Ironically, one of the first critics of Anselm's argument was not an atheist, but a Christian monk by the name of Gaunilo. In his letter On Behalf of the Fool, Gaunilo argues that simply because we can conceive of something does not mean that we can infer that it exists in reality, no matter how great we conceive it to be. As an example, Gaunilo conceives of an island which can be described as that island than which no greater island can be conceived. By Anselm's logic, this island must exist in reality because any island which exists solely in the mind is less great than it would be if it existed in reality. However, given that this is clearly absurd, Anselm's argument must be absurd as well.

At first glance, it appears to be a thoughtful argument on the part of Gaunilo. However, Anselm is alacritous to retort that Gaunilo’s analogical comparison between God and an island is unwarrantable because, while it may be conceivable that there be an island which happens to be greater than all other existing islands, it is utterly inconceivable that there be an island which is such that no greater island can be conceived. For no matter how great one conceives an island to be, s/he can always conceive of one that is greater, simply because the greatness of an island is based upon things which have no intrinsic maximum, e.g., trees, weather, riches, size, and the like. In essence, Gaunilo's rebuttal lacks any cogency because a greatest conceivable island is logically impossible; islands are imperfect by their very nature, from which it follows that to conceive of an island than which no greater island can be conceived would be to contradictorily conceive of something that is both perfect and imperfect. By contrast, God has a degree of greatness which is based upon the category of being, which itself does have an intrinsic maximum. As such, God is not merely the greatest being, but He is the greatest conceivable being.

From all of this, it is clear that Gaunilo's objection fails. But this does not mean that Anselm's argument is sound. For it was Immanuel Kant who delivered what many take to be the staunchest objection to the argument. As an interesting footnote, Kant was actually the first person (as far as we know) to refer to the argument as the "ontological argument." Moreover, even though many philosophers consistently invoke Kant as being one of Anselm‘s chief detractors, it is questionable as to whether or not Kant himself was directing this rebuttal towards Anselm specifically. Nevertheless, according to Kant, the central flaw in the inference to God’s real existence from the contents of the idea is the treatment of existence as being something which a subject possesses, i.e., a predicate. To Kant, existence itself is not anything which is added to a concept; it is merely the is of a judgment, which serves to connect a subject to its predicate. As such, the statement "God is" is hardly a statement at all. Instead, it's an incomplete sentence, which, from the perspective of the opposing interlocutor, says nothing meaningful about the idea which it attempts to put forth. For it simply posits the object in relation to whoever is conceiving it, which may be demonstrative of the possibility of the object, but not of its actuality. For Kant, we can never infer the actual from the possible. Otherwise, the currency of a hundred possible dollars would be equal to that of a hundred actual dollars, which is clearly absurd. Therefore, according to Kantians, Anselm's argument may support the possibility of God, but not His actuality.

For many, it is taken for granted that Kant soundly defeated Anselm. But is it true? In order for Kant's objection to work against Anselm, it must be established that Anselm somehow had a misconception about the idea of existence. The problem, however, is that it is not so clear that this actually applies to Anselm's argument. Kantians would probably point specifically to the third premise, which states that something existing solely in the mind is less great than it would be if it existed in reality. But it can be argued that what Anselm treats as a predicate here is not existence, but concreteness and/or abstractness. As such, it does not appear that Anselm has any difficulty operating in accordance with Kant’s semantic guideposts; given the set of all that is contained in the concept, concreteness or abstractness would contribute to the cardinality. Thus, once the atheist grants that God is the greatest conceivable being, s/he becomes caught in a self-contradiction; inevitably adhering to the idea that the greatest conceivable being can be, insofar that it is greater to be concrete than it is to be abstract, conceived to be greater than He is. This is true, even if existence is not a predicate. Therefore, Kant's objection fails against Anselm.

The failure of Kant's objection notwithstanding, there still remains something unsatisfactory about this formulation of the argument. For it inevitably raises the question: In what sense can we say that a real being is greater than an abstract entity? Thus far, we've only been appealing to intuition, where it seems obvious, for instance, that a hundred dollars in reality is greater than an imaginary hundred dollars. However, there are other scenarios in which this idea becomes counterintuitive. For example, are we equally justified in arguing that the Pythagorean Theorem is qualitatively less great than an amoeba simply on the grounds that the amoeba exists in reality as opposed to the Pythagorean Theorem which is only in the mind? If so, what heuristic not trading upon personal whim could we possibly have implemented in order to arrive at such a conclusion? Even if one argues that the aforementioned measurement of greatness applies only to situations where the greatness of a concrete entity is measured against that of its own concept (for example, if one says that while it is not necessarily true that the Pythagorean Theorem is less great than an amoeba, the real issue is whether or not an abstract Pythagorean Theorem would be less great than a concrete Pythagorean Theorem), the general problem still remains.

But in the view of some philosophers, Anselm avoids this problem insofar that in contextualizing his argument with other chapters of Proslogion, the proposition that concrete existence provides additional greatness does not seem to be what Anselm was attempting to defend in the first place. For such an endorsement would admittedly make the argument far less tractable than it ought to be. For some, Anselm’s metric of greatness seems to be more pertinent to the distinction between contingent beings and necessary beings.

In essence, the argument itself becomes a practice in what is known as "modal logic." Modal logic is a formal system of logic which provides a convenient way for logicians to make arguments using modal terms such as possibly, contingently, and necessarily. More specifically, modal logic provides a body of axioms and theorems which direct our usage of such terms, allowing us to formulate arguments, such as Anselm's ontological argument, more rigorously. Applying modal logic, it could be stated that something x is possible if and only if there is a possible world where x is instantiated. Likewise, something x is necessary if and only if x is instantiated in every possible world. Finally, something x is contingent if and only if x is instantiated in one or more possible worlds but not every possible world.

Applying the aforementioned principles, Anselm’s argument has been subject to revision by contemporary philosophers. This revision has come to be known as the “modal ontological argument.” There are two main versions of this argument whose relative ubiquity shall render them the primary focus of the ensuing discussion. The first version was formalized by Charles Hartshorne and Norman Malcolm. Although Hartshorne and Malcolm did not work together, I shall, for the sake of brevity, discuss both of their arguments in the context of one formulation, given that their respective versions are quite similar to one another. The second version, formalized by Alvin Plantinga, seems to be unique in its own right.

The argument formalized by Charles Hartshorne and Norman Malcolm largely reflects what Anselm wrote in Chapter 3 of Proslogion. In it, Anselm puts forward a premise, which, for Hartshorne and Malcolm, constitutes the foundation for the contemporary metaphysical understanding of “necessary” and “contingent”; an individual whose nonexistence is logically impossible is qualitatively greater than one whose nonexistence is logically possible. Thus, in the May 1944 issue of The Philosophical Review, Hartshorne interprets Anselm to be arguing that God, the greatest conceivable being, must be a necessary being because it is greater to be necessary than it is to be contingent. Norman Malcolm, in the January 1960 issue of the very same journal, echoes Hartshorne’s sentiments by positing that if God is understood properly as the greatest conceivable being, then He cannot be understood as having begun to exist nor can He be understood as existing whilst having the potential to not exist because anything which begins to exist or stops existing must be an effect of some cause to which it cannot comparatively be greater. Hence, according to the analyses of both Hartshorne and Malcolm, positing that God is not instantiated in the actual world is tantamount to arguing that, in the worlds where God does exist, there is some being that is qualitatively greater than the greatest conceivable being, which, of course, is a metaphysical impossibility. As such, the structure of the argument gives way to the following exclusive disjunction: Either the existential proposition of God is analytically true or it is logically contradictory. And, according to the argument, since the proposition is not contradictory, it must be analytically true. Hartshorne and Malcolm’s argument can be formalized in the following way:

(1) God is the greatest conceivable being [definition of “God”].

(2) The greatest conceivable being is either necessary or impossible or contingent [premise].

(3) The greatest conceivable being is neither impossible nor contingent [premise].

(4) The greatest conceivable being is necessary [from 2 and 3].

(5) The greatest conceivable being exists in all possible worlds [from 4].

::. God exists in the actual world [from 1 and 5].

Alvin Plantinga formalized what many take to be the most famous modal version of the argument. The principal weakness that Plantinga found in Hartshorne and Malcolm's formalization of the argument was that it was not made clear in any of their premises that God's existence in the actual world included all of His great-making properties, which is to say, perhaps God's properties in possible world W are greater than His properties in actual world W'. As Plantinga states:

"It doesn't follow that the being in question has the degree of greatness in question in Kronos, the actual world. For all the argument shows, this being might exist in the actual world but be pretty insignificant here. In some world or other it has maximal greatness; how does this show that it has such greatness in Kronos (The Analytic Theist, Alvin Plantinga, edited by James Sennett, 1998, p. 66)."

Plantinga thus revised the argument to say that God, as understood by Anselm, possesses His great-making properties in every possible world. Plantinga refers to the instantiation of God's great-making properties (omnipotence, omniscience, omnipresence, moral perfection, etc.) in every possible world as "maximal greatness," whereas the instantiation of such properties in one world is called "maximal excellence." Plantinga reformulates the argument as follows:

(1) There is a possible world in which maximal greatness is instantiated [premise].

(2) Necessarily, a being is maximally great if and only if it has maximal excellence in every possible world [definition of "maximal greatness"].

(3) Necessarily, a being has maximal excellence in every possible world if and only if it is omniscient, omnipotent, omnipresent, wholly good, and eternal in every possible world [definition of "maximal excellence"].

::. A being instantiates omniscience, omnipotence, omnipresence, moral perfection, and eternality in the actual world [from 1 to 3].

How do atheists respond to the newly formed modal versions of the argument? One objection is that granting the possibility of God in these instances is strictly epistemic, which is to say that as far as we know, God is possible. Along similar lines, we can argue that it is possible that the one billionth digit of Pi is 8, simply on the grounds that we have no knowledge whatsoever of the one billionth digit of Pi. And for the atheist, this is the only sense in which we can say that God is possible; we have no knowledge whatsoever of God, therefore we can say that God is possible, if “possible“ is understood in a trivial epistemic sense. Thus, we cannot accept the logic of the modal ontological argument because in doing so we would have to conclude that since the one billionth digit of Pi is 8 in some possible world, it therefore must be 8 in every possible world since all mathematical truths are logically necessary. But clearly, there is something wrong with this conclusion because we‘ve already conceded that we do not know if the one billionth digit of Pi is 8. In the same way, we cannot conclude from God’s epistemic possibility that He actually exists.

In response, the theist can argue that it should be made clear that, in the context of the argument, "possibility" strictly refers to modal possibility, i.e., occupying some possible world. In this case, the term "God" has a clearly defined meaning, allowing us, by way of its logical consistency, to posit with certainty that such a being is modally possible. In terms of the one billionth digit of Pi, we cannot apply this same metric simply because the assessment of its logical consistency is coupled with the application of counting, which creates an epistemological gap between ourselves and the value of the mathematical constant equal to the one billionth digit of Pi. As a result, we can only know that necessarily there is a one billionth digit of Pi and that, letting 0 < x < 9, if the one billionth digit of Pi is x in possible world W, then it is x in every possible world. However, our metric for determining what x can possibly be equal to is much less manageable and therefore, we cannot say one way or the other if the one billionth digit of Pi is possibly 8. Rather, we just simply do not know. Thus, the epistemological gap does not apply in both cases.

But then the atheist may ask the following question: How can we know for sure that "God" is a logically consistent idea? For the concept itself may contain a hidden contradiction which we are unaware of. Thus, it may in fact be the nonexistence of God which is logically necessary. In fact, one can point out that it is possible for us to affirm the real existence of contradictory ideas if we fail to realize that such things are contradictory. The contention that “God” is a contradictory idea is referred to by Hartshorne as “positivism.”

Understandably, theists may ask the following question in response: What exactly does this position do for the atheist? Does the alleged possibility of "God" being a contradictory term vindicate his or her position? If anything, it would place the burden of proof on his or her shoulders. Moreover, the tactic itself seems to be an ad hoc maneuver on the part of the atheist if s/he normally argues against God from the standpoint that a world where God exists would be entirely different from the one that we happen to occupy (for example, the problem of evil argues that the existence of evil is inconsistent with the existence of God, which would show that the atheist grants the coherency of the idea of God insofar that s/he is speaking of worlds where God exists). Thus, it would appear that, at least to the theist, positivism is an untenable position.

But though it may be clear that atheists will have their own burden of proof with respect to the positivist position, isn't it just as well that God's conceivability requires further justification on the part of the theist? In fairness, the lack of prima facie contradictions in the proposition “God exists in reality” seems to apply equally to the proposition “God does not exist in reality.” At this stage, then, it seems to be the case that the tenability of the ontological argument is, in any one of its formalizations, contingent upon one's worldview. Hence, while the argument itself will work for those whose set of presuppositions allows that there be something than which nothing can conceivably be greater, it will have not even a modicum of currency for the atheist interlocutors who deny that “God“ is even meaningful. Thus, the ontological argument does not appear to stand on its own two feet, as it requires us to make additional arguments in support of the set of presuppositions under which it is sound. Given these facts, the atheist does not seem to be fully blameworthy for his or her skepticism. For it holds true that if an entire worldview is not justified, then arguments which are defended only under its auspices cannot be justifiably accepted.

St. Thomas Aquinas had argued along similar lines, claiming that the existence of God, while self-evident, is not necessarily self-evident to us. God is self-evident in Himself, as it is clear to Him, in His omniscience, that nonexistence is not an option for Him. But, as Aquinas would probably have argued, in order for the truth of this existential proposition to be clear to us, we will need intellectual assent provided from beyond the mere utterance of the word "God." Thus, according to Aquinas’ reasoning, it seems that the ontological argument, even if we grant its validity, cannot provide us with grounds for saying that the atheist’s tendency toward doubt is without excuse.

It appears, then, that the greatest charge someone can make against the ontological argument is that it's superfluous. For it seems that it only works once the truth of the proposition "God has real existence" is established a posteriori, at which point God's real existence is already proven.

One possible counterargument is as follows: If we follow Charles Hartshorne‘s understanding of God‘s nature, then it is inconceivable that positivism be true. Hartshorne states that unlike regular abstractions such as "human" or "cat," the abstraction "perfect" cannot be shared by many beings. As such, God's existence does not occur in place of other things which could have shared in His divine category. The essence of God is, in fact, noncompetitive. This means that there is no moment at which God's existence competes with His nonexistence or with the existence of others because such dichotomous relationships are predicated only of contingent things. Taking this one step further, we can argue (as philosopher Eugene Peters does) that God, in His divine essence, constitutes the ground for possibility itself, since the ultimate source of any contingent thing would consist in something that's necessary. Hence, one may argue that God cannot be modally impossible because the very notion of possibility presupposes God. Therefore, so the argument goes, the ontological argument can work without recourse to a posteriori arguments.

The problem with this proposed solution is that if the positivist is right and "God" is not meaningful, then the term, regardless of what the theist intends for it to signify, does not actually signify anything, anymore than does “squared circle” actually signify a four sided figure that contains only closed curves. What follows is that in putting forth this objection against the atheist, the theist is making an accusation of self-contradiction whilst unwittingly presupposing that the atheist grants the coherency of the term, which cannot be the case in positivism. The only recourse for the theist, then, would be to put forth another argument justifying the coherency of "God," which, as previously mentioned, would make the ontological argument superfluous.

So, the question remains, what place does the ontological argument have in the ongoing dialectic between theists and atheists? One could argue that it could be useful in explicating the theistic position, given that the argumentative modus operandi of the atheist may be based on a misunderstanding of what “God” means. Furthermore, as Alvin Plantinga notes, even if the argument does not establish its conclusion incontrovertibly, it may still lend credence to the rational acceptability of theism, given its deductive validity and the fact that its central premise, i.e., God is possible, contains no prima facie contradiction. One could also argue that the argument is a useful tool for engaging philosophy novices (especially those who are atheists, given their antipathy towards the argument’s conclusion) in the contemplation of metaphysical issues, since, as Plantinga mentions, many of the central issues in metaphysics meet in this argument, such as the nature of existence, the possibility of knowledge without experience, the relationship between concepts and objects, and so on.