The Ontological Argument

Talk given at the Centre for Philosphical Studies

King's College, London

on March 4th, 1998


Mr J.R. Lucas

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The ontological argument has run for a long time, regularly refuted, regularly re-appearing in a new form. Something can be learnt from its longevity. Its proponents must be on to something, or it would not have survived its many refutations. But equally, it must have been much misformulated, or it would not have seemed evidently fallacious to its many critics. Perhaps it does express a deep philosophical intimation. Certainly it has been taken to prove more than it really can establish. Like many other philosophical arguments it has suffered by being made out to be more rigorous than in the nature of the case it can be. For some philosophers addressing some questions it may have been decisive in leading them to adopt one of the few options open to them: but it is quite inconclusive for others, with different presuppositions or different problems, and cannot be reduced into a valid proof cogent for all comers and compelling them to accept the conclusion it claims to demonstrate.

The standard version of the Ontological Argument is that refuted by Kant. Descartes had argued that God has every ``perfection'', and hence that of existence: for every predicate ascribing a perfection, F,G,H, . . , Fg,Gg,Hg, . . ., because E [for Exists] is a predicate ascribing a perfection, it is alleged to follow that Eg. But it does not follow, Kant says, that Eg, because, Existence is not a Predicate. In modern symbolic logic we can say that we should turn the E round and instead of writing E(x) write (x) [or (\exists x)(x=g)], and say existence is not a Predicate but a Quantifier. If that be the case, we cannot argue that a Perfect Being would have all predicates, and hence, among them, that of existence. All we can say is that the Perfect Being, IF He exists, has all perfections. Kant distinguishes in intellectu from in re, not as a simple distinction easily overreached, but a fundamental one. In intellectu goes with `well-formed', `not self-contradictory', `syntactic': in re with `semantic', concerning a definite proposition which is based on empirical evidence and is capable of being actually true. Questions of existence are always to be decided a posteriori by evidence, and cannot ever be settled a priori; ``. . if . . we admit, as every reasonable person must, that all existential propositions are synthetic, how can we profess to maintain that the predicate of existence cannot be rejected without contradiction?''

Kant's argument is valid against some formulations of Descartes' argument, but claims too much. Mathematicians regularly affirm that there exist prime numbers between 12 and 21, that the nine-point circle exists, and the like; and, contrary to Kant's own view, at least some of these judgements are analytic.1 More generally, there are many uses of `exist' which cannot be represented simply as a quantifier. If we restrict ourselves to first-order logic, then indeed, the ontological argument cannot be formulated within it: but that may reveal an inadequacy in first-order logic rather than in the ontological argument itself.

Even within first-order logic questions of existence arise that cannot be dealt with in purely quantificational terms. Indeed, often we need to assume a non-empty universe of discourse----one in which some things exist---before we can use quantifiers at all. Questions of existential import arise when we use universal terms, as they do also with definite descriptions. Russell's exegesis of the latter, though fail-safe, does not fit our ordinary conversational usage. We can best elucidate one aspect of the word `exists' if we view its negation as a conversation stopper. If I start telling you about the greatest prime number, which I have tracked down on my computer, and has many mystic features, you stop me short by saying that it doesn't exist. Unless I can rebut the claim of non-existence, it is pointless to go on talking about it. So too with the King of France, Ryle's youngest son, the golden mountain and the round square. Once you point out that they do not exist further discussion about them ceases to signify. Hence, contrapositively, the role of existence proofs in mathematics. The reason for proving that the nine-point circle exists is to license further discussion of its properties, forestalling and refuting any claim that it does not exist.

There are, of course, different modes of discourse, and something may properly be discussed in one even though not in another. In the Zoology Department it is no good discoursing on mermaids, centaurs and unicorns, but when among historians or students of literature it may be perfectly legitimate. The relation between these universes of discourse is complex, but sometimes we can view one as a sub-universe of the other, and the use of the existential quantifier in the larger can indicate the non-emptiness of the latter, and hence the propriety of using referring terms within it.2

Questions of existential import can to some extent be dealt with in terms of existential quantifiers, but other senses of the word `exist' are altogether distinct, and are used, indisputably, to express assessments of ontological privilege. We can see this if we consider, once again, the statement:

There exist prime numbers between 12 and 21

and the purported inference from it to the conclusion:

Numbers exist.

Anyone who sought to use that inference as a knock-down proof of mathematical realism would show that he did not understand what was at issue. We may be able to cite the way we talk about numbers as evidence against nominalism, but the fact that we use the existential quantifier in mathematics does not mean that we accept the existence of the natural numbers in the sense that the nominalist denies.

There are many disputed questions of ontological status. Besides the fundamental question of whether the natural numbers exist, mathematicians have sometimes had doubts about negative numbers, real numbers and imaginary numbers. Outside mathematics, philosophers have on occasion doubted whether material objects exist, whether other minds exist, whether space exists, whether laws of nature exist, whether atoms, electrons, or quarks exist. In each case we can understand what is at stake. It is not a linguistic question---we may speak with the vulgar, but assign or deny a fundamental significance to the locutions they use and what those locutions refer to. In some cases the doubts of the philosophers may have been silly, but it is difficult to dismiss them all without abandoning philosophy altogether.

We may therefore question whether Kant's formulation of Descartes' argument really captured what he was trying to say. We need to ask two questions:
1. What does `ontological' mean?
2. What does God do for Descartes?
(1) The word `ontological' comes from the Greek ontos masculine and neuter genitive of on (compare feminine ousa, and its derivative, ousia, substance or essence) present participle of verb einai, to be, to exist; esti, is, there is, exists; to on, used by philosophers for Being, or What There Is; toi onti, in fact, indeed; ontos, really.3 The word `Being' in English does not sound right: we would more naturally say `Reality'. That word was not available in Anselm's time. Anselm uses the phrase in re, from res a thing, to mark the distinction between God merely as an idea and God as really existing. The Schoolmen later coined the adjective realis, and the abstract noun `reality' is derived from it.
(2) The part God plays in Descartes' system, once He has got him out of his solipsistic prison, is small. Although Descartes uses the language of traditional Christianity, the God whose existence he proves does not do very much for him in the way of forgiving his sins, assuring him of salvation, or offering a hope of a future life. The only perfections God has that signify are those of existing and not being a deceiver. Having made Descartes, God can be relied on not to deceive him, but otherwise leaves him alone, to get on with mathematics and natural science on his own. The latter function, of being a reliable non-deceiver, is really a reality principle. If I believe that there is some reality apart from myself, I have reason enough to reckon that my sense experiences are not all merely the figments of my imagination, but are experiences of something other than myself; they are not mere appearances, but indications of how things really are. Reliable reality is what Descartes needs, and that is all that the ontological argument in his hands can properly prove.

If we adopt the maxim that in order to make out what a philosopher means, we should consider what his arguments for the thesis actually prove, and what, in his opinion, follows from it, then Descartes' `God' is to be construed as `Reality'. Spinoza, following in Descartes' footsteps, talks of Deus sive Natura. And it is noteworthy that even Anselm uses the neuter id quo maius nequeat cogitari. The language of the Proslogion shows a significant shift from the personal language in which he addresses God at first---Ergo, domine, qui das..., da mihi,.... quia res... et hoc es....---to the neuter which he uses for his argument---Et quidem credimus te esse aliquid... and thereafter it is always aliquid, or id, or id ipsum, quo maius cogitari non possit. The neuter is taken over in the standard scholastic definition ens realissimum (mistranslated as `necessary being'), not Ens Realissimus.

Nonetheless, the later Schoolmen revert to the neuter; after the word realis had been coined, `God' is defined as If the neuter is correct, and Descartes really means `Reality', how does the Ontological Argument look? Does it look like proving that Reality Exists? It looks better in Greek: to on esti; or in Latin, ens est. These look like tautologies, decidedly difficult to deny. Could Reality not exist? No; it would be a contradiction in terms. The Ontological Argument is valid: but it proves something different from what its advocates supposed. It proves the existence of Reality rather than a specification of what it was like. In the terminology of the Schoolmen it answers the question An sit? rather than Quale sit? Although in the key section of the Proslogion Anselm uses the neuter, later he lapses---if `lapse' be the right term---back into the personal mode of address, and takes it for granted that the Ultimate Reality he has proved to exist is the Christian God who created the world and raised Jesus from the dead. Provided we leave Reality undescribed, we can argue for its existence, but once we have specified the nature, or essence, of anything, whether the Perfect Being, or the traditional God of the Judaeo-Christian tradition, we cannot go on to define Him into existence.

Anselm's God was not just real, but superlatively real. Descartes' `perfection' is similarly superlative in sense. The Ontological Argument argues for the existence not just of Reality, but of Ultimate Reality, Ens Realissimum, and much of metaphysics is guided by a search for the superlative. But are we entitled to posit a maximum? Can we even make sense of maius, `more existing', realius, `more real than'? Even if we can, need there be a most real, realissimum? Undoubtedly, assessments of ontological status can be expressed in terms of reality as well as of existence. But do we talk of one thing existing more than another? The question arises whether such assessments form an ordering, whether we can properly speak of one thing being more real than another. It is not obvious that we can.

We need, in all, to ask four questions about realius, `more real than':
1. Are there gradations of reality---does `more real than' make sense?
(i) Perhaps `real'/`unreal' marks a single contrast, and there are no degrees of reality, no sense on saying one thing is more real than another. Our assessments of reality are highly heterogeneous. Following Aristotle, Austin points out that the contrasts are dominated by the negative: `unreal' wearing the trousers. Even in philosophy there are many different marks of reality we customarily recognise, as the annexed list shows.
(ii) Nevertheless we do sometimes recognise degrees of reality: the greatest prime number and the square circle are logically impossible, whereas the golden mountain only happens not to exist. Hallucinations, dreams, delusions, illusions, shadows, rainbows, material objects, scientific accounts and fundamental laws are successively less unreal. Perhaps we can give sense to `more real than', Anselm's maius, and begin to offer purchase to his argument.
2. If so, is the relation realius, `more real than', serial?
(i) We can make sense of one number being greater than another without being committed to there being a greatest number. Hegel seems to suggest that philosophy is a never-ending quest, which never reaches a satisfactory conclusion, but as soon as one system is evolved, it begins to generate its antithesis. Gregory of Nyssa speaks of a continual stretching forward rather than any point of arrival.
(ii) All the same, we can envisage infinite totalities as a whole. Perhaps the ens realissimum is an ``omega point''.
3. If not serial, does it have maximal elements or a single maximum one?
(i) Even if there are maximally real elements, the ordering induced by `more real than' need not be a linear ordering, so that there might be many maximally real entities; Anselm starts by talking of aliquid quo maius nequeat cogitari, definitely extremal, but possibly along a different branch of being more real than.
(ii) Still, we have ideals of unity. Physicists seek a Grand Unified Theory of Everything, and discuss what it would be like if we had one---if we had arrived at the point Plato sought, hoi aphikomeno, hosper hodou anapaula an eie kai telos tes poreias, a resting place, when we had got there, and an end of our journeying.4 At this point the ontological argument begins to merge with the cosmological argument. But since explanatory power is one mark of reality, that is not surprising. At the very least, it is not far-fetched to seek some unified schema of explanation, and we were to think we had one, it would be natural to hold that we had a correspondingly unified order of reality, in which the ultimate reality would be that in terms of which everything was to be explained; and within that context it would be inconsistent to deny that ultimate reality existed. Kant acknowledges that the Ontological Argument merges with the Cosmological Argument,5 and Mackie more or less concurs.6
4. If maximum, then what? Although we may not know what Ultimate Reality is like, there are certain formal constraints; Anselm's argument rules out the possibility of the Ultimate Reality being, like Plato's Demiurge, subordinate to the Forms; or its being merely a matter of happenstance whether God exists or not.

The last implication is important and easily misunderstood. The ens realissimum is not a contingent being, it was often said, but a necessary one. This was not, in the terminology of the Schoolmen, a de dicto necessity, but a de re one. That is, it is not a necessity attaching to the proposition `Ultimate Reality exists', but a necessity attaching to the Ultimate Reality itself. De dicto necessities we find it fairly easy to explain: `Reality exists' is necessarily true in virtue of the meaning of the words `reality' and `exists'---if someone denies that reality exists, he shows that he does not understand the words `reality' and `exists' in the way we do. We are much less sure what de re necessities might be. They are not logical necessities. Atheists are not contradicting themselves. Nor are rival metaphysicians unable to communicate when they are putting forth different world-views. Each thinks he is saying something substantial, and not just mouthing platitudinous tautologies. To that extent metaphysical necessity is more like causal necessity than logical necessity, though it is much less vulnerable to empirical refutation than are particular claims of causally necessary connexions. But though a metaphysician may agree that he could be wrong in his views about Ultimate Reality, he is unwilling to concede that Ultimate Reality just happens to be the way it is, and could equally well have turned out to be different. The nature of Ultimate Reality is so intimately linked with the rationality of Ultimate Explanation, that when we have understood it properly, we just cannot see how it could be other than it is.

The Ultimate should have the superlative virtues of being unique, single, singular, simple---virtues Spinoza sought for his Deus sive Natura; one line of argument requires Ultimate Reality to be complete in itself (compare Aristotle's characterization of the Good, being autarkes, self-sufficient, in Nicomachean Ethics, I.), and hence non-relational. Substance may have qualities, but cannot be related to other substances, or it will in some way depend on them. Leibniz held that the monads could have qualities, but not to be related to any others; Bradley's account of the Absolute sought to have it entirely unconditioned.

Another line of argument leads to the limit. Although we naturally think of the Ultimate Reality as being the greatest, often metaphysicians have sought to understand Nature in terms of its smallest constituents. Materialists generally, and the Corpuscularians of the Seventeenth Century in particular, held that the ultimate constituents of reality must be indivisible, atoms, point-particles, or corpuscles. Leibniz also had his universe composed of minimal monads. Descartes sought to direct his thoughts in an orderly way, beginning with the simplest objects. Logicians posit the Axiom of Extensionality, that it is only the members of a set that constitute what it is, and the Axiom of Foundations, which stipulates that ur-elements exist. The thought that fundamental explanation must be through analysis into minimal components, and that is all there is, underlies much of contemporary anti-holism. We do not always follow Anselm in seeking for the mostest, often now regarding the leastest or simplest as more fundamental, but in our metaphysical moments we still yearn for the extreme.

Anselm's Proslogion was primarily a prayer addressed to God, and the argument occurs as a digression, a put-down for the Fool, who said in his heart that there is no God. The fool was not a Victorian atheist, like George Eliot, who was ``serious about metaphysics'', but a frivolous insipiens, who is not engaged in the problem of God, not greatly bothered, and Anselm is needing to convince him that life is real, and that the Fool should be in earnest and not take a short-term egocentric view. Anselm could reasonably argue that the Ultimate Reality existed, and was therefore a matter of ultimate concern. The Ontological Argument has protreptic force: it bids us be serieux; reality, ultimate reality, exists, and once we recognise that fact, it is reasonable to accept the invitation to join in the metaphysical quest. Anselm, however, took it for granted that the Ultimate Reality was personal---the Proslogion was a prayer, in which Anselm addressed God, es Thou art. We cannot take it for granted that the Ultimate Reality is personal. We may be able to maintain without fear of contradiction, that Ultimate Reality exists, but do so at the price of not being able to say what it is like. We cannot in the same logical breath establish both whether it exists and what sort it is: the two questions are, as sometimes in physics, incompatible and cannot both be answered at once. Anselm may ask whether ultimate reality exists, and may be able to argue that it does; but may not, at that juncture, take a position on its nature or essence, bar the single fact that it exists.

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1.Critique of Pure Reason, , A 598, B626; tr. Norman Kemp Smith, p.504.
2. See T.J. Smiley, ``Syllogism and Quantification'', Journal of Symbolic Logic, 27, 1962, pp.58-60; and R. Harré, ``On the Structure of Existential Judgements'', Philosophical Quarterly, 5, 1964-5, pp.43-52.
3.. Republic V, 490a, and X, 597d.
4. Republic VII, 532e.
5. Critique of Pure Reason, Transcendental Dialectic, Bk II, ch.iii, Section 5, A 608-609, B 636-637.
6. The Miracle of Theism, , Oxford, 1982, pp.81-84.