Is a Sound Argument for the Nonexistence of a God Even Possible?* (1998)
Jeffery Jay Lowder
If I were asked to prove that Zeus and Poseidon and Hera and the rest of the Olympians do not exist, I should be at a loss to find conclusive arguments.
-- Bertrand Russell, "What Is an Agnostic?" 1953 
A common objection to atheism -- one stated by many scholars and laymen, theists and nontheists -- is that it is impossible to prove the nonexistence of God. Yet the atheist response to this objection has been virtually non-existent. This response is the purpose of this paper. Whether the atheist has a burden of proof, and whether any arguments for the nonexistence of a god have been successful, are issues beyond the scope of this paper. Rather, I want to examine the mere possibility of a sound argument for the nonexistence of a god, by considering several objections to such an argument. Along the way, I shall argue that such an argument is indeed possible and does not require omniscience.
Objections from the Right
The Unprovability Objection: is it possible to prove a universal negative?
In his book Truth in Religion, Mortimer Adler distinguishes "logical disproof of religious belief" from universal negatives (or what he calls "negative existential propositions"). The former focuses on some proposition that is an "article of faith," a proposition that cannot be proved but can be "disproved by the proof of propositions that are their logical contraries or contradictories." For example, the Islamic belief that the prophet Muhammad received the Koran directly from Allah is classified by Adler as an "article of faith," because it cannot be proven. Yet, according to Adler, a disproof of an article of faith is possible. If a contradictory of an article of faith could be proven, then by the law of noncontradiction the article of faith would be disproven. Adler offers the following example of how an article of faith might be disproven by a contradictory:
It may be useful here to offer an example, in the case of Christianity, of scientific and technological advances that may call an article of faith into question. If the prediction of computer technologists and researchers into artificial intelligence is ever realized -- that machines can be constructed in the future, the behavior of which will be indistinguishable from the behavior of human beings -- then the Christian belief in the immortality of the human soul will be challenged. That belief depends for its rational support on the immateriality of the human intellect.
If purely material machines can do everything the human intellect can do, in a manner that is indistinguishable from the performance of the intellect, then there is no philosophical ground for affirming the immateriality of the intellect.
Yet Adler believes that this sort of disproof can only go so far. According to Adler, a "negative existential proposition," a proposition which "denies the existence of some thing," "cannot be proved." Just exactly why Adler believes this to be so is unclear, for he does not directly defend his claim. Perhaps Adler believes that negative existential propositions are not or cannot be disproven by proving contradictory, positive existential claims (which he admits can be supported "beyond a reasonable doubt"). Yet even William Lane Craig, an outspoken critic of atheism, recognizes that this position is false. According to Craig, the claim that "you can't prove a universal negative" is
false. In the first place, of course you can. For example, you could disprove the statement that "there are polka-dotted geese." That would be a universal negative and you can disprove that. But more importantly, the claim that 'God does not exist' is not a universal negative. It's a singular negative. And certainly you can prove negative singular statements, such as, 'There is no planet between Venus and the Earth.' You can provide arguments to show that a singular negative statement is true.
Indeed, there are actually two ways to prove the nonexistence of something. One way is to prove that it cannot exist because it leads to contradictions (e.g., square circles, married bachelors, etc.). I shall refer to arguments that rely on this method as "incompatible-properties arguments." Because incompatible-properties arguments attempt to demonstrate a logical contradiction in the very concept of the thing in question, incompatible-properties arguments are deductive arguments.
Incompatible-properties arguments can also be applied to states of affairs involving several objects. In other words, it may be logically impossible for two objects to exist simultaneously. For example, some gods cannot coexist with other gods. The god of Islam (Allah) and the god of Christianity (Jehovah), despite their common origin in the god of Judaism (Yahweh), are mutually exclusive. Jehovah and Allah, at least as traditionally understood, cannot both exist at the same time. Both claim to be the Creator of the universe, but they have contradictory attributes (e.g., Christianity claims that there are three "persons" known as God but Islam claims that there is only one). Therefore, Allah and Jehovah cannot both be "God"; at least one cannot exist.
Thus, the Christian theist who makes the positive existential claim that the Christian god exists, is implicitly making the negative existential claim that all gods contradictory to the Christian god do not exist. Similarly, the Islamic theist who makes the positive existential claim that the Islamic god exists is implicitly claiming that all gods contradictory to Allah do not exist. And both the Christian and the Islamic theist presuppose the nonexistence of the god of Deism, an impersonal Creator of the universe.
The other way to prove the nonexistence of something is, in the words of Keith Parsons, "by carefully looking and seeing." The basic idea is that some objects are said to be detectable in some way. Either their existence is directly observable or their existence is not directly observable but the object causes effects which are directly observable. For example, consider the existence of an ordinary rattlesnake. Suppose someone standing next to you claims that a rattlesnake is directly in front of you. You look down and see nothing. In such an instance, it would follow that there is no rattlesnake in front of you. This same method allows us to know that such things as the Loch Ness Monster, Bigfoot, the Abominable Snowman, etc. do not exist. In the context of arguments for the nonexistence of God, I will adopt Theodore Drange's terminology and refer to arguments which rely on this "looking and seeing method" as "God-vs.-world arguments."
But the most decisive refutation of Adler's claim that "negative existential propositions cannot be proven" is the fact that the claim that "negative existential propositions cannot be proven" is itself a negative existential proposition. If negative existential propositions cannot be proven, then that implies there are no proofs for negative existential propositions. But the claim that "there are no proofs for negative existential propositions" is itself a negative existential proposition. Therefore, Adler could never claim to have any proof for his claim that negative existential propositions cannot be proven.
The Omniscience Objection: is it possible to know a universal negative?
Hank Hanegraaff, Ron Rhodes, and Kenneth R. Samples take a slightly different approach. They argue that atheism is unknowable. This is because, in the words of Hanegraaff,
Simply stated, a person would have to be omniscient and omnipresent to be able to say "there is no God" from his own pool of knowledge. Only someone capable of being in all places at the same time -- with a perfect knowledge of all that is in the universe -- can make such a statement based on the facts. In other words, a person would have to be God to say there is no God. Hence, the assertion is logically indefensible.
Yet it is not clear why the person who asserts that a particular god does not exist must be "capable of being in all places at the same time -- with a perfect knowledge of all that is in the universe." To be sure, theists who make the claim that "a specific god exists" do not feel that they must be omniscient and omnipresent. So why must the atheist be omniscient and omnipresent in order to affirm the opposite conclusion? Ron Rhodes has an answer to this question. He writes:
This point can be forcefully emphasized by asking the atheist if he has ever visited the Library of Congress in Washington D.C. Mention that the library presently contains over 70 million items (books, magazines, journals, etc.). Also point out that hundreds of thousands of these were written by scholars and specialists in the various academic fields. Then ask the following question: "What percentage of the collective knowledge recorded in the volumes in this library would you say are within your own pool of knowledge and experience?" The atheist will likely respond, "I don't know. I guess a fraction of one percent." You can then ask: "Do you think it is logically possible that God may exist in the 99.9 percent that is outside your pool of knowledge and experience?" Even if the atheist refuses to admit the possibility, you have made your point and he knows it.
Of course, in response, the atheist could simply ask the theist, "Do you think it is logically possible that a knock-down, deductive disproof of your god may exist in the 99.9 percent that is outside your pool of knowledge and experience?" If the theist replies, "Yes, it is possible that there is such a disproof", then on Rhodes' reasoning the theist should not claim to know that God exists. If, however, the theist answers, "No, it is not possible that there is such a disproof," then the theist apparently thinks she can know a negative existential proposition to be true without being omniscient.
Even in Rhodes' scenario, all that is necessary is that a particular god's existence logically imply something that we know is false within the .1% of knowledge that Rhodes says we have. It then logically follows -- we have a deductive proof -- that that particular god does not exist. If Rhodes is going to claim that all propositions having any kind of deductive relationship to "god exists" are outside of what we know, then Rhodes has the burden of proof to show that.
Indeed, many theological statements entail negative existential propositions, yet I doubt that many theists would claim they are omniscient:
Similarly, all of the theistic arguments for the existence of God assume negative existential propositions. For example:
Finally, certain theological doctrines entail negative existential propositions. For example:
The General Considerations Objection: what would we have to know about an object to prove its existence or nonexistence?
A final objection from the right to the possibility of an atheological proof perhaps may be found in Dallas Willard's commentary on the debate between J.P. Moreland and Kai Nielsen. I emphasize the word "perhaps" because it is unclear whether Willard is arguing that atheistic arguments are inherently more difficult to prove than theistic arguments in light of their negative existential status; Willard may believe that atheistic and theistic arguments are on equal footing in terms of what they must accomplish in order to be successful. Here is what Willard writes:
["There is no God"] is a negative existential, and looking for God here or there, finding or proving this not to be God and that not to be God, does nothing to budge it one bit toward or away from the status of knowledge or even of justified belief. To make any headway at all with the atheist's project, we will have to settle on some general considerations that will provide a structure within which particular facts may evidentially count for something. For example, take the general consideration that if God exists, suffering will not be allowed. Given this, the particular fact of this child being sexually abused by a drunken relative gains evidential significance for the existence or nonexistence of God. But then, of course, we have the task of securing the truth of this particular general consideration. A notoriously difficult undertaking!
This, of course, is perfectly compatible with my earlier observation that there are two ways to prove something does not exist: one way is to demonstrate a logical contradiction and the other way is to simply look and see. Willard's "general considerations" are simply an analysis of the attributes of the object in question, and that is a prerequisite for both negative and positive existentials. We must have an adequate understanding of what an object's existence entails before we can argue for or against its existence. Positive existentials do not have an advantage over negative existentials in this sense. In other words, we must have an understanding of the nature of a god before we can determine whether that god exists.
Willard suggests that "securing the truth" of his particular example of a general consideration, "that if God exists, suffering will not be allowed," will be "notoriously difficult." Now I would certainly join Willard in rejecting that particular consideration, for even theism is compatible with some suffering. But I would also suggest that there is some suffering -- namely, pointless suffering -- which is incompatible with theism. So let us consider a slightly modified version of Willard's example, "the general consideration that if God exists, no pointless suffering will be allowed." I think this consideration is fairly uncontroversial. I therefore conclude that there is at least one such consideration -- agreed upon by both theists and atheists -- which demonstrates the possibility of an atheological argument.
Moreover, with respect to the existence of a particular god, there is a sense in which negative existentials have an advantage over positive existentials. According to the principle of indifference, when we don't have any evidence favoring any of a set of alternatives over the others, we should count each alternative equally likely. Since there is literally an infinite number of logically possible gods, the prior probability of any individual god existing is very small. I shall have more to say about the significance of this fact later on in this essay.
Objections from the Left
The Noncognitivity Objection: is the concept of "God" factually meaningless?
Some writers have suggested that religious language (including God-talk) is factually meaningless. If their claim is correct, then by definition the statement, "God does not exist", would be neither true nor false. Therefore, if God-talk is factually meaningless, a sound argument for the nonexistence of God would be impossible. Following Theodore Drange's terminology, I shall refer to this objection as the "Noncognitivity Objection".
In order to understand this objection, consider the following proposition:
(1) God exists.
According to the noncognitivist, (1) is neither true nor false because there is no evidence that would count for or against it.
Now, without a clarification of the concept of "God" being used in (1), I am willing to grant that it might initially be unclear what sort of evidence would count for or against (1). I agree that certain types of God-talk are difficult to understand, if not just pure gibberish. And I might even be willing to go along with the claim that the concept of theism in general is vague, slippery, and possibly meaningless. But other statements that contain the word "God" seem quite meaningful to me. Consider, for example, the following claim:
(1') There exists a being called God whose properties include:
I have absolutely no problem whatsoever imagining evidence that would count for or against (1'), and therefore conclude that (1') is a factually meaningful statement. But what about other conceptions of "God" than the one considered in (1')? The factual meaningfulness of a God-concept must be evaluated on a case by case basis. While I think the majority of God-concepts (including those embraced by the major world religions) are factually meaningful, I allow for the possibility that some God-concepts may be factually meaningless. Yet even if some God-concepts turn out to be factually meaningless, that fact would have no bearing on the other God-concepts which are factually meaningful.
The Deductive Argument Objection: Must an atheological argument be deductive?
Yet another objection to the possibility of a sound argument for the nonexistence of a god can be found in the writings of Bertrand Russell. In order to understand the basis for Russell's objection, we must first understand how Russell defined the terms 'atheist' and 'agnostic':
An atheist, like a Christian, holds that we can know whether or not there is a God. The Christian holds that we can know there is a God; the atheist, that we can know there is not. The Agnostic suspends judgment, saying that there are not sufficient grounds either for affirmation or for denial. At the same time, an Agnostic may hold that the existence of God, though not impossible, is very improbable; he may even hold it so improbable that it is not worth considering in practice. In that case, he is not far removed from atheism.
On Russell's view, while the agnostic is a person who holds that the existence of a god "is so improbable that it is not worth considering in practice" is "not far removed" from the atheist who holds that we can know that god does not exist, apparently they are removed far enough for Russell to insist upon the distinction. Yet what is the distinction in question here? If the agnostic who holds that the existence of a god "is so improbable that it is not worth considering in practice" is not an atheist, then, on Russell's view, the atheist who holds that that same god does not exist must have a deductive proof for the nonexistence of that god.
But why must the person who claims that a specific god does not exist be able to prove so deductively? Russell never says. And there is good reason to reject Russell's view. Inductive arguments form the basis for many of our beliefs, such as the belief, "The sun will rise tomorrow." Moreover, there is nothing inherent in the concept of a god that somehow makes it inappropriate to form probabilistic conclusions about the existence of that god, in the light of all the available evidence. Moreover, what Russell wrote elsewhere seems to contradict his position:
None of us would seriously consider the possibility that all the gods of Homer really exist, and yet if you were to set to work to give a logical demonstration that Zeus, Hera, Poseidon, and the rest of them did not exist you would find it an awful job. You could not get such proof.
Yet Russell does not state that he is "agnostic" concerning the existence of such a deductive proof; rather, he knows "you could not get such proof" even though he does not prove so deductively. Granted, there may be no way to *deductively) disprove certain interpretations of the Greek gods, if they are defined so that there are no contradictions either internally or with the observable world. But other possible gods are falsifiable. They have self-contradictory properties or logically entail empirical data other than what we in fact see, and Russell never demonstrates the impossibility of disproving those gods. The possibility of a logical disproof of one particular god does not depend upon the success of a logical disproof of another god.
The Prior Probability Objection: if the existence of an object has a low prior probability, can that fact alone be used to prove the nonexistence of the objection in question?
My friend and colleague Rich Daniel has objected to my position on entirely different grounds. Daniel agrees with me that negative existential propositions can be proved using one of the two methods I mentioned at the beginning of my paper. Yet, Daniel argues, I have missed a third method of proving a negative existential proposition:
For example, consider the hypothetical god X: Most of the time the universe (which X created) runs according to physical laws that X invented, but X gets to interfere exactly 3,141,592,654 times. Cosmic forces beyond X's control limit the number of miracles.
Now clearly there is nothing about the number 3,141,592,654 that makes it more probable than 0, or 1, or 2, or a very large number of other numbers. So even though X is unfalsifiable by Jeff's definition, the probability of X's existence is very low. At least one valid kind of argument is missing from his list.
What are we to make of hypothetical god X? Before considering Daniel's proposed atheological argument, let's first run through the two types of arguments for the nonexistence of a god I described earlier. The concept seems coherent; I don't see how the idea of god X leads to self-contradictions. What about a God-vs.-world argument? If the existence of X entails that human beings should be able to observe at least one of the 3,141,592,654 miracles in their lifetime and no human so far has observed a miracle, then that fact would constitute evidence against X. But if the existence of X does not entail such public miracles, then the "looking and seeing" method cannot be used to prove the nonexistence of X. In that situation, I claim that there is no way to prove the nonexistence of X.
Let "Y" refer to the number of times god X gets to interfere with physical laws. According to Daniel, the probability that Y equal 3,141,592,654 is low. After all, what's so special about the number 3,141,592,654? The value of Y could have been any number. Whatever the value of Y, we have no reason to expect that value over any other possible value. Thus, if we assume that all possible values of Y are equally likely, the likelihood that Y would be equal to any particular value is extremely low indeed. Call this likelihood the "prior probability of Y".
But does the nonexistence of X follow from the low prior probability of Y? I can't think of any reason why it would. On the hypothesis that god X actually exists, we would expect exactly the state of affairs which Daniel describes. If god X actually existed, we would expect there to be nothing special about the number 3,141,592,654 -- the value of Y would be unlikely -- even though god X existed. The fact that an object has a low prior probability, by itself, neither entails nor makes probable the non-existence of that object.
Nonetheless, I do think Daniel is onto something. If a claim has a low prior probability, the standard of evidence we would normally require before accepting that claim is increased. For example, consider the following two claims:
(2) I drove to work today.
(3) I flew to work today by flapping my arms quickly.
I suspect that most people would not even think twice before believing (2). The notion of someone driving to work is an everyday occurrence; the idea that I might be such a person is not should not be in any way surprising (assuming I am employed, can afford my own vehicle, etc.). Therefore, most people would probably accept (2) at face value; they would not demand proof of (2) beyond my claim that (2) is true.
But what about (3)? As far as I can tell, (3) is a coherent statement. Yet there is nothing in human experience to suggest that I, much less any other human being, is capable of self-sustained flight through the air. Therefore, on the basis of prior probability alone, rational people would rightfully demand evidence (beyond my word) for the truth of (3) before they believed me. The initial improbability of a claim does not constitute evidence against the claim; rather, it increases the standard of evidence by which the claim could be shown to be true.
The Presumption of Nonexistence Objection: is there a presumption of nonexistence?
Some writers have suggested a methodological principle which works as follows: the burden of proof is always on the one who claims the existence of something and if that burden is not fulfilled then it is reasonable to claim that the thing in question does not exist. Is this methodology an additional "method" for proving the nonexistence of something?
I don't think so. In the first place, proponents of this methodology argue that despite the lack of evidence for the nonexistence of the thing in question, we should just assume the thing does not exist. This is not an argument for the nonexistence of the thing in question. One might even argue that this methodology violates the principle, "Proportion your beliefs to the evidence."
Second, those who argue for a presumption of nonexistence do so on the basis that negative existential claims cannot be proven. If, as I have argued in this essay, that assumption turns out to be false, then there is no reason to adopt such a methodology.
Third, I agree with Theodore M. Drange who points out that this sort of methodology is not employed in science:
The main drawback to such a line of thought is that there is no good support for the methodological principle in question. It is not a principle observed in scientific research. For example, scientists do not deny the existence of, say, tachyons (faster-than-light particles) simply because no good evidence has been produced that they exist. And the same is true for other entities postulated in other hypotheses. Scientists do not reason to the nonexistence of the postulated entity merely from the current absence of positive evidence for its existence. The burden-of-proof principle is therefore not one employed in the sciences.
As Drange writes, "Certainly things may exist even if there is currently no good evidence for their existence. In order for it to be reasonable to deny a thing's existence [on the basis of lack of evidence], there needs to be some reason to think that if it were to exist, then by now we would have found good evidence of that fact." But that is my second method for proving the nonexistence of something. I therefore conclude there is no reason for a presumption of nonexistence to govern debates on whether a thing exists. In the absence of evidence for and against the existence of something, we should suspend judgment.
A sound argument for the nonexistence of a god is possible, if the concept of "God" in question is factually meaningful. I think this conclusion is one which even many theists should be willing to accept. After all, the mere possibility of a sound argument for the nonexistence of a god is logically compatible with theism; what theism requires is that there actually are no sound arguments for the nonexistence of God.
* This is the third edition of this essay.
I am grateful to Jim Lippard, Mark Vuletic, Michael Martin, Theodore Drange, David McFadzean, Bill Schultz, and Rich Daniel for suggestions which improved this essay.
 Only a couple of atheists have directly responded to this objection. See Mark Vuletic, "Is Atheism Logical?" (</library/modern/mark_vuletic/logical.html>, 1996) and Douglas M. Krueger, What Is Atheism? (Buffalo, NY: Prometheus, 1998).
I suppose that it might be objected that anyone who has published an argument for the nonexistence of a god has implicitly refuted the objection that such an argument is impossible. This is true, to the extent that such arguments are sound arguments. But the atheist response to the objection that "it is impossible to prove the nonexistence of God" need not depend on the soundness of such arguments. Even if all arguments for the nonexistence of gods failed, that would still not prove the impossibility of a sound argument for the nonexistence of a god.
 Methodological atheists, in contrast to metaphysical atheists, do not necessarily hold the positive belief that a particular god does not exist. A methodological atheist is simply a person who acts as if a god does not exist.
 On the former, see "Does the Atheist Bear a Burden of Proof? A Reply to Prof. Ralph McInerny" (<URL:/library/modern/keith_parsons/mcinerny.html>, 1997), and God and the Burden of Proof (Buffalo, NY: Prometheus, 1989), both by Keith M. Parsons. As for the latter, atheist philosophers are contributing a growing number of books and articles on atheological arguments. See Jeffery Jay Lowder (ed.), "Arguments for Atheism", The Secular Web, /library/modern/nontheism/atheism/arguments.html.
 Adler 1990, pp. 31-32.
 William Lane Craig in William Lane Craig and Frank Zindler, Atheism vs. Christianity: Where Does the Evidence Point?, cassette recording of a debate held on June 27, 1993 at Willow Creek Community Church, South Barrington, IL.
 To be precise, it is quite easy to prove that two-dimensional "square circles" cannot exist. In contrast, as Richard Swinburne points out, proving the coherence of any proposition is very difficult because there always remains the possibility that an actual contradiction has not yet been discovered. See Richard Swinburne, The Coherence of Theism (revised ed., New York: Oxford University Press, 1993), pp. 38-49.
 Drange 1998, p. 22.
 Parsons 1989, p. 25.
 Drange 1988.
 Hank Hanegraaff, "The Folly of Denying God" Christian Research Newsletter (<URL:http://iclnet93.iclnet.org/pub/resources/text/cri/cri-nwsl/crn0028a.txt>, 1990); Ron Rhodes, "Strategies for Dialoguing with Atheists" (<URL:http://home.earthlink.net/~ronrhodes/Atheism.html>, 1989); and Kenneth R. Samples, "Putting The Atheist on The Defensive" Christian Research Journal (<URL:http://www.iclnet.org/pub/resources/text/cri/cri-jrnl/crj0131a.txt>, 1992).
 Hanegraaff. Michael Martin, following the lead of Roland Puccetti, has developed an incoherence argument called "the argument from unrestricted existential statements" which attempts to demonstrate the incoherence of gods which purportedly have all factual knowledge. Martin argues that negative existential propositions are unknowable if they are completely unrestricted. See Martin, pp. 294-295.
 Rhodes 1989.
 I am grateful to Jim Lippard for this argument.
 According to the late Greg Bahnsen, "The claim of the presuppositionalist is there is no atheist in the world. There are people who profess atheism." See Bahnsen, Michael Martin Under the Microscope tape 1, (Nash, TX: Covenant Tape Ministry, n.d.), audiocassette. For a refutation of this argument, see Michael Martin, "Are There Really No Atheists?" (<URL:/library/modern/michael_martin/no_atheists.html>, 1996).
 Theodore Drange 1998, p. 74.
 Martin 1990, p. 47.
 Russell 1961, p. 577.
 See Michael Martin, The Big Domino in the Sky and Other Atheistic Tales (Buffalo, NY: Prometheus, 1996), pp. 48-49.
 If Russell feels that he can know such a thing without deductive proof, then he cannot consistently insist that the atheist must have a deductive proof in order to know that a specific god does not exist.
 Rich Daniel, "Other Ways to Disprove Specific Gods" (<URL:http://www.dnaco.net/~rwdaniel/other_disproofs.html>, 1998).
 Drange 1998.
"Is a Sound Argument for the Nonexistence of a God Even Possible?" is copyright © 1998 by Jeffery Jay Lowder.
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