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The Krueger-McHugh Debate: Theism or Atheism (2003)

Doug Krueger

First Rebuttal by Doug Krueger

In this first rebuttal I will address some of the problems with McHugh’s argument for the existence of god. Subsequent posts will address his rebuttals to the arguments in my opening statement.

McHugh has chosen as his sole weapon for his case the ontological argument. This argument has never been popular outside of academia, and for good reason. To many, it seems to be little more than suspicious wordplay. Alvin Plantinga, one of the premier champions of the ontological argument in the twentieth century, admits that “at first sight, this argument smacks of trumpery and deceit.”[1] Plantinga holds that the argument can be somewhat rehabilitated, but for many the ontological argument is decidedly unconvincing. McHugh presents two versions of the ontological argument, I will focus my critique mainly on McHugh’s own version and agree with him that Hartshorne’s argument falls short of demonstrating god’s existence. I will show that McHugh’s ontological argument is not without problems, and that it too fails to serve as a proof of the existence of god.

Before addressing McHugh’s ontological argument, I would like to address one of his preliminary remarks because I think that it is very telling about the position he holds regarding the relationship between concepts and reality. McHugh writes,

Consider that there are some things that cannot possibly be unreal. For example, logical laws and mathematical truths do not have the possibility of being mere fictions. In any possible world, there are certain truths like A=A and 2+2=4.

Note how McHugh moves easily from the notion that “statement t is true” to that of “there is an object t that is real.” Indeed, he refers to logical and mathematical truths as “things,” as if these truths are some sort of objects existing in an immaterial realm. In fact, I think that this is exactly how McHugh probably views such truths. McHugh even contrasts such truths with those whose objects have the possibility of not existing. He writes:

Of course, there are some things that do have the possibility of unreality. For example, there are possible worlds in which the Statue of Liberty does not exist.

So necessary truths seem to be interchangeable with necessary beings. This Platonic view of mathematical truths has had a long history and a great influence on the field of philosophy, but antirealist philosophical movements in the 20th century have undermined much of the attraction of such views. There are antirealist explanations of numbers and mathematical truths that do not posit the existence of real, mathematical objects to explain the truth of mathematical statements. In other words, one can explain the truth of mathematical statements and nevertheless maintain that these are “fictions” in the sense that these statements do not refer to existing abstract objects. Consider: “Sherlock Holmes is a detective.” In the context of discussing the works of Sir Arthur Conan Doyle, one would hold that this statement is true. Yet this does not imply that there is an existing detective that is Sherlock Holmes. “A unicorn is a horse-like animal with a single horn”; we would say that this is true, but the truth of this statement does not imply that there are unicorns. “2 + 2 = 4” is true, but we needn’t understand this to imply that some object must exist because of it, and even if we grant that this statement is true in all contexts in which it occurs, this does nothing to show that the truth of the statement implies the existence of something–at least, if we must understand the mathematical statement to imply the existence of something, McHugh will have to argue for this. I don’t see any reason to hold that mathematical truths are statements about the existence of anything. Truth and existence are different things, and to prove the former is not to prove the latter, or at least argumentation would be required to show otherwise. I mention the case of numbers because I think McHugh’s move from “statement t is true” to “there is an object t that is real” is unjustified. It has not been shown that mathematical statements are existence statements, and I think this questionable move illustrates the basic error that lies at the heart of the ontological argument. It is not at all clear why we should think that showing that something is true of a concept demonstrates that the same thing is true in reality. I can show that a triangle must have three sides, but that doesn’t prove that there are triangles. It could be true that a triangle necessarily has exactly three sides, yet it could also be true that there are no triangles. I can show that it must be true of bachelors that all bachelors are unmarried, but this doesn’t show that there are bachelors. It could be that “All bachelors are unmarried” is true, yet it could also be true that no bachelor exists. One can imagine that someone learning about the concept of a bachelor could be taught that no bachelor is married and yet still wonder whether there are any bachelors. There is a big difference between showing something about a concept and showing something about an object (a nonconceptual, existing thing) in the world. The philosopher Robert Paul Wolff wrote: “Whenever I read the Ontological Argument, I have the same feeling that comes over me when I watch a really good magician. Nothing up this sleeve; nothing up the other sleeve; nothing in the hat; presto! A big, fat rabbit.”[2] The ontological argument begins by talking about a concept and ends up talking about the thing which is purportedly described by that concept, but this hat trick, while entertaining, has always been plagued with problems, as McHugh does well to admit. At the end of his opening statement, McHugh explains that such criticism can be forestalled because the conclusion of his argument is logically necessary, and the logical necessity of a conclusion guarantees its metaphysical possibility, and furthermore “metaphysical possibility is a species of real possibility.” What is “metaphysical” and what is “real” are terms that must be clarified if we are to believe that McHugh can prove that something exists simply by analyzing the concept of it, and given the plausibility that proofs about numbers, triangles, and other “necessary” concepts are not also proofs about the existence of objects, McHugh has his work cut out for him.

McHugh refers to Hartshorne’s ontological argument, and he concedes that Michael Martin’s criticism of the argument may have some force. Martin brings up several points against Hartshorne’s ontological argument, and McHugh cites Martin’s criticism of premises (1) and (7). Let’s look at the problems with premise (1) of Hartshorne’s proof and whether McHugh has adequately addressed those. The first premise of Hartshorne’s proof is that if god exists, then god exists necessarily. Michael Martin writes:

Hartshorne seems to mean by “it is necessary that q” that it is logically necessary that q. However, there does not seem to be any reason to suppose that, if a perfect being exists, the existence is logically necessary.[3]

Martin refers to an article by R. L. Purtill, who observes:

It seems to be contrary to our idea of logical necessity that whether or not a statement is logically necessary should be determined by the existence or nonexistence of something. If by “logically necessary statement” we mean “theorem of a logical system” or “tautology” or “analytic statement,” it seems quite clear that the existence or nonexistence of something is irrelevant to the question of whether or not a statement is a theorem, or a tautology, or is analytic. Even if our idea of logical necessity is claimed to be wider than any of these notions, it seems unlikely that any plausible account of logical necessity would allow it to be dependent on existence.[4]

In other words, Hartshorne’s first premise, that if god exists, then god exists necessarily, seems implausible. To support this premise, then, more argumentation would be needed. However, McHugh understands Martin’s criticism of premise (1) to be primarily the question of whether the argument can be parodied to produce proofs of other entities besides god (a point he concedes for the sake of argument). Until support for premise (1) is forthcoming, it would seem that we cannot know that premise (1) is true, and thus the argument would fail as a proof. Later in his article, McHugh uses the same premise in his own argument (“q ->Nq”), so it can also be said of McHugh’s argument that it cannot serve as a proof until it can be shown that premise (1) is true. What kind of logical necessity can is this that is dependent upon existence, as indicated in the first premise?

Let’s examine McHugh’s attempt to circumvent problems with premise (7) of Hartshorne’s proof. Martin’s problem with premise (7), specifically, is that because the concept of god is contradictory, then it is not the case that it is possible that god exists. It is an important part of Hartshorne’s proof that it is possible that god exists, but instead of attempting to rebut Martin’s arguments for the incoherence of the concept of god, McHugh constructs his own version of the ontological argument designed to overcome the incoherent attributes problem. McHugh draws on Richard Gale’s work that shows that sets of negative terms of differing qualities are compatible. So in order to avoid the charge of incompatible properties, McHugh constructs a definition of god that is a set of negative properties. Is this successful? It seems to be problematic. Note that Gale specifies that negative properties are compatible, but that a compatible set of negative properties “must be restricted to qualitatively homogenous properties; for non-red color, an obviously negative property, is incompatible with some other property of the same quality–non-colored.”[5] If some of McHugh’s stated properties for god–or what he calls a “Godlike” being–imply a property that is incompatible with some of the other negative properties, then the concept is incoherent despite the use of negative properties. Some of the negative properties used by McHugh are so vague that they can be easily interpreted to imply conflicting properties. Let’s look at possible examples of conflict. “Not being natural” and “Not being deficient in any sense.” Why would not being natural not be a deficiency? The same could be asked of the property “Not being spatiotemporal.” If a being could be Godlike in other respects and could also be spatiotemporal, wouldn’t that be a being greater than one that had similar properties but which lacked spatiotemporality? And wouldn’t then the lack of spatiotemporality be a deficiency? It seems that instead of the standard Anselmian appeal to great-making properties, McHugh is removing lesser-making properties in the hopes of constructing an objection-proof concept of god. But why is something that is spatiotemporal lesser than something that is not? How is that not a deficiency “in any sense”? Furthermore, to say that a being is not spatiotemporal is to say that the being is unable to engage in activities that require a spatiotemporal context, such as walking around and juggling. Those activities cannot be performed except in a spatiotemporal environment. So if the Godlike being is not spatiotemporal, the being cannot juggle, ride a bicycle, speak, and engage in other common activities. How is that not being deficient “in any sense”? It would seem that a Godlike being that has most of the attributes of McHugh’s being but which could also exist in the spatiotemporal realm would be superior to McHugh’s Godlike being, so how is the lack of spatiotemporality not a deficiency? Despite McHugh’s attempts to avoid conflicting attributes, his concept seems to have at least a few. If so, then he has not avoided problems with premise (7), and his ontological argument is unsuccessful.

One can also point out a serious difficulty with McHugh’s premise (6): “Not being a logical law, a number, a mathematical truth, a Platonic form or some other abstraction.” This premise is presumably designed to eliminate the possibility that one could simply appeal to an alleged “abstract object” such as the set of integers or the Platonic form of Good and explain how that satisfies the definition of a Godlike being yet it is not what is typically considered to be god. If this were to happen, the problem would be that McHugh’s proof would have as its conclusion something that most people would reject as god, and thus this would not be a proof of god’s existence at all. So narrowing down the field of what is Godlike to things that are usually called “god” is important. But the phrase used to narrow the field, “some other abstraction,” is vague. It is vague because it is not clear whether McHugh is not saying that god is an abstraction and “some other abstraction” besides god does not qualify as Godlike. But what other abstractions cannot qualify as Godlike beings? Presumably, those other than god. But which ones are those other than god? Those that do not satisfy the definition of Godlike. But McHugh is in the process of giving us that definition. In other words, if McHugh asks us to eliminate abstractions from Godlike candidacy by telling us that those that are not Godlike don’t count, then his definition is circular. And if is saying that abstractions that are not like the standard definition of god are eliminated, if McHugh has another definition of god that informs the distinction between god abstractions and nongod abstractions, let’s see it so we can determine whether that other definition has contradictory attributes. On the other hand, if McHugh simply means by “some other abstraction” that god is not an abstraction, so that anything that is an abstraction is not Godlike, we must ask what he considers to be an abstraction. It looks like a loaded term, and unless McHugh cashes out the details, it looks like an ad hoc method of limiting the definition of Godlike to the sort of being McHugh has in mind. Another problem McHugh must face is that since he is committed to using only negative properties, it is not clear that he can limit his definition of Godlike to what people typically consider god. The Tao of the Taoist religion seems to satisfy all of McHugh’s criteria, so can his argument be used by a Taoist? Or is the Tao an “abstraction”? The Tao is not personal nor does it have other attributes often associated with god (i.e. it is not a person, it is not conscious, it does not respond to prayer, etc.). So isn’t the Tao Godlike, since it satisfies McHugh’s definition? In fact, it satisfies McHugh’s definitions admirably, perhaps better than the Judeo-Christian-Islamic god, since traditionally no positive properties at all can be associated with the Tao, and it has all of McHugh’s negative properties essentially. Premise (6) seems to be clearly problematic. Why should we think that the being described in McHugh’s argument is god? Ludwig Wittgenstein wrote: “If you want to know what is proved, look at the proof.”[6] McHugh’s proof describes something that could be what we often call god, or it could be other things, such as the Tao, the Hindu concept of Brahman,[7] the Buddhist concept of Nirvana, or still other concepts. One would expect that a proof of the existence of god would take the concept of god and show that there is such a being that is correctly described by that concept. As a proof of the existence of god, this isn’t one. McHugh’s conclusion can apply to a number of different concepts.

One long-standing problem with the ontological argument has been that it can be parodied. In other words, instead of using “god” as the subject of the argument, one can use “the perfect island,” “special fairies,” and other substitutions to “prove” the existences of those beings that everyone would affirm do not exist, and the argument seems to work in those cases too, reducing the argument to absurdity and thus showing that there is a flaw in the argument somewhere. So can McHugh’s argument be parodied? Can it be used to show the existences of beings that are not typically called “god”? Yes, admits McHugh. He allows that one could use his argument for a Godlike being to show that a similar being, called Godlike* (with an asterisk at the end; it doesn’t mean there’s a footnote), exists even though this being has the negative properties of being non-good and non-powerful. This is called “biting the bullet.” McHugh accepts a proof that should be a reduction to absurdity of his own argument. How can McHugh hold that this is really no problem? He appeals to the “apophatic” tradition in Christian mysticism, the “theology by way of negation.”[8] Such mystics deny that human language can ever categorize god, and thus nothing positive can be truly said of god, including that god is all-good or all-powerful. This limits the appeal of McHugh’s proof because few believers in the Judeo-Christian-Islamic tradition would be willing to endorse a proof of god that can be used to exclude that god is omnipotent and omnibenevolent. To the extent that some mystics are online to see this, he may find a sympathetic ear, but most believers would accept that any proof that accommodates god as non-good or non-powerful has been reduced to absurdity. McHugh indicates that statements such as “God is that on which the universe depends,” and other claims, are compatible with the god produced at the conclusion of his proof, but of course the god in his argument is also compatible with “God is not that on which the universe depends,” and “God is not the creator of the universe.” If we were to construct an argument for a “Godlike+” being similar to McHugh’s (with a plus sign added), but which has the property “Is not that on which the universe depends,” would McHugh allow that this being also exists, and that it exists alongside a “Godlike&” being to which we would add the property that it “is that on which the universe depends”? We can “prove” that both the “Godlike+” and the “Godlike&” beings exist, so do they each exist? If so, doesn’t this reduce his argument to absurdity? And what about the concept of “a noncontingent unicorn.” Let us specify that, unlike other unicorns, this one is noncontingent. Let’s call such a unicorn a “nunicorn.” The concept of a unicorn does not seem to entail contingency, so we could say of a nunicorn that it’s existence is either logically impossible or logically necessary, just as McHugh asserts of his Godlike being. The basic structure of McHugh’s argument would prove that a nunicorn exists.

Either the existence of a nunicorn is logically necessary or logically impossible. It is not the case that the existence of a nunicorn is logically impossible. Therefore, the existence of a nunicorn is logically necessary. [From 1 and 2] Therefore, a nunicorn exists.

This parodies McHugh’s proof. It would seem that a reduction to absurdity is still possible because of the apparent invention of what seem to be fictitious beings allowed by the structure of McHugh’s argument. If his argument “proves” the existence of beings that we’d say do not exist, why should we think that McHugh’s Godlike being exists based on the same type of proof?

Those who use the ontological argument should be reminded that the philosopher Schopenhauer wrote: “Considered by daylight…and without prejudice, this famous Ontological Proof is really a charming joke.” Although McHugh’s version may avoid some standard objections, it seems subject to at least some familiar problems as well as bringing with it problems of its own.


[1] Alvin Plantinga, God, Freedom, and Evil (Grand Rapids, MI: Wm. B. Eerdmans Publishing Co., 1977), pg. 87.

[2] Robert Paul Wolff, About Philosophy (Upper Saddle River, NJ: Prentice-Hall, 1998), pg. 285.

[3] Michael Martin, Atheism: A Philosophical Justification (Philadelphia: Temple University Press, 1990), pg. 89.

[4] R.L. Purtill, “Hartshorne’s Modal Proof,” Journal of Philosophy, 63, 1966, pg. 408. Cited in Martin, pg. 89.

[5] Richard M. Gale, “Negative Statements,” American Philosophical Quarterly, Volume 7, Number 3, 1970, p.215. Cited by McHugh.

[6] Ludwig Wittgenstein, Philosophical Grammar, Rush Rhees, ed., Anthony Kenny, tr. (Berkeley, CA: U. of Cal. Press, 1974), pg. 369.

[7] Here the term “Brahman” is used to refer to the concept in Hinduism of the one supreme, absolute, all-pervading Spirit that is, strictly speaking, “beyond attributes,” as explained in Hindu scriptures. The word with identical spelling is often used to refer to Hindus of the highest of the four varna classes, but that is not the use here.

[8] Pagan proponents include Philo and Plotinus, and Christian advocates include Gregory of Nyssa and Psuedo-Dionysius the Areopagite.

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