1. God is that than which nothing greater can be conceived.
2. What cannot be thought not to exist is greater than that which can be thought not to exist.
3. So if that than which no greater can be conceived could be thought not to exist, then there could conceivably be something greater still.
4. But it is absurd to say that that there could conceivably be something greater than that than which no greater can be conceived.
5. So that than which no greater can be conceived cannot be thought not to exist.
6. So God cannot be thought not to exist.
7. So God exists.
You cannot properly understand this argument unless you read it in the context of the Platonic-Augustinian tradition that forms its background. Knowing something about the later Scholastic tradition would be very useful too. And that is why modern readers typically do not understand the argument. For example, they often think it is an attempt to “define God into existence,” as if Anselm believed that arbitrarily attaching certain meanings to certain words could tell us something about objective reality. But this is to confuse what Scholastics call a nominal definition – an explanation of the meaning of a word – with what they call a real definition – an explanation of the nature or essence of the objective reality a word refers to. Anselm is ultimately concerned with the latter, not the former. While he no doubt thinks that any reflective language user will agree that the notion of “that than which nothing greater can be conceived” is implicit in his use of the word “God,” the more important point he is driving at is that being that than which nothing greater can be conceived must as a matter of objective fact be of the essence or nature of being divine, just as (to use a stock modern example) being a compound of hydrogen and oxygen is of the essence of water.
Of course, many modern philosophers deny that there are any essences or natures to be discovered, and would on that basis reject any distinction between nominal and real definitions. But to make such a denial is, by itself anyway, simply to assert that the essentialism presupposed by Anselm and other Scholastics is wrong, not to show that it is. Hence it cannot constitute a non-question-begging objection to Anselm. In any event, what is relevant here is what Anselm meant to be doing in giving a definition, not what a modern philosopher would be doing in giving one.
Modern readers also often assume that questions of better and worse, great and less great, are ultimately subjective. But this too, if left merely as an assumption, simply begs the question against Anselm. Here the Platonic-Augustinian essentialist background to the argument is crucial. To advert to some of my own stock examples, that a Euclidean triangle drawn with a straight edge is a better triangle than one drawn freehand (and therefore having only roughly straight lines) is a matter of objective fact, given what it is to be a Euclidean triangle. That a squirrel with four legs and a furry tail is a better squirrel than one which has lost its tail and a leg after a fight with a cat is also a matter of objective fact, given what it is to be a squirrel. And so forth. A better triangle is just a more triangle-like triangle, and a better squirrel is just a more squirrel-like squirrel. Better and worse, greater and less great, have to do with how perfectly or imperfectly a thing instantiates the nature that makes it the kind of thing it is. And if some form of classical essentialism is true (whether Platonic, Aristotelian, or Scholastic), then since the natures in question are objective realities, so too are the standards of better and worse that they entail.
Now part of what Anselm is saying is that existence is no different in this regard from being a triangle or being a squirrel. Having straight sides makes a thing more “triangle-like,” and having four legs makes it more “squirrel-like.” Similarly, to be that which cannot possibly not exist, to exist necessarily – which is what Anselm is getting at when he speaks of what cannot be thought not to exist – is, you might say, to be more fully existent, more “existence-like,” than to be the sort of thing which can possibly not exist, something which exists only contingently. And just as to be more perfectly triangle-like makes a thing better qua triangle, and being more perfectly squirrel-like makes it better qua squirrel, so too having necessary existence makes it better qua existing thing.
Now you can’t get more existence-like than existence itself, and Aquinas would, of course, later characterize God as He whose essence just is existence, Being Itself rather than a being among other beings. But something like this doctrine existed already in the Platonic tradition that preceded and influenced Anselm, and it is surely lurking in the background of his conception of God as that which cannot even be thought not to exist. Throw in the Scholastic doctrine of the convertibility of the transcendentals (which entails that being, goodness, and unity are all the same thing considered from different points of view) and it is easy to see why someone would judge that that than which nothing greater can be conceived and that which cannot be thought not to exist must be one and the same thing, and something utterly unique. Throw in also a broadly Platonic metaphysics of essences, and the conclusion that God so conceived of must exist in reality seems to follow straightaway. For how could that which is Existence Itself fail to exist? And if God just is Existence Itself, how could He fail to exist?
It is also easy to see, in light of all this, why Anselm would be unmoved by Gaunilo’s objection (i.e. “Why couldn’t such reasoning be used to prove that, say, a greatest conceivable island must exist (which would be absurd)?”). Islands and other examples of the sort appealed to in Gaunilo-style “parody objections” to the ontological argument are simply not the sort of thing to which its reasoning could in principle apply, given what has been said. For not only islands and other material things, but also anything less than Being Itself, anything in which essence and existence are distinct, could in principle be thought not to exist.
To be sure, I am not claiming that Anselm reasoned in exactly the way I have suggested here, or that all of the concepts involved, much less the terminology, are explicit in his writings. I am saying instead that something like this line of thought is surely implicit in what he did say, given the intellectual milieu within which he thought. Some of themes in question already existed within the tradition in a fully articulated way, others were fully articulated only later, but all are relevant to understanding what Anselm was getting at. (Compare: If future historians of philosophy want to understand what is going on in J.J.C. Smart’s famous article “Sensations and brain processes,” they would do well to read it not only in light of the general materialist tradition that preceded it, but also in light of the specifically functionalist version of materialism that came after it, insofar as Smart’s notion of “topic-neutrality” represents an inchoate version of the basic functionalist idea. And if these future historians happened to be Aristotelians, they would be making a grave mistake if they assumed that Smart means by “matter” what they do, or that functionalists mean by “function” what they do – as mistaken as contemporary philosophers are when they unwittingly read their own assumptions back into an Aristotle, Anselm, or Aquinas. That philosophers of the past should be read in light both of the traditions that preceded them and those that succeeded them is a theme I have addressed earlier, e.g. here and here.)
Most of the standard objections to Anselm seem to me to rest on a failure to appreciate this larger philosophical context of his argument. But not all of them. As my readers know, I hate to come across like a doctrinaire Thomist. But it does seem to me that Aquinas’s objection to Anselm is the one that really gets to the nub of the matter. Aquinas agrees that to grasp God’s essence would be to see that He cannot possibly not exist. God’s existence is in that sense self-evident in itself. But it is not self-evident to us, given the way we have to come to know things (ST I.2.1). For one thing, as an Aristotelian, Aquinas is committed to the view that all our knowledge, including knowledge of God, must derive from the senses. For another, he holds that for us to grasp a thing’s essence is to grasp its genus and specific difference. But when we come to know through the senses (and in particular through the Five Ways) that there is a God, what we come to know is that there is an uncaused cause of the world who is purely actual and in whom there is no distinction between essence and existence. This entails that He is the sort of thing which could not possibly not exist, but also that He is absolutely simple and thus not composed of a genus and specific difference (or of anything else for that matter). Hence we cannot grasp His essence, and thus cannot know what we’d need to know in order for Anselm’s argument to serve as a way for us to come to know God’s existence. In effect, we come to know a posteriori that there must in fact exist exactly the sort of God Anselm tells us exists, while at the same time coming to know that Anselm’s a priori way of getting to Him cannot succeed.
The lesson is not that Anselm’s argument is unsound so much as that it presupposes knowledge (i.e. of God’s essence) that we cannot have. Moreover, the idea that reason points us to the existence of that than which there can be nothing greater is something Aquinas himself endorses as long as it is developed in an a posteriori fashion, as it is in Aquinas’s Fourth Way. (I explain how, and explain and defend the other key metaphysical ideas referred to above, in Aquinas.)