Charles Hartshorne
Professor Malcolm’s recent exposition,1 correct so far as it goes, of Anselm’s second ontological argument (there are indeed two) can be partly formalized in a chain of valid inferences as follows:
1. (∃x)Px → N(∃x)
Px The existence of perfection can only be necessary.
2. ~ N(∃x)Px → N ~ N(∃x)
Px The non-necessity of perfection entails its necessary non-necessity (modal status, in the absolute logical sense, is always necessary).
3. N ~ N(∃x)Px → N ~ (∃x)
Px The necessary falsity of the consequent entails the necessary falsity of the antecedent (1 and a modal form of modus tollens).
4. N(∃x)Px ∨ N ~ (∃x)
Px Either perfection exists necessarily or its existence is impossible (taut. and 2, 3).
5. ~ N ~ (∃x)
Px The existence of perfection is not impossible.
6. N(∃x)
Px Perfection exists necessarily (4, 5).
Concerning 1. For an individual, to exist contingently is an imperfection; hence no individual so existing can exemplify perfection. Malcolm has well explicated this principle, Anselm’s great discovery; so has J. N. Findlay, from an anti-theistic point of view.2 Well or ill, I have expounded it on various occasions, without rebuttal from my philosophical colleagues.3
There is some difficulty about the interpretation of the variable x. The necessity, formally regarded, requires only that there be some individual or other exemplifying perfection. However, it is an old insight that perfection characterizes a unique individual, not a class of possible perfect beings. There can here be no principium individuationis. Hence, if perfection were capable of non-existence, we should have to admit what logicians rightly regard as absurd, a merely possible yet individual entity. Thus the necessary connection between perfection and uniqueness is an additional reason supporting 1. There are still others, which I here pass over.
2 applies a fairly standard axiom in modal logic. I do not believe that the objections some have made to this axiom are here relevant.
4 infers the disjunction of the consequents of the tautological disjunction (∃x)Px ∨ ~ (∃x)Px and its implications via 2, 3.
5 is the most problematic assumption. Its justification lies outside the ontological argument proper. However, even without 5, the reasoning proves that perfection cannot contingently fail to exist and cannot contingently exist; it must either exist necessarily or be logically incapable of existence. “Empirical theism” and “empirical atheism” are alike illogical.
Malcolm’s attempts to justify 5 are weak. Worse than that, he fails to rebut Findlay’s objection that the argument appears to derive the concrete from the abstract, from a mere conceptual definition. Since in the divine omniscience the entire riches of all reality must be comprised, if the necessary existence of perfection is identical with the divine actuality, we face the contradiction that the more follows from the less, the concrete from the abstract. Malcolm’s rebuttal, through an attempted distinction between “concrete” and “contingent,” does not meet the difficulty. God’s reality must be more than can be contained in a mere empty definition, couched in general terms like “that,” “than which,” “nothing,” “greater,” “can be conceived” (or however the term “perfect” is defined). Besides, it is evident upon reflection that the necessary can logically be but the common denominator of all possibilities, and what is that if not something highly abstract? A necessary proposition, as Lewis said, is entailed by any and every proposition, even the most abstract and empty: thus its meaning can only be the most universal or abstract element in the meanings of propositions in general. The concrete reality of God cannot be such an abstraction, at least if God is the proper object of worship.
What is the conclusion? Findlay says (I interpret him rather freely) that God cannot exist, since his existence must be necessary and, therefore, would represent the absurdity of a most abstract thing that at the same time was concrete.
There is another possible conclusion: that God is both necessary and contingent, hence both abstract and concrete, or that He has an essential but abstract character which is bound in any possible state of affairs to be actualized or concretized somehow, the how being always contingent. This is not the most usual conception of deity; indeed it is hard to find it prior to Socinus, and it has been somewhat rare down to our own time. I have argued in various places that this conception alone can remove the paradox of the step from the abstract to the concrete which is the real difficulty with the ontological argument. For according to the “Socinian”view, the bare “existence of God” as necessary is utterly abstract, since it says only that the essence “perfection” is somehow concretely actual, no matter how. This amounts to saying, to put it in one of numerous equivalent ways, that whatever world there may be, it is fully and infallibly known and sustained by the divine power. Let the world be anything you please concretely, and let the particular state of infallible knowing of that world take any shape it can, so long as the mere form of infallibility is embodied, God exists. Infallibility is compatible with any content whatever; it is an empty form, in itself. Just such an empty—though, as we have seen, individual—form is perfection, in abstraction from its contingent modes of actualization with respect to contingent contents.
The justification of 5 cannot be adequately affected without revising the idea of God as above suggested, and one must also employ forms of theistic argument other than the ontological; to this extent the ontological argument is not self-contained. On the other hand, quite without 5, the argument can come to the aid of the other proofs, for what these need from the ontological proof, as Kant’s analysis showed, is merely the exclusion of contingency from the existence of perfection, this existence meaning its being concretized somehow. In turn, to effect this exclusion, neither 5 nor the other proofs are required. There need not, then, be a vicious circle in employing all the proofs together. However, the other proofs, too, and the definition of “God” to be supported by them, must be correspondingly altered, somewhat as we have altered the ontological proof and its conclusion.
It will be a splendid achievement if Malcolm’s fine article causes the philosophical world to take a fresh look at what has, for many decades now—but deceptively—appeared as a well-solved problem. Quite the contrary, there are many unexplored possibilities for its further elucidation; only a book could do any justice to them. An article can but hint at the subtleties of this topic.
Notes
1. Norman Malcolm, “Anselm’s Ontological Arguments,” Philosophical Review, 69: 41-62 (January, 1960).
2. See Findlay’s brilliant essay, “Can God’s existence be disproved?,” Mind (1948). Reprinted in A. Flew and A. Macintyre, New Essays in Philosophical Theology (London, 1955), pp. 47-56.
3. For example, in Hartshorne and W. L. Reese, Philosophers Speak of God (Chicago, 1953), pp. 96-106, 134-37.
Source:
The Journal of Philosophy, Vol. 58, No. 17 (Aug. 17, 1961), pp. 471-473.