let me summarize the proof. If God, a being greater than which cannot be conceived, does not exist then He cannot come into existence. For if He did He would either have been caused to come into existence or have happened to come into existence, and in either case He would be a limited being, which by our conception of Him He is not. Since He cannot come into existence, if He does not exist His existence is impossible .... Thus God's existence is either impossible or necessary. It can be the former only if the concept of such a being is se1f contradictory or in some way logically absurd. Assuming that this is not so, it follows that He necessarily exists. 3 What Malcolm writes here is a considerable departure from what Anselm actually says. Anselm does not claim, in the envisaged argument, that if God does not exist, then his existence is impossible. This is in fact demonstrable. (One way of demonstrating it is to point out that (1) the denial of the conclusion of modal argument M (Chapter 5), namely, that God exists, entails the denial of one of M's premisses and (2) the premiss which affIrms God's logical possibility is the best candidate for being rejected.) But Anselm does not demonstrate it - at least not in connexion with the present proof.4 Another defect in Malcolm's interpretation is that Anselm evidently intends to reach his conclusion via modus tollens, but there is no hint of this in Malcolm's interpretation.5 4. Let me say more about the modus tollens character of Anselm's proof. One not implausible interpretation of the proof is as follows: TWO ARGUMENTS OF ST. ANSELM 145 (1) If God does not exist, then if God existed, his non-existence would be possible. But (2) if God existed, then his non-existence would not be possible. So (3) the antecedent of (1) is false, i.e., God exists. (From (1) and (2) by modus tollens.) On this interpretation, Anselm holds that "If God existed, his non existence would be possible" is contradicted by "If God existed, his non-existence would not be possible". But in fact it is doubtful that these are contradictories. For, again, it is demonstrable that if God does not exist, then it is logically impossible that he exists. So if God does not exist, the antecedents of the allegedly contradictory condi tionals are neessary falsehoods. But then, if we treat them as counterfactual conditionals, they are, if David K. Lewis is right,6 both vacuously true and, hence, not contradictories.

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