Defining God into Existence: The Presumptuous Ontological Argument

The ontological argument for God’s existence has tantalized theologians and philosophers for centuries because the argument seems at first glance to prove that God exists even though all the argument does is analyze the concept of God. Take, for example, the philosopher Alvin Plantinga’s modal version of the argument, which begins by stating that God’s existence is at least possible. The argument next points out that “God” is defined as a maximally great being, meaning not just that God is all-powerful, all-knowing, and all-good, but that “God” is defined as a necessary being rather than just another contingent thing that comes and goes. Anything dependent on something else wouldn’t be God, by definition. S5 modal logic, the system which specializes in simplifying strings of modal operators, includes a (very dubious) rule of inference that says if it’s possible something is necessary, the thing is simply necessary, meaning that if there’s a possible world in which the thing exists in all possible worlds, the thing must simply exist in all possible worlds. The only way it could exist necessarily in some possible world is if it really does exist in all possible worlds. And if that’s how the thing exists, it exists in the actual world, which means God exists as a matter of fact just because God’s existence as a necessary being is possible.

So wasn’t that easy? God’s existence can be proven with just a few sentences. That’s as we would expect it to be if God wanted us to know easily that he exists. Unfortunately, God’s existence is intuitive to creatures like us who thrive on reading each other’s intentions and projecting mental properties onto everything in nature, as was commonplace in our animistic past and in our individual childhoods. By contrast, reason has conflicted more and more with how we naively intuit the world. We felt we were central to the universe, but empirical investigation proved that intuition is wrong. We naively trust in our clan’s religion, but then discover there are many cultures and so we acquire the perspective of postmodern irony, which compels us to doubt our myths even as we struggle to remain civilized rather than give in to multicultural vertigo. Thus, the ontological argument would be a strange bird indeed if the argument were rationally compelling.

As the Stanford Encyclopedia of Philosophy article on the argument points out (in section 7), the soundness of a deductive proof of anything is a trivial matter, if the issue is the more general question of whether we should accept the conclusion. Take this argument, for example:

(1) Either God exists or else 2 + 2 = 5.

(2) 2 + 2 do not equal 5.

(3) Therefore God exists.

The second premise is true, the first premise isn’t obviously false, and the argument is valid since the disjunction in (1) can be interpreted as exclusive (even though there is no clear reason for doing so). But if (1) is comparable to a statement such as “Either it’s daytime here and now or it’s nighttime here and now,” (1) excludes the scenario in which both sides or disjuncts are true, so that once one side is eliminated, the other must be true if the disjunctive statement as a whole is true. So because 2 + 2 do not equal 5, the other half of that disjunction must be true, if (1) as a whole is true, and so God exists.

Again, wasn’t that easy? According to deductive logic, God exists! Yet the reason this argument wouldn’t convince anyone even though it might technically be sound is that it’s wildly incomplete. Again, there’s no reason to think (1) is true and it needn’t be up to logic or the analysis of concepts to determine the relation between “2 + 2 = 5” and “God exists.” A random falsehood is merely being attached to another dubious notion (since the concept of God is arguably incoherent), and then the dubious notion is proved by presuming that the pair counts as a logically decidable statement so that the falsity of the arithmetical part entails the truth of the other part. Likewise, I could “prove” the following:

(1) Either I have a trillion dollars or there is a dinosaur in my shirt pocket. 

(2) There is no dinosaur in my shirt pocket.

(3) Therefore I have a trillion dollars.

But of course I don’t have a trillion dollars. Or we could make a more obvious fiction real by the following wave of a magic wand:

(1) Either Darth Vader exists in reality or Mickey Mouse has square ears.

(2) Mickey Mouse does not have square ears (his ears are round).

(3) Therefore Darth Vader exists in reality.

We know on the contrary that Darth Vader is a fictional character, so this argument must be flawed even though technically, at first glance at least, the argument might seem sound. 

Cosmicism and Cognitive Games

The main defect of the ontological argument was indicated by Gaunilo’s parody of Anselm’s original version of the argument and by Kant’s point that “existence” isn’t a predicate, but bringing in medieval or Kantian philosophy would only obscure the issue. A better place to look for an explanation of the defect is the evocation theory of mathematics by Smolin and Unger. In The Singular Universe they point out that there’s a third option between thinking of mathematical objects as discovered (pre-existing) or as invented (as having no rigid properties). The third option is to think of them as evoked, as in the evoking of rules of a game like chess. Once the rules of chess are established, for example, some moves in the game become possible or impossible. You can move the king only one square at a time and moving the king from one end of the board to the other all in one turn is impossible as a legitimate move in chess. The modality in this case rests on the fact that the game of chess is evoked into being. Games can be created to have rigid properties, and their rigidity rests not on any immaterial platonic realm but on our willingness to enter into intersubjective agreements. The rules work as conventions, like the convention that driving on the left side of the road is illegal in certain countries. The difference is that mathematics is a more universal practice than the national business of managing the flow of car traffic. We think of games as being mere entertainments, but we can think of games more broadly as being a set of moves permitted by certain rules or conventions, where the latter are just intersubjective agreements about what should be done in some context.

The difference between playing and violating a game becomes clear if you imagine playing a game of chess with an adult, and trying to play one with a child. Both adults know the rules, so the game unfolds in the legitimate fashion. The child, however, has no idea how to play and instead of moving the pieces correctly, takes them and throws them across the room or smashes the board and scatters the pieces willy-nilly. In the latter case, both players may be seated at the board and may be handling the pieces, but no game of chess occurs because the rules aren’t in charge of the players’ movements. Were the child to observe the game played by the adults, the child would find the game strange and arbitrary if she couldn’t figure out the rules or the purpose. In the same way, the game of cricket might baffle outsiders. Only when the rules are understood and when the players agree to follow them do you have a game complete with its possible, necessary, and impossible moves. Again, those moves have that modal status only for the purpose of playing that game; the rest of the universe couldn’t care less about what we’re playing at.

So Gaunilo thought Anselm’s original ontological argument could be parodied. In addition to proving that God, the so-called perfect being exists, as Anselm thought, we could go ahead and prove that a perfect island exists. This is because Anselm reasoned that “perfection” entails real existence, since it would be better to exist than not to exist. So the perfect island must exist too, and so must the perfect house, the perfect leaf, and so on. If it’s better to exist in actuality than to be merely imaginary, every perfect thing must actually exist, by definition, because the thing is stipulated to have the quality of being perfect. Anselm didn’t reply directly to Gaunilo, but he said that only God, the most perfect being conceivable, gets to have all the perfections, including the perfection of actually existing. The perfect island is better only than all other islands, whereas God, by definition, is better than everything else. It’s true that God would be expected to have all the perfections, if he’s the maximally perfect being, and so we wouldn’t expect the perfect island to have qualities that would be perfect only for things belonging to different kinds. For example, the perfect island wouldn’t include a starship engine. The more perfections we add to the island, the more the island resembles God (assuming God could turn himself into an island or a starship). However, Anselm begs the question in assuming that the perfection of existing in reality pertains only to the most perfect conceivable being. On the contrary, whereas “starship engine” clearly pertains to spaceships and not to islands, “real existence” isn’t obviously relevant only to God and not to perfect islands or houses or leaves. Instead, the matter of modality, of possible, actual, or necessary existence is neutral with regard to our concepts of types of things—and that was the essence of Kant’s point that “existence” isn’t a predicate (or that existence isn’t a property).

In any case, let’s return to the modal version of the ontological argument. The essential flaw of this argument and of all versions of the ontological proof is that they take our concepts too seriously. Concepts, after all, are rules or conventions, and to think in terms of a concept is to play a game in the broad sense. To be sure, thinking needn’t be just for fun; indeed, thinking can be a life or death matter. But thinking is game-like in that when you think outside the box, nobody else has to care about what you’re doing. The standard concept of swans was of a certain large white bird with a long neck that lives in the water, so all licensed thoughts of swans had to follow that assumption; otherwise, you weren’t playing the intersubjective game of thinking about swans. The world didn’t care about that stereotype, however, and went ahead and produced black swans, which were found in Australia. Our concepts are models which summarize our knowledge of one type of thing or another, and we choose to participate in a collective enterprise when we follow the conventional models in our thinking, which makes our thinking game-like. Suppose, for example, I’m speaking to someone about trees and I say, “Trees can walk just like people can.” Assuming I’m being serious, the other person would assume that I’m working with a nonstandard concept of trees, which would be like treating a piece in checkers as if it were a piece in chess. Any tree which could walk like a person would likely be a member of a strange new type of life form, which means my thought that trees can walk is forbidden by the conventional concept of trees.

So take the concept of God and grant the theist everything she wants to include in her definition and thus in the concept. God, then, is the maximally perfect being, God has all the perfections, and let’s even say existence is a property something can have. Let’s also waive the objection about the incoherence of the notion of God, and grant that God’s existence is possible. Using a certain rule of modal logic (which I’ll come to in a moment), we can then argue that if God is possible, God must really exist. So we have an argument that forces us to conclude that God really exists. The argument is deductive, which means it’s actually an analysis of certain concepts, especially the concept of God. Thus, we have certain concepts or mental models that force us to make certain cognitive moves, assuming we choose to play some cognitive game. But just as a child can pick up a chess piece and throw it across the room, and just as the rest of the world doesn’t follow our rules of chess or our earlier stereotype of swans, the real world is quite free to disregard our concepts and models.

Even if we were forced to conclude that God really exists, according to some logic and conceptual analysis, that wouldn’t mean God would really have to exist. All that would be entailed is a certain move in a cognitive game. Only thoughts are logically or conceptually entailed, not non-mental events such as something’s coming into existence outside our thoughts. (Incidentally, this is why the slippery Stoic and Christian notion of the Logos or the divine Word is misleading, since it projects a human property onto everything else in nature as though natural order has to be logically planned or called into being.) The modality, that is, the actuality of God’s existence would depend entirely on the fact that the prescriptive aspect of our concept of God is merely evocative. Contrary to the Cartesian and the medieval Dominican presumption that human thinking can mirror reality, because God created us and wants us to know the truth, which obviously begs the question of theism, our thinking is more like an animal’s desperate flailing to survive in a world that couldn’t care less whether we understand anything at all. Our commitment to our concepts should be pragmatic, not assumed to be metaphysically grounded. We play certain games because they’re fun, and we agree to follow certain social or cognitive conventions because doing so is useful. It may even be socially useful to believe that God exists, but that doesn’t mean the world outside our concepts or our games cares either way or is magically forced to correspond to even our best way of thinking.

Were the theist at this point to say that the concept of God is uniquely realistic and not pragmatic, she would be begging the question with the Dominican rationalist and making a special plea on behalf of God. There is no reason to think only our concept of swans is a fallible model or simplification and that our commitment to it should therefore be tentative, whereas our concept of God transcends its social conventions and utility and magically hooks up with reality outside our thoughts. True, our concepts contain information which indicates some features of the concepts’ source, because our thoughts are built up from experience. We can learn about causes from their effects and so we can learn about the world by examining the mental maps we’ve learned to form. But deduction won’t suffice to establish a real-world foundation of a thought. If Sherlock Holmes forms an elaborate hypothesis of how a crime was committed, which leads him to deduce the identity of the killer, his reasoning won’t compel the police to arrest the person Holmes has in mind. Instead, Holmes will have to gather empirical evidence to support his hypothesis, and only then would the police have reason to act on Holmes’ suspicion. This is because our concepts, analyses, and deductions needn’t mirror the external world: only when our thoughts are corroborated by empirical evidence in connection with our understanding of certain causal relations are we rationally entitled to think that a legitimate move in a mental game derives from some real pattern out in the rest of the world—just as our basic mathematical categories (number, geometry, algebra, etc.) derive from elements of human experience.

The ontological argument should, then, be supported by an empirical account of the origin of our concept of God. Without such an account, our stance towards the idea of God should be pragmatic, which means we can use it as we will but should withhold belief in the idea’s applicability to a real deity until our deductive reasoning on that subject is corroborated by direct or indirect evidence. At any rate, that would be the rational course of action. Of course, any such non-question-begging empirical explanation of the evolution of religion ideas will more likely support the atheistic hypothesis that the idea of God is traceable to common fallacies, naïve, anthropocentric intuitions and mental projections, and misunderstandings of altered states of shamanic consciousness.

God’s Incoherence and Implausibility

At this point, the theist could be expected to declare victory, after all, since if deductive reasoning entails the thought that God exists, that’s proof enough for her! Again, all that would be entailed in the case of Plantinga’s ontological argument would be the fact that if you consent to play certain cognitive games, including entertaining the notion of a maximally perfect being and working with a dubious pruning rule in S5 modal logic, you should think God exists. Whether that thought would be correct somehow in reality would depend on the reliability of our concepts in general, especially of our childish and vain notion of God and of the game of S5. Are those games realistic or could the rest of the world get on just fine if indeed all human cognition proved to be foolhardy? To the extent that the theist doesn’t consider this latter, cosmicist possibility, she’s likely begging the question in the Cartesian or medieval rationalist’s manner. Indeed, the ontological argument is as arbitrary as the above argument that begins by assuming that either God exists or two and two are five. In the latter argument, two radically unrelated things are combined in a disjunctive premise, and the argument appeals to a fishy interpretation of the disjunction as being exclusive. In the former argument, we have the arbitrariness of an anthropomorphic notion of ultimate reality, according to which human qualities are deemed relevant to the maximally perfect or primary being, and the argument then appeals to an even fishier rule of modal logic.

Let’s look for a moment at that inference rule. Is it intuitive to think that if it’s possible that something is necessary, the thing is automatically just necessary (and thus actual)? Of course not. Suppose someone discovers what she takes to be a law of logic, but she’s not certain her analysis is correct. Still, she concludes there’s a chance the proposition is, after all, a law of logic, in which case it’s just possible the proposition is true in all possible worlds. Does that mean we should disregard her caution and barrel along to the conviction that the proposition is a genuine law of logic—and all for the sake of ensuring the tidiness of statements in a system of modal logic? After all, as the Stanford Encyclopedia article on modal logic points out (see section 2), S4 and S5 are meant to simplify uselessly longwinded chains of modal operators, as in “necessarily necessary p” or LLp, which in S4 can be read as “necessarily p” (Lp). S5 permits modal operators of both types, both possibility and necessity, to be simplified even when they’re combined in a statement and even though “possible” and “necessary” have many different meanings in English. So “possibly necessary p” (or MLp) becomes “necessarily p” (Lp) in S5. The first modal operator in any pair of them can be just deleted in S5 (since S5 contains S4).

In the above example, “possibility” has a psychological meaning since the question is whether the logician is certain she hasn’t made an error in her analysis. Suppose the logician hasn’t made any analysis but is only guessing about her purported law. Just because she guesses she’s discovered a new law of logic, doesn’t mean she’s succeeded. So just because there’s a possible world in which her guess proves correct doesn’t by itself increase the probability that her guess is in fact correct, such that her proposed law holds true in all possible worlds. Indeed, using the ontological argument’s bogus logic, we can show just as easily that any mathematical claim which might be true but is as yet unproven is necessarily true, since mathematical claims, too, are defined as necessary. So a mathematical conjecture magically becomes necessarily and thus actually true just because the conjecture is possibly true, which is preposterous. Some conjectures turn out to be false.

An evangelical Christian on YouTube responds to that latter objection (beginning at around 20 seconds into the video) by saying that we don’t know whether unsolved mathematical problems are true in any possible world, because they tend to involve infinite quantities so we can’t confirm the mathematical concepts are coherent, whereas we do know everything about God (!), so we can know that God’s existence is at least possible. This assumes that God’s nature doesn’t transcend human comprehension, contrary to Aquinas, Judaism, religious mystics, and the like. It also presupposes the arrogance of an American evangelical Christian. Most theists would prefer to worship something much greater than themselves not just in degree but in kind, since only such a largely unknowable being could make them happy for eternity. But if any part of God is beyond our comprehension, like an infinite set, we should be just as uncertain about the plausibility of the concept of God as about the coherence of the mathematical concepts. To the extent that we do fully understand God’s nature, we’re only childishly projecting our self-image onto the cause of the universe. 

The reason the S5 pruning rule might come to seem intuitive is due to confusion between two interpretations of what it means to say that X is necessary in some possible world. This can mean that X really is necessary there, in which case X is true in all possible worlds—which is how modality is treated in S5, because S5 assumes the only modal operator that matters is the right-most one. But that statement can also mean that X isn’t really necessary at all and is true only according to a faulty view of what’s possible. X then is only possibly necessary. This latter interpretation is more in line with the subtlety of natural languages and with our understanding of the frailty of human psychology. The emphasis in MLp can thus be on the M or on the L operator, contrary to draconian S5. In short, whatever the motivation behind the strong interpretation of the modal operators in S5, according to which a string of them can always be collapsed, that interpretation conflicts with the more nuanced ones that are available in natural languages.

More specifically, when we say God’s existence is possible, what do we mean? Honestly, when atheists grant this possibility, they likely don’t mean that God exists in a possible world. Instead, what they mean is that atheists can afford to condescend to theists by granting them their nonsense for the sake of argument, because the theistic argument in question is bound to have a thousand other flaws, what with theism being anachronistic foolishness from top to bottom. So if that’s the more nuanced sense of “possibility” in mind, need we concede that the pruning rule in S5 works as a translation of that sort of remotest possibility? Obviously not. Just because an atheist concedes out of charity that some theistic jibber-jabber amounts to an imaginary possibility, doesn’t mean that that possibility can be whisked away by modal logic, leaving the atheist with just the stipulation that God would exist necessarily, by definition, in which case God ends up existing in fact. What we have here are two separate cognitive games (in that broad sense of “game”). As per the above discussion, the real world needn’t play either of those games nor any combination of them. Those games are for thinking creatures like us. But leaving that aside, there’s the game of thinking in a charitable fashion because of the embarrassment of riches which theism leaves to the atheist. Then there’s the game of taking seriously S5 with its counterintuitive reduction rules. The first game entails one sense of God’s possibility, the second game a different sense, and Plantinga’s ontological argument equivocates on them.

The theist wants to say, instead, that God is possible because the notion of God is at least coherent. Philosophers of religion have raised paradoxes to dispute that point. For example, there’s the issue of whether an omniscient being could create a rock so heavy even he couldn’t lift it. The theist responds by saying God is bound by logic, so omniscience doesn’t entail the ability to do what’s logically impossible. The atheist should then say that this anthropocentric view of human logic begs the question, by discounting the cosmicist or mysterian possibility that human reasoning should be viewed pragmatically since nonhuman reality needn’t play our games or follow our rules. In any case, the philosopher Yujin Nagasawa proposes a version of the modal ontological argument which stipulates that God has only the maximally consistent set of perfections. So God might not be all-powerful, after all, but only powerful enough for his power to be consistent with some high degree of knowledge and goodness.

Underlying these traditional questions about the coherence of the concept of God is the issue of the plausibility of any such anthropocentric bit of metaphysics. Regardless of whether God’s attributes can be modified to resemble those of a possible person, the notion that the ultimate cause of nature is any sort of person is still embarrassingly self-indulgent. Leaving aside the additional implausibility that for the monotheist this maximally perfect person would be all alone for eternity, would have no gender (or would somehow be just male or female but with no sexual origin), would have no necessary social life (but would somehow still be civilized rather than insane or feral), would have no beginning or end (but would still somehow be a person with a definite character), and would have no body or brain (but would still somehow have a mind)—leaving those incoherencies aside, the monotheist would also be maintaining that fundamental reality is personal in the first place. Even if the notion that a person is the primary cause of the natural universe weren’t self-contradictory, it would still be so implausible—given the extent to which scientific knowledge has depersonalized nature—that the atheist would admit only to that god’s possibility being of a negligible variety. God’s possibility for the atheist would be such that were God to exist in reality, the atheist would spit in the deity’s face on Judgment Day because the atheist would still be honour-bound to think of the question of God’s existence as being stupid. This is yet another shade of the meaning of “possible,” and it’s up to the proponent of the modal ontological argument to show that the kinds of possibility which are relevant to the atheist’s admission that God’s existence is possible are adequately translated by S5 modal logic or its equivalent.

In The Nature of Necessity, Plantinga concedes that his modal versions of Anselm’s argument “cannot, perhaps, be said to prove or establish their conclusion. But,” he nevertheless insists, “since it is rational to accept their central premise [that God’s existence is possible], they do show that it is rational to accept that conclusion” (221). So Plantinga thinks the modal argument is still worth making, since it establishes the rationality of theistic belief even though the problem with using the S5 pruning rule vitiates the modal argument as a proof. However, the modal version doesn’t argue for God’s possibility; it only asserts that possibility. Thus, the argument doesn’t add any credibility to the prior assessment of God’s possibility, given, for example, the question of the coherence or incoherence of the concept of God. In any case, even if that premise were reasonable, it still wouldn’t be rational to think God exists, just as it wouldn’t be rational to think that anything which is only possible as far as we know is in fact actually real, whether the thing is a leprechaun or Darth Vader or the truth of a mathematical conjecture. On the contrary, rationality dictates that we discard every trace of anthropocentrism from our worldview, including theism, unless that silly vestige is entertained pragmatically or with postmodern irony, as something like a tradition respected for its aesthetic merit or for its reminder of the human penchant for foolishness.