Philosophical Disquisitions: Anselm's Ontological Argument: A Guide for the Perplexed

St Anselm (allegedly)

The ontological argument for the existence of God is remarkably resilient. Originally formulated by Anselm of Canterbury in the late 11th century, it has been continuously debated, reformulated, critiqued and resurrected over the subsequent millennium. Very few philosophers find it, or its descendants, convincing; most think it must be wrong in some way; but many concede that it is hard to pinpoint exactly what is wrong with it.

In this article, I want to examine Anselm’s original argument in some detail. I will do so by first formulating what I believe to be an accurate but also comprehensible version of it (one that does not rely on abstruse symbolic or modal logic). I will then discuss the major criticisms of this argument. My overall perspective is sceptical: I think the argument makes too many controversial assumptions to be wholly convincing, and it is hard to escape the view that it is little more than a parlour trick (as one famous philosopher once suggested). Nevertheless, I hope that this article will be of value to all readers, regardless of their perspective, particularly for those that are puzzled by the argument, interested in what it claims, and eager to learn more.

There have been many reformulations of the ontological argument over the years. Some of these differ quite substantially from that offered by Anselm. Some are efforts at improving what Anselm had to say. Some are new attempts to arrive at the same conclusion. Descartes, Kurt Gödel, Alvin Plantinga and Robert Adams are just some of the people that have attempted to alter or shore up the argument from its traditional criticisms. For better or worse, I will not focus on these versions of the argument. I am going with the OG - Anselm himself - and what he had to say.

1. The Structure of Anselm’s Argument

Although my focus is on Anselm, I will attempt one initial, general, formulation of the ontological argument. For all their complexity and symbolic trickery, ontological arguments typically work like this:

(1) The concept of God is such that one of God’s properties is that of necessary existence.

(2) If it is possible for God to exist then he must, necessarily, exist (from 1).

(3) It is possible for God to exist.

(4) Therefore, God must exist.

Some readers will see echoes, in this formulation, of the version of the ontological argument defended by Alvin Plantinga. This is deliberate. I think Plantinga does a good job capturing the essence of the argument although, to be clear, the preceding version does not exactly replicate what Plantinga says.

Where the different formulations vary is in how they arrive at the conclusion that the concept of God is one that implies necessary existence and how one then justifies the claim that it is possible for him to exist. Anselm, as we shall see, has a particularly complicated way of arriving at this conclusion.

What then of Anselm’s argument? It comes from his famous work, the Proslogion. There is some interpretive difficulty here. Anselmian scholars have pointed out that Anselm can be taken to defend two ontological arguments in chapters 2 and 3 of the Proslogion. Most discussions of the argument focus on the version from chapter 2 and I will follow suit here.

The critical passage is the following one (translation taken from Millican 2004):

Now we believe that [God is] something than which nothing greater can be thought… ‘the Fool has said in his heart, there is no God’? [Psalms 14:1; 53:1] But surely, when this same Fool hears what I am speaking about, namely, ‘something-than-which-nothing-greater-can-be-thought’, he understands what he hears, and what he understands is in his mind, even if he does not understand that it actually exists. For it is one thing for an object to exist in the mind, and another thing to understand that an object actually exists. Thus, when a painter plans beforehand what he is going to execute, he has [the picture] in his mind, but he does not yet think that it actually exists because he has not yet executed it. However, when he has actually painted it, then he both has it in his mind and understands that it exists because he has now made it. Even the Fool, then, is forced to agree that something-than-which-nothing-greater-canbe-thought exists in the mind, since he understands this when he hears it, and whatever is understood is in the mind. And surely that-than-which-a-greater-cannot-be-thought cannot exist in the mind alone. For if it exists solely in the mind, something that is greater can be thought to exist in reality also. If then that-than-which-a-greater-cannot-be-thought exists in the mind alone, this same that-than which-a-greater-cannot-be-thought is that-than-which-a-greater-can-be-thought. But this is obviously impossible. Therefore there is absolutely no doubt that something-than-which-a-greater-cannot-be-thought exists both in the mind and in reality.

If you are anything like me, you will probably find this passage very difficult to follow on a first reading. One issue with it is the repeated uses of the phrase “that-than-which-nothing-greater-can-be-thought” or some derivation of this phrase. It is cumbersome and conceptually complex. It hurts your brain to read it. Each time you have remind yourself of what it means.

As a first step toward making the argument more comprehensible, I suggest accepting at the outset that, for Anselm, God is defined in the following way:

God = The greatest possible being (a being greater than which no greater being can be thought), where greatness is usually cashed out in terms of the traditional “omni”-properties (omnipotence, omnibenevolence, omniscience etc)

With that definition locked away in your mind, simply replace all instances of the phrase “that-than-which-nothing-greater-can-be-thought” with “God”. I have taken the liberty of doing that in the following version, along with making some other key amendments to the text that make it easier to parse:

Now we believe that [God is] something than which nothing greater can be thought… ‘the Fool has said in his heart, there is no God’? [Psalms 14:1; 53:1] But surely, when this same Fool hears what I am speaking about, namely, God, he understands what he hears, and what he understands is in his mind, even if he does not understand that it actually exists. For it is one thing for an object to exist in the mind, and another thing to understand that an object actually exists. Thus, when a painter plans beforehand what he is going to execute, he has [the picture] in his mind, but he does not yet think that it actually exists because he has not yet executed it. However, when he has actually painted it, then he both has it in his mind and understands that it exists because he has now made it. Even the Fool, then, is forced to agree that God exists in the mind, since he understands this when he hears it, and whatever is understood is in the mind. And surely God cannot exist in the mind alone. For if He exists solely in the mind, a greater being can be thought to exist in reality also. If then God exists in the mind alone, this same God [the one existing solely in the mind] is not the greatest possible being. But this is obviously impossible. Therefore there is absolutely no doubt that God exists both in the mind and in reality.

Clearer? A little. But we still need to reconstruct the logical form of the argument. I have read many attempts at this over the years (and I revisited several before writing this piece). None of them has ever struck me as being fully satisfactory and, ironically, several of them don’t make clear the exact inferential pattern at work in the argument (i.e. which premises are being used to support which conclusions or sub-conclusions). Graham Oppy, in some of his reformulations of the argument, comes closest to providing a simple and logically clear reconstruction of the reasoning (without reverting to the esoteric realm of symbolic logic). With some minor modifications, my reconstruction draws heavily from his work.

Structurally, the argument can be broken down into three key steps. In the first step, Anselm makes a general point to the effect that there are two kinds of existence: (i) existence in the mind (the “understanding”) and (ii) existence in reality. The painting-painter analogy in the middle of the quoted passage is meant to both clarify this distinction and highlight that it is possible for something to exist in the mind alone. If you accept that the painting exists in the mind of the painter prior to the actual painting of it, then you accept that things can exist in the mind alone. This is important because the first step of the argument claims that even the Fool (i.e. the atheist), understands the concept of God and hence God can be said to exist in his mind. As follows:

(1) The word God ("that than which no greater can be conceived") is understood, even by the atheist.

(2) For any expression E, if E is understood, then E exists in the understanding.

(3) Therefore, God exists in the understanding (even for the atheist)

The second premise here is taken from Oppy’s reconstruction and is crucial to the success of the argument as a whole. It is a general principle stipulating that understanding a concept implies the mental existence of the concept.

The argument then proceeds to the next step, in which (3) becomes one of the starting premises. In this next step, Anselm argues that if God exists in the understanding, he can be conceived to exist in reality but if he can be conceived to exist in reality then he would be greater than if he only existed in the understanding (existence in reality = a great-making property). This then implies that God would be greater if he existed in reality rather than only in the understanding. More formally:

(3) God exists in the understanding (even for the atheist).

(4) If God exists in the understanding, then God can be conceived to exist in reality.

(5) If God exists in reality then He would be greater than if he existed only in the understanding.

(6) Therefore, If God exists only in the understanding, then God is not the greatest possible being (a greater version would exist, namely, the version of him that exists in reality as well).

This middle step is, in many ways, the key bit of the argument because it includes the crucial axiological premise (5) stating that if something exists in reality it is better/greater than if it exists solely in the understanding.

This then leads to the final step, which is short and sweet. It is a reductio ad absurdum. Anselm argues that there cannot be a greater being than God. This is a contradiction in terms since God is the greatest possible being. So God cannot exist solely in the understanding because this would imply the existence of a greater being in reality. He must also exist in reality. This is basic modus tollens reasoning: if P, then Q, not-Q, therefore not P. As follows:

(6) If God exists only in the understanding, then God is not the greatest possible being (a greater version would exist, namely, the version of him that exists in reality as well)

(7) God is not something than which a greater being can be conceived; God is the greatest possible being.

(8) Therefore, on pain of contradiction/absurdity, God must exist in reality as well.

The diagram below illustrates the full structure of the argument. This diagram was created using the free MindMup argument visualisation software. I apologise for the fact that the numbering of the premises is different from what I just gave. The software automatically numbers premises and I am not aware of any way to change this automatic setting.

Click for a larger and clearer version

Is the argument any good? Most people don’t think so but, as noted, many philosophers find it intriguing. It purports to achieve a lot with very little: from the mere concept of God we get the conclusion that God must exist. It seems too easy; too quick. But what exactly is wrong with it? In the rest of the article I take it premise-by-premise and consider the major objections that can be raised. I will also dedicate a separate section to the infamous parodies of the argument and see whether they are any good.

2. Problems with the Premises

Let’s start then by considering premise (1) and the claim that even the atheist understands the concept of God. Is this true? It’s not clear. As Nicholas Everitt once observed (in his book the Non-Existence of God), it is important to distinguish between ‘linguistic competence’ and genuine understanding. It’s possible that the atheist knows how to use the word ‘God’ and has some sense of what the theist is trying to refer to when using that term (“the creator of the universe”, “the greatest possible being”), without truly understanding it.

Consider an analogy. I know how to use the phrase “a square circle”. If pushed, I can even vaguely imagine what a square circle might look like (a square with rounded edges perhaps). But do I really understand the concept? I would say “no” because the concept itself is logically or conceptually possible. You cannot have a square circle. It could well be that the concept of God is a bit like this. We have some vague sense of what it means, but when we drill down into the details, we realise that the concept is inconceivable - not capable of being understood. This is not the place to rehearse the usual arguments against the possibility of omniscience, omnipotence and omnibenevolence, but if we take these arguments on board, even acknowledging various responses from theists, the idea of God gets very murky. We have, at best, a shadow conception of Him. Not something clear and distinct.

Ironically, Anselm himself seems to acknowledge this murkiness. In chapter 15 of the Proslogion, he suggests that God is “not only that than which a greater cannot be conceived…but also something greater than can be conceived.” In saying this, Anselm (and his interpreters) are quick to point out that he was not claiming God was utterly inconceivable. He thought we could have some conception of God. But this is still, arguably, a sticking point for premise (1): do we have a sufficiently clear conception of God (qua “greatest possible being”) to grant that we understand Him. I don’t think so. If you are interested, Stephen Maitzen explores this issue at greater length in his 2005 article ‘Anselmian Atheism’, suggesting that Anselm’s view could be taken to imply utter mysticism about the concept of God. (Though, to be clear, Maitzen rejects utter mysticism and argues, instead, that this has the unwelcome implication, for the theist, of making atheism the more acceptable view.)

Premise (2) is a more significant premise. We could easily grant that the concept of God is understood, without accepting that this implies God’s existence in any sense of 'existence'. Premise (2) is supposed to undercut this scepticism by suggesting, in the first instance, that if a concept is understood it must exist in the understanding. What do we make of that? It is worth starting by emphasising that this is a long way from accepting that God exists in reality. There are, after all, lots of things that could be said to exist in the understanding without existing in reality. Right now, I am imagining a levitating purple unicorn. I have a very clear conception of it. It’s not murky in the slightest (unicorns, after all, are just horses with horns). But obviously the levitating purple unicorn does not exist in reality. Mental existence does not imply actual existence (as a general rule). The innovation of the ontological argument is to claim that it does in the case of God.

But what does it mean to say that something exists in the understanding? This gets us into some philosophically abstruse waters. The premise is supposing at least two realms of existence: real existence and mental existence. Real existence, in itself, is conceptually contested. Is ‘real’ existence only physical/material existence? Not for theists or mind-body dualists since God or mind is usually taken to exist in some non-physical realm. So there are different grades and forms of real existence, whatever it may be. What of mental existence? Is this more straightforward? On the one hand, it’s not clear what is to be gained by positing mental existence. Kant’s famous objection to the ontological argument — that existence is not a predicate — could be mentioned at this point, but I don’t find Kant overly convincing on this and so I will set that objection to the side. For me, the puzzling thing is the nature of mental existence, if it is accepted as a general idea. It seems like a very strange and ephemeral kind of existence. If I am thinking about the purple unicorn at T1, about an orange dragon at T2, and a purple unicorn again at T3. What happens, existentially, to the purple unicorn during this period of time? Does it briefly pop into existence and then out of existence, and then back into existence again? Is the purple unicorn at T3 the same unicorn as at T1? Do identity relations hold in mental existence? Or does the purple unicorn sustain its existence throughout, no matter what my occurrent thoughts might be? I don’t know that there are good answers to these questions, but puzzles of this sort suggest to me that little is gained by talking of mental existence. We can just say that we think about different concepts at different times — we imagine or. conceive of them — without taking the further step of accepting that these concepts exist in some meaningful sense.

Premise (2) also raises the spectre of Meinongianism, a doctrine named after the Austrian philosopher Alexius Meinong. In brief, Meinong posited a distinction between existence (in reality) and subsistence (in some shadow metaphysical realm). Meinong argued that the distinction was necessary to make sense of the intentionality of mental states and the relatively common propositions we make about fictional characters ("Sherlock Holmes lived on Baker Street"), obviously non-existent things (“Pegasus has wings”), and the past (“Albert Einstein was a physicist”). The objects of these propositions do not exist in reality, but the propositions make sense and have truth value. So they must be about something or other, right? Meinong suggested that this was right and the objects of these propositions can be said to subsist, but not exist. In this sense, subsistence was seen as a lesser or easier-to-acquire form of existence.

Some philosophers have argued that Anselm’s argument is perhaps best if retranslated into the language of Meinongianism since it seems to imply this distinction between existence (in reality) and subsistence (in the mind). Peter van Inwagen, for example, in his 2012 article “Three Versions of the Ontological Argument” suggests that Anselm endorses the “Meinongian Existence Thesis” to whit the term “God” denotes an item that, at a minimum (even for the atheist), enjoys the lesser form of existence that is subsistence.

Ironically, Van Inwagen thinks that this undermines Anselm’s argument since, according to him, “Meinongianism in any form is simply wrong”. Van Inwagen has reasons for believing this, but his statement is a little bit too definitive for my liking. Meinong’s distinction is not obviously or simply wrong. There is something to the idea. It is, however, metaphysically controversial and it remains unclear exactly what subsistence is, when contrasted with existence. For example, if subsistence is less demanding than existence, does this mean that logically or metaphysically impossible things — like the square circle — can subsist, even if they cannot exist? If so, the ontological argument might be in trouble when it tries to make the leap from subsistence to existence. Similarly, we can ask questions about whether subsistence really makes sense. Do objects pass in and out of subsistence on a whim? How stable and reliable are our intuitions about subsistence vis-a-vis existence?

The bottom line, then, is that Premise (2) is questionable and controversial. It is not something we should simply accept and move on from. (Brief aside: Peter Millican has formulated a version of Anselm’s argument that focuses on the instantiation of a perfect nature, as opposed to the existence of a perfect being. This focus on instantiation as opposed to existence could be taken to sidestep the debate about Meinongianism, although similar(ish) questions can be raised about the distinction between an instantiated and uninstantiated nature. In any event, it is worth noting that Millican thinks his reformulation of the argument reveals a ‘fatal flaw’ at the heart of Anselm’s argument: it is crucially vague on this notion of instantiation and what it means. It is too complex to cover here, but worth reading if you are interested extended criticisms of the argument)

Premise (3) is uncontroversial since it is the conclusion drawn from (1) and (2). If there is a problem with it, it lies in the preceding steps of the argument. This brings us to premise (4) as the next potentially controversial one. This premise claims that if God exists/subsists in the understanding, then he can be conceived to exist in reality. On an interpretive note, I should point out that I don’t find this premise in Anselm’s text. As best I can tell, he does not say anything approximating it. Nor, as best I can tell, is the premise logically necessary for the argument to go through. The middle step of the argument seems to work without it. Nevertheless, several credible philosophers have argued that something like this premise should be added to the argument. For example, Graham Oppy and Tyron Goldschmidt (both ontological argument experts) include a variation of this premise in their reconstructions of the argument. Who am I to question them?

Granting that the premise is needed, there are objections one can raise to it. Indeed, both Oppy and Goldschmidt raise some. The crucial objection brings us back, again, to the difference between mental existence and existence in reality. If something can subsist in the mind without many of the demands or restrictions we place on existence in reality, then is it really possible to conceive of the object existing in reality? Perhaps not. It is tempting to speak of square circles again but consider a different example. Can ghosts be conceived to exist in reality? It is obviously the case that people think about ghosts, write about them, depict them in fictional media (books, films, paintings) and so on. If anything is a plausible candidate for subsistence, it seems like ghosts are. (And yes, of course, I know that some people think they exist in reality as well.) But even if we can conceive of ghosts in our minds, can we actually conceive of them existing in reality? Anyone that tries to do this quickly runs into problems.

Ghosts are typically conceived to be immaterial, ethereal beings. They are not bound by ordinary physical and biological laws and represent the souls or spiritual essences of deceased beings. But then we can ask: if they are not physical material beings, why are they often depicted as wearing clothes? Do clothes have souls or spiritual essences that can exist in an immaterial realm? How do ghosts generate noise if they do not exist in the physical world? Sound requires the compression of air waves. Can ghosts do this? If ghosts can pass through walls and other material objects, why don’t they just fall through floors or, more dramatically, the ground? How is it that they can sometimes physically interact with the world? How can they do this selectively? Questions of this sort abound and they are not unique to ghosts. We can ask similar questions about concepts such as time travel (specifically into the past) and faster-than-light transportation. We commonly conceive/imagine these things, but can we actually conceive of them existing in reality? This is much more debatable.

The problem with premise (4), in a nutshell, is that even if we accept the notion of mental existence/subsistence, it does not automatically follow that objects existing in the mind can be conceived as existing in reality. When we make the leap into the real world, even in our imaginations, we might find that the concept breaks down. Arguably, this is one of the things that happens when we start to think of God as existing in the real world.

We thus move on to premise (5). This is the last significant premise of the argument. Premise (6) is just the conclusion drawn from (3), (4) and (5), and premise (7) seems pretty unobjectionable since it is just a restatement of the stipulated definition of God (the greatest possible being). Premise (5) is the lynchpin of the argument. Without it, the reductio in the final step would not work. It makes an axiological claim to the effect that existence is a great-making property: it is better (greater) for things to exist in reality than for them to exist merely in the understanding. It then weds this to the notion that God is the greatest possible being so, if he is to satisfy one of the axiological conditions of his existence, he must exist in reality, not just the understanding.

There are a few problems with this premise. First, it is not obvious that existence in reality (whatever that means) is a great-making property. Again, Kant’s general observation that existence is not a predicate is worth mentioning here: if Kant is right, existence adds no value to a thing since existence is not a property that can be added to a thing: it is already presupposed in the concept of the thing. I don’t quite follow Kant on this point, but it is an influential critique and it would be remiss of me not to mention it. More plausible, to me, is Graham Oppy’s objection that for us to accept premise (5) we would have to able to compare two things that it is not obvious we can compare:

This claim [premise 5] can only be true if we can make sense of counterfactual claims about what objects that exist in reality would be like if they existed only in the understanding. But it is not entirely clear that we can make sense of such claims if we suppose that objects that exist both in the understanding and in reality have the very same properties in the understanding that they have in reality.

(Oppy 2011)

As is typical of Oppy, the point is complex and densely stated. Let’s unpack it a little. For Anselm’s argument to work we need to be able to evaluatively compare an object that exists only in the understanding with the very same object if it existed in reality (or, vice versa, an object in reality if it only existed in the understanding). But then what properties does an object that exists only in the understanding have? Does the mental version of the object have all the same properties as the actual version? More specifically, does the mental version of God have all the properties we associate with the greatest possible being: omnipotence, omnibenevolence, omniscience etc? If so, it is not clear what differentiates Him from the version that exists in reality? It’s neither clear that the comparison is a meaningful one, nor, if it is, that existence has made God greater.

To push the point a bit further, it is at least somewhat plausible to suppose that mental existence alone could be superior for some kinds of things. For instance, the love affair I have with Scarlett Johansson in my mind is, I suspect, a lot better than the one I would have in reality. The messy imperfections of the real world would mar and undermine the idealistic triste I can imagine and re-live, over and over again (just as, sometimes, our memory of what happened to us is superior to what actually happened). This might sound like a trivial or irrelevant example but I would argue it is prima facie plausible and, if so, it undercuts the general principle implied by premise (5). Existence in reality is not necessarily greater than mental existence alone.

This is just one line of objection to premise (5). Another, more influential, one is that if existence is a great-making property, weird things may follow. For any X, if we stipulate that X is the greatest conceivable instance of its kind, X must exist in reality too since, if it didn’t, X wouldn’t be the greatest instance of its kind. But this means we can arbitrarily pick or stipulate any X and prove its existence in the same manner. That cannot be right.

This is the objection that underpins the famous parodies of the ontological argument. These parodies are sufficiently important and influential to warrant a separate discussion.

3. Parodying the Argument: Gaunilo’s Infamous Island

As noted, Anselm’s argument has always struggled to win acceptance. People were suspicious of its apparent logical trickery from an early stage. The earliest and perhaps most influential critic was from Gaunilo of Marmoutier, a fellow Benedictine monk. In his response to Anselm — cleverly titled ’In Behalf of the Fool’ — Gaunilo parodied Anselm’s argument by suggesting that the very same logic could be used to prove the existence of the ‘greatest possible island’ (or, indeed, any other ‘greatest possible X’).

This island (so the story goes) is more plentifully endowed than even the isles of the blessed with an indescribable abundance of all sorts of riches and delights…Suppose someone tells me all this…and so I understand it. But if this person went on to draw a conclusion and say “You cannot any longer doubt that this island, more excellent than all the others of the earth, truly exists somewhere in reality. For you do not doubt that this island exists in your understanding, and since it is more excellent to exist not merely in the understanding, but also in reality, this island must also exist in reality. For if it did not, any land that exists in reality would be greater than it. And so this most excellent thing that you have understood would not in fact be most excellent.” — If, I say, he should try to convince me by this argument…I would think he was joking.

(Gaunilo, translation from Goldschmidt 2020, 15-16)

Gaunilo’s parody can be construed as a specific objection to the idea that existence is a great-making property but also a more general objection to the logic of the ontological argument. It is a reductio (a reductio of a reductio, as it were). If you take the following as the definition of Gaunilo’s Island:

Gaunilo’s Island = The greatest possible island - an island greater than which no other island can be conceived.

And then go back into the version of the ontological argument that I formulated above, you can replace each and every instance of “God” with “Gaunilo’s Island” and end up with a logically identical argument. But there must be something wrong with this latter argument. Anyone that proffered it as serious proof of the existence of Gaunilo’s argument would have to be joking or irrational. In other words:

(9) If the ontological argument for God were sound, we would have to accept the ontological argument for Gaunilo’s Island.

(10) We ought not to accept the ontological argument for Gaunilo’s Island (the argument must be unsound).

(11) Therefore, the ontological argument for God cannot be sound.

In principle, Anselm and his defenders could bite the bullet and reject premise (10). They could argue that, yes, the perfect island must exist in reality too. But, as far as I know, no one does this and it is easy to see why not. If you did, you would have to start accepting the existence of an indefinite (infinite) number of greatest things. That would be ontological extravagance run amok. Instead, they reject premise (9) and the purported analogy between the greatest possible being and the greatest possible island. There is, they argue, something about the concept of the greatest possible being (God) that makes the argument sound in His case, but unsound in the case of the greatest possible island. What might that be?

Charles Hartshorne and Alvin Plantinga have presented the most commonly cited objections to Gaunilo’s parody. Patrick Grim, in his 1982 article ‘In Behalf of ‘In Behalf of the Fool’, offers cogent responses to both. At least, I think they are cogent (indeed, Grim’s article is a paragon of clarity and rigour, something that I find rare in the brain-melting world of the ontological argument). I will briefly summarise the back and forth between Grim and the two critics.

First up, Hartshorne argues that the parody doesn’t work because islands are contingent things, not necessary things. Indeed, islands are, in some sense, essentially contingent things. But since Gaunilo’s parody implies that there could be a necessarily-existent island, it cannot be right. Beings, on the other hand, could be necessarily existent. So there is a critical difference between the ontological argument for God and the ontological argument for Gaunilo’s island.

There are three problems with this reasoning. First, it’s not clear why we should accept the view that islands are essentially contingent. What’s the argument for this? Grim suggests that the only available evidence is our knowledge of islands in our world. We know, for example, that Madagascar and Iceland are contingent. By induction (or maybe abduction) we can reason that all islands must be similarly contingent. But then why doesn’t the same reasoning hold for beings? All beings we have encountered — human beings, animals, etc — are contingent. Based on our experience of beings, there is no reason to think that there could be a necessarily existent being.

Second, Grim argues that it is possible to construct a version of the ontological argument (and, by proxy, the Gaunilo parody) that does not rely on necessary existence. I’m not sure I agree with this: as best I can tell, ontological arguments must, at some point, lead to the notion of necessary existence. Nevertheless, in his article Grim does construct a version of the argument that uses the concept of a locally maximal being, where this is defined as having magnificence (specifically, the three omni-properties) in the actual world (not all possible worlds). Maybe this ‘locally maximal’ version has the same structure as the traditional ontological argument. If so, it can be parodied by an argument for a locally maximal island, without relying on the idea of necessary existence.

Third, even if islands are essentially contingent, it would be possible to construct a parody that relied on the concept of a necessary being that lacked some perfection. For instance, ’Shmod’ could be defined as a necessarily existent being that lacked the property of omniscience (could even be ‘maximally ignorant’). We have the concept of this being (sort of - at least as much as we have the concept of God). Therefore, Shmod exists in the understanding. Therefore, we can conceive of Shmod existing in reality. But if it could exist in reality, given its necessary existence, it must exist. Therefore, Shmod does exist. This is as effective a parody as Gaunilo’s original.

Grim also points out that it is possible to construct a parody that presumes multiple necessary beings. This would be a polytheistic parody of Anselm and it could work too (though only if we follow Hartshorne and insist on necessary existence being the focus; it doesn’t work if we focus on the idea of a greatest possible being).

Plantinga’s critique is marginally more complex. He argues that the concept of a ‘greatest possible island’ is fuzzy and imprecise in a way that the concept of a ‘greatest possible being’ is not. More precisely, he argues that there are no upper bounds or limits to the properties that could be possessed by a greatest possible island. Therefore, the concept is vague and indeterminate. It would be a push to say that it even existed in the understanding. To illustrate, Plantinga considers a property that a great island might be thought to require. He uses the examples of ‘Nubian maidens’, ‘dancing girls’ (h/t to sexism in philosophical thought experiments), ‘coconuts’, and ‘palm trees’. He argues that there is no limit to the number of these things that can be added to an island to make it greater. You could always add one more (in your mind) and imagine a greater possible island. God, according to Plantinga, is not like that. There are inherent limits to the properties of ominscience, ominpotence, and ominbenevolence. For instance, an omniscient being is simply one that, for every proposition P, knows whether or not P is true. That seems like a well-defined property.

So there are two aspects to Plantinga’s critique: (a) there is no real concept of a greatest possible island because there are no inherent limits to an island’s greatness; and (b) there are inherent limits to God’s greatness. Both aspects can be challenged.

For one thing, as Grim argues, Plantinga seems to mistakenly assume that the greatest island is going to be the one characterised by having the most number of X (where X is something like dancing girls or coconuts), and that since numbers are infinite there cannot be such a thing. There is, however, no reason to think that ‘greatest’ is equivalent to ‘maximum possible number of X’. A more appropriate characterisation would be something like:

Greatest X = The version of X with the optimal number of each great-making property P1…Pn

So, in the case of the island, there is an optimal number of coconuts. If you go beyond this, the island ceases to be great. We may not know what that number is, but it is intuitively plausible to suppose that each great-making property has an optimal number. This is, after all, the idea that is at the heart of the economic doctrine of diminishing marginal returns: eating a Mars bar is nice, eating two is even better, but once you eat the third or fourth you start to feel sick. There is an optimal number of Mars bars you should consume. If you go beyond this number, they no longer have the value you desire.

The other problem with Plantinga’s argument is that it is not clear that the concept of God avoids this alleged issue. Consider, for example, the property of omnibenevolence (which I would argue is the most important of the traditional ‘omni’ properties). Plausibly, this could be defined in terms of the number of good deeds an agent performs. But is there some upper limit to the number of good deeds that can be performed? No matter what number you posit, it seems like you could always add one more and thereby imagine an even greater being. Similarly, Grim argues you could always imagine a being with a little bit more power. One aspect of power could be the number of people that a being rules over, or has authority over. And you can always imagine a world with more people that God could rule over.

Plantinga, in other words, may be hoist on his own petard in his critique of Gaunilo.

This does not mean that Gaunilo’s parody completely undermines Anselm’s argument. As noted, you could just bite the bullet and accept that the argument works for some other greatest possible Xs. Furthermore, as Grim notes, the success of each parody depends on whether the people accept that X could, conceivably, exist in reality. In principle, this could be denied for each and every parody, but retained for God (ignoring, for now, the problems discussed above regarding God’s possible existence). What the parody does show, however, is that there are significant consequences to granting the possibility of existence and assuming that existence is a great-making property.

The image below provides a complete map of the original argument and each of the criticisms discussed in this article.

Click for a larger clearer version

4. Conclusion

Anselm’s argument is intriguing. Its original statement takes up a paragraph of text and yet, from this humble beginning, it has entranced and bewitched philosophers and logicians for more than a millennium. Would that we could all achieve such citation impact. Nevertheless, as I have suggested in this article, there is a lot to question about the argument. It relies on dubious presumptions regarding the conceivability of a greatest possible being, the difference between mental and actual existence, the possible existence in reality of a greatest possible being, and the great-making function of existence in reality vis-a-vis solely mental existence.

I think Goldschmidt sums up the fate of the argument best when he says:

… where there are many assumptions at work in the argument, there is an asymmetry that puts opponents of the argument in a better position. Their success depends on any one of the metaphysical questions turning out the right way for them. One successful objection is enough to sink the argument. But the success of the proponents depends on all the metaphysical questions turning out the right way for them.

(Goldschmidt 2020, 23)

Add to this the fact that many of the underlying metaphysical questions are not capable of being satisfactorily answered (by humans at least), and you can see why it is easy for the Fool (the atheist) to resist Anselm’s charms.

Philosophical Disquisitions

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Thursday, December 21, 2023

Anselm's Ontological Argument: A Guide for the Perplexed

2. Problems with the Premises

3. Parodying the Argument: Gaunilo’s Infamous Island

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