Introduction. The argument for God’s existence in Chapter 2 of St. Anselm’s Proslogion may be one of the most elusive arguments on the subject, and attempts to validate or invalidate it are often akin to nailing Jell-O to a wall. The argument is also commonly classed with and is one of if not the most famous of the a priori arguments for God’s existence, viz. that God is per se nota (though one look at this elusive argument may force one to doubt even that!), as opposed to a posteriori arguments grounded in human experience or more traditionally reasoned from the effects to the cause. For the purposes of this paper, however, I intend to demonstrate that Anselm’s argument begs the question.
I first present Anselm’s argument and briefly explain it in Section II. Afterwards I distinguish between what I call a variable feature and what I call a definite feature of an object in Section III. Then I provide a critique of the argument premise-by-premise in Section IV and list objections to my critique in Section V. Following this I conclude in Section VI.
The Argument. St. Anselm gives his argument in Chapter 2 of his Proslogion. Anselm writes,
So even the fool must admit that something than which nothing greater can be thought exists at least in his understanding, since he understands this when he hears it, and whatever is understood exists in the understanding. And surely that which nothing greater can be thought cannot exist only in the understanding. For if it exists only in the understanding, it can be thought to exist in reality as well, which is greater. So if that than which a greater cannot be thought exists only in the understanding, then the very thing than which a greater cannot be thought is something than which a greater can be thought. But this is clearly impossible. Therefore, there is no doubt that something than which a greater cannot be thought exists both in the understanding and in reality.
Because elements in this argument can be difficult to follow, particularly with the references to something than which nothing greater can be thought, I will designate something than which nothing greater can be thought as S. Also important to note, S will refer to the something, not to the phrase: something than which nothing greater can be thought. I will refer to the phrase, “something than which nothing greater can be thought” as “S”, such as when Anselm says that the phrase “S” can be understood (even by the fool). This should also eliminate confusion when there are slight alterations to S. All of those instances involving alterations will be written out in full.
Here is a representation of Anselm’s argument with numbered premises:
1. The phrase “S” can be understood, and because of this S can exist in the intellect (because S must be thought or referred to in order for one to make sense of “S”).
2. But if S can exist in the intellect, then S can be thought to exist as well.
3. This then means that even if S does not exist (and so exists only in the intellect), nevertheless S can be thought to exist, which is greater than if S did not.
4. But if S does not exist, then S is something than which something greater can be thought (the fool can think of S as existing) which is a contradiction.
5. Therefore, S exists in reality.
A few points of clarification are in order. First it is necessary to note Anselm’s claims about the fool’s understanding of S and of the “S” are minimal. When Anselm says that the fool can understand the phrase, “S”, Anselm means that the fool can see that the phrase syntactically makes sense and designates something that harbors no obvious contradictions. The phrase is not equivalent to phrases such as, the ran car alley sunset, which syntactically does not make sense, or the triangle with four sides, which harbors an obvious contradiction and cannot designate a real thing.
Then, when Anselm claims that the understanding of the phrase “S” means that S can exist in the intellect, he does not mean to say that the fool can understand S, but rather that the intellect acknowledges S as something to make sense of the phrase, “S”. Thus S must exist in some minimal way in the intellect so that the fool can make sense of the phrase. I will further explain this in Section IV.
Lastly, this argument works as a reductio, which in my rephrasing of the argument is found in premise 4. If S did not exist, I could nevertheless think of S as existing, which would be greater. But if it is greater, then that means I can think of something greater than something than which nothing greater can be thought. So a denial of S’s existence leads to an absurd, contradictory claim.
Definite Features and Variable Features. To argue that Anselm’s argument begs the question, I employ the use of two different terms: definite features and variable features. A definite feature is an aspect or attribute that is used in the act of designating a particular object. Let us suppose I looked into a crowd of four women with different hair colors: one blonde, one red, and two white, and I said to Henry, “Jane Seymour is the blonde in this crowd.” Blondeness taken in my reference into the crowd to Jane is a definite feature and cannot change without at best changing which thing I am designating and at worst failing to designate anything.
Thus if I change this definite feature to red hair, the statement changes to, “Jane Seymour is the redhead in the crowd.” Which person I designate as Jane changes entirely. Jane is no longer the same Jane I designated when I designated her as the blonde; Jane is now the redhead and thus someone else entirely. But now let us suppose I said, “Jane Seymour is the one in the crowd with white hair,” then not only does which object I designate change, but my statement also becomes ambiguous. Jane could be either one. But if I said, “Jane Seymour is the brunette in the crowd,” then I have a new problem: there is no brunette in the crowd. So now I do not designate anything, which is a problem because my statement assumes that there is someone with the definite feature I used in my designation.
Contrary to a definite feature, a variable feature occurs when an aspect or attribute of a designated object can be thought to change once the object is designated. Here I will switch and use hair color as a variable feature. Let us suppose I say, “Jane is the third wife of Henry VIII.” The definite feature is Jane’s relation as the third wife of Henry VIII. Now let us suppose we do not know her hair color: is she a blonde, brunette, redhead, etc.? I can think of Jane as being any of these without changing which object I have designated; otherwise it would seem that I would need to know this to make sense of the phrase, the third wife of Henry VIII. So here hair color is not used as a definite feature but rather is used as a variable feature. Once we already know that Jane is a blonde, we could still treat hair color as a variable feature and imagine or think of Jane as hypothetically having brown or another color hair without changing which object is designated. She could have dyed it or survived childbirth to live to a more advanced age. After all, if Jane’s hair color did change most would agree that she would remain the same woman or at least the same object of designation.
From this the definite/variable feature distinction I have made is inconstant and obviously not rigidly fixed to the designated object, since the same feature of the same designated object can go back and forth between being either kind of feature. The classification of these features depends on how the object is referenced, viz. how these features play their roles in the act of designating.
I would like to push this point a little, so now let us suppose that I again designate Jane as the blonde in the crowd. Now while it is true that I cannot change the definite feature, viz. I cannot designate Jane as having any other hair color without changing the designated object or failing to designate anyone, still once I have designated Jane as the blonde in the crowd I can imagine or think of Jane as hypothetically having red or brown hair instead of blonde without changing which person I am designating. I can do this because Jane’s hair color could conceivably change (e.g. she could dye it, it could turn gray, etc.) without Jane becoming a different person. When I make this move, I immediately make the switch from speaking of Jane’s blondeness as a definite feature to speaking of it as a variable feature. Which one is Jane? Jane is the blonde in the group, but what would Jane look like if she dyed her hair brown or was born with brown hair instead of blonde? Here, the switch was done in one breath. As things are, however, we cannot hypothetically designate her as the brunette, because then we designate nothing; neither can we hypothetically designate her as the redhead, because then we designate something else, as I have said.
Let us complicate things further by saying, “Jane would be prettier if she were a brunette.” Now my statement hinges on two variable features: hair color and prettiness, where the latter is contingent on the former. I can think of Jane as having brown hair, and I can think of Jane as being prettier than she already is.
But let us suppose I said, “Jane as a brunette would be prettier than Jane as a blonde.” Now my statement hinges on hair color as a definite feature, because I designate the hypothetical Jane as a brunette and compare it to the other designated hypothetical, viz. Jane as a blonde. Because the feature used to designate the objects changes, viz. hair color changes, the objects I’m designating must change somehow. I am now designating two different versions of Jane, unlike the single version referred to in the above paragraph employing variable features, which are based on the same designated object.
These two different things (or versions of the same thing) do not need to exist nor does even one of them need to exist, because the statement could still be true if it read: existence or no, Jane as a brunette would be prettier than Jane as a blonde. In fact, there would still be no problem if the mood changed to indicative, with it reading: existence or no, Jane as a brunette is prettier than Jane as a blonde. Hypothetical brunette Jane does not need to exist for one to designate her by brown hair. What has been designated does not exist in reality, but it can still be thought.
Before I move on, I should briefly distinguish this definite/variable feature distinction from the substance/accident distinction. It should be clear that since accidents have been used throughout this explanation as both variable and definite features, the distinction between variable and definite features is not the same as the substance/accident distinction.
Critique. Now that this distinction has been made, I will take this argument premise by premise.
1. The phrase “S” can be understood, and because of this S can exist in the intellect (because it must be thought or referred to in order for one to make sense of the phrase).
When Anselm writes, something than which nothing greater can be thought, the fool can understand the phrase because Anselm uses a definite feature to designate S (otherwise we would not know what he was talking about). What is the definite feature? The definite feature is that whatever S is, whatever properties S has, and whether or not S exists (all could be variable features), nothing greater than S can be thought. The fool understands that if he were to think of something T, and there were something else greater than T that could be thought, then no matter how great T is, T is not S.
As I noted in Section II, the fool’s understanding of the phrase ensures the existence of S in his intellect. Not that the fool understands S, but if the fool can understand the definite feature Anselm defines and uses to designate S, then the fool can be aware that there is something, namely S, that is being designated. For example I can point my finger into the woods and ask, “What is that?” I do not know or understand what that is, but I am aware that there is something (I know I am pointing to it!). So while I do not understand what that is, I am still aware of it and to a minimal degree possess it in my intellect. The fool may not even understand anything else about S, as Anselm gives the example that the fool may not even understand that S exists in reality. For our purposes then, this premise in not controversial.
2. But if S can exist in the intellect, then S can be thought to exist as well.
Now that Anselm has designated S using a definite feature, Anselm proposes we discuss a variable feature, viz. existence. Without knowing whether S exists or not, the fool can nevertheless suppose that S exists or think of S as existing in reality. Anselm is not implying that S does exist or even that S can exist; rather he is merely asserting that from what the fool knows of S, he could think of S as existing.
This is akin to our Jane Seymour example. Let us designate Jane Seymour as the third wife of King Henry VIII: definite feature. Given this and without knowing her hair color, I could, without changing which thing I am designating, think of Jane Seymour as having blonde or brown hair: variable feature. Similarly Anselm has designated S as that than which nothing greater can be thought: definite feature. Then he says that the fool can think of S as existing in reality: variable feature. Like the first premise, this premise is for our purposes uncontroversial.
3. But then this means that even if S does not exist (and so exists only in the intellect), nevertheless S can be thought to exist, which is greater than if S did not exist.
This premise is akin to our example of Jane when we already had the prior knowledge of her blondeness. Though Jane is a blonde, nevertheless I can think of Jane as having brown hair (e.g. she could dye it): variable feature. In a world where S did not exist, nevertheless, I could still think of S as existing in reality: variable feature.
The premise goes one further, however, when it mentions that existence would be greater for S. This is similar to our example: Jane would be prettier if she were a brunette. Here, as I stated in Section III, I juggle two variable features for my statement to work: hair color and prettiness. Thinking of Jane as a brunette (variable feature) allows me to think of her as prettier (variable feature) than she already is.
This parallels the premise. Supposing S did not exist, nevertheless, if S did exist (variable feature) then S would be greater (variable feature) than it already is. Like the first two premises, nothing in this premise then is controversial for our purposes.
4. But if S does not exist, then S is something than which something greater can be thought (the fool can think of S as existing), which is a contradiction.
Now Anselm makes a move comparable to our phrase, Jane as a brunette is prettier than Jane as a blonde. As I said in Section III, hair color is now used as a definite feature. But as we noted earlier as well, we could say, existence or no, Jane as a brunette is prettier than Jane as a blond. The prettier version of Jane is designated as the brunette, not as a thing that exists, so even if it does not exist, we can still designate brunette Jane. This version of Jane does not exist, but it is still prettier than blonde Jane.
Let us try to do the same thing with S: existing S is greater than inexistent S. But can we say: existence or no, existing S is greater than inexistent S? If S does not exist, however, then I do not designate anything at all when I say existing S. Existence is here being used as a definite feature. Anselm is free to say, “If S existed then it would be greater than it would be in a hypothetical scenario of S not existing.” He is also free to say, “If S did not exist then S would not be as great as it would be in a hypothetical scenario where S existed.” He is however not free to say, “if S does not exist then I can think of something greater: S existing,” because if I think of S existing, I designate a version of S by means of existence, a definite feature. But if S does not exist, then I am not designating anything at all. If this is the case, then Anselm does not have anything to compare with inexistent S without assuming (another) S’s existence. This is closer to the example where I tell Henry, “Jane Seymour is the brunette in the crowd” (a crowd with no brunettes!). I do not designate anything here. So if S does not exist, then I cannot think of anything greater. I can acknowledge that S has room for improvement, but that does not constitute thinking of a greater version of S.
Then to designate anything at all in order to compare it with inexistent S, Anselm must assume that (an) S exists. If S does not exist after all, then Anselm is no better than when I pointed into a crowd with no brunettes and whispered to Henry, “Jane is the brunette in the crowd.” But S’s existence is exactly what Anselm is trying to prove, so Anselm is begging the question.
Objections. One could object saying that Anselm is really designating S existing in a hypothetical world. That way, Anselm designates something to compare with inexistent S without assuming the existence of S in the real world.
To this I would reply with the following question: is S existing in a hypothetical world really greater than S assuming S does not exist? Neither of these actually exists, so assuming S did not exist, S existing in this hypothetical world would only be greater than inexistent S if inexistent S did not exist in this other hypothetical world (and only then in that particular hypothetical world!). If S does not, then S is not S, but that does not bring us any closer to saying this S existing in a hypothetical world exists in reality. The solution to the dilemma, if there is a dilemma, is to say that whether or not S actually exists, S must exist in every hypothetical world with room to suppose the existence of (any) S. This still does not help Anselm.
One could also object that Anselm really means that the version of S which is greater than S if S does not exist is the version with the variable feature of existence, viz. thinking of S as hypothetically existing would make it greater than S if S did not exist. The version of S that I can think about that would improve on S if S did not exist, namely, my ability to think of S as existing assuming S did not, is greater than S if S did not exist.
To this I would reply with the following. What does it mean to say that I can think of a version of S that hypothetically exists? To say that I can think of S as existing is different than to say that I can think of an S that exists. So what does it mean to say that I can think of an S that hypothetically exists? This is to say that either I can think of S as existing or that there is some hypothetical world where S exists. I just dealt with the latter, and I already dealt with the former in Section IV.
There I stated that I can think of S as existing, but this is not equivalent to thinking of an S that exists. I could think of a version of Jane with brown hair, but that is because her definite feature is not existence. Inexistent Jane with brown hair still has brown hair: I still designate something by that phrase, even if that something does not or no longer exists. The phrase, inexistent S that exists, harbors a contradiction and does not point to anything real. Inexistent S that I think about as existing is still inexistent S.
To be further exhaustive, what would it be like to think about the fact that I can think of S as existing (variable feature), which would be greater? This, after all, is not thinking of an existing S, but rather thinking of the thought where I think of S as existing. In this case, however, I am thinking about an activity of the mind (which is why, might I add, the wording sounds so backward), not a something. But thinking of the activity of the mind where I can think of S as existing if S does not exist is not itself a greater thing to be thought.
One may further object that I have imposed a structure on Anselm which begs the question and that no begging of the question is inherent in the actual argument. This is so since by reframing Anselm’s argument in terms of variable and definite features, I have imposed an alien interpretation on an argument that would otherwise commit no logical fallacies (or at least would not beg the question in the manner I have suggested).
To this I reply that while it is true that I have explained a certain theory that I think helps us better understand what is going on in Anselm’s argument, I have not altered Anselm’s actual argument nor added anything to it. There are neither extra nor altered premises. Now I have used this framework to ask what this or that premise means (e.g. what does it mean to say that I can think of S as existing if it in fact does not exist?). To ask this question, however, one at least needs to use some framework, whether it is my own or someone else’s. What framework is appropriate to Anselm’s argument is a legitimate matter of dispute, and while I may have gone into more detail in explaining the premises’ meanings than what is intuitively grasped from reading the text, this can hardly on its own constitute an objection to my method without the aid of pious but nevertheless unmerited scruples or other substantive objections.
Neither is there evidence that I have imposed this fallacy on Anselm. If there were something inherently erroneous in the framework without which this fallacy would not be present, then the fallacy would be imposed. But again I claim to not have added anything to the argument itself but rather to have tried to explain what this or that premise means.
The Ongoing Debate. I do not have such an outrageously high opinion of myself as to have finally put the matter to rest. At best I have contributed to the ongoing controversy of Anselm’s argument ignited by Gaunilo of Maurmoutiers and continuing to this day. At the worst (and the more likely scenario), I have contributed to the many silly and trivial things written concerning Anselm’s ontological argument.
In either event, what I have tried to show is that using this definite/variable feature distinction that I have attempted to outline, it is possible for us to see that Anselm’s argument begs the question.
 Anselm, “Proslogion,” Anselm: Basic Writings, ed. and trans. Thomas Williams (Indianapolis: Hackett Publishing Company, 2007), 82.
 In this paper I interpret this to be saying that S would be greater if it existed, not S would be greater if it were thought to exist.
 My use of the term real thing is not to be confused with an existing thing. By my use of the terms, all existing things are real, but not all real things exist. By a real thing I mean an object that has an inner consistency in its designated features.
 I use the term two different versions instead of two different people to make my comment feel more agreeable. The mind does not want to agree with my saying, “two different people,” because the only difference between the two Janes is hair color. But if I designate and compare two versions of Jane differing only in hair color (blonde Jane is prettier than brunette Jane), my reference if taken literally should designate two different hypothetical people identical in all features but hair color. Often the phrase is used analogically to mean the same person at two different instances (Jane after her hair is dyed brown versus before), but this is not necessarily the literal meaning.
 This statement is probably possible if I am designating something as existing in a hypothetical world, just not in a strictly literal sense. I treat of possible or hypothetical worlds in Section V (objections).
 See an earlier footnote (3).