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Is a Proof of the Non-Existence 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 [1]
A common objection to atheism -- one stated by many scholars and laymen, theists and nontheists -- is that it is impossible to prove the non-existence of God. Yet the atheist response to this objection has been virtually non-existent.[2] This response is the purpose of this paper. Whether it is the responsibility of the methodological atheist to prove metaphysical atheism[3], and whether any atheists have actually proven the non-existence of any gods, are issues beyond the scope of this paper.[4] Rather, I want to examine the mere possibility of an atheological proof. I shall argue that there is no a priori reason why the disproof of a specific god is impossible.
Mortimer Adler
In his recent book Truth in Religion, Mortimer Adler distinguishes "logical disproof of religious belief" from universal negatives (or what he calls "negative existential propositions").[5] 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.[6]
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 this position is false, for there are actually two ways to prove the non-existence of something. One way is to prove that it cannot exist because it leads to contradictions (e.g., square circles[7], married bachelors, etc.). The other way is, in the words of Keith Parsons, "by carefully looking and seeing."[8] This is how we can know that such things as the Loch Ness Monster, Bigfoot, the Abimonable Snowman, etc. do not exist.
Using the first method, we learn that the existence of one possible god may entail the non-existence of one or more other possible 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).
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 non-existence of the god of Deism, an impersonal Creator of the universe.
Indeed, all of the theistic arguments for the existence of God have equivalent, negative existential propositions. For example:
The ontological argument is equivalent to the proposition, "There is no being greater than the greatest being."
The cosmological argument is equivalent to the proposition, "There is no thing that came from nothing."
The teleological argument is equivalent to the proposition, "There is no naturalistic origin for the design and order of the universe."
The transcendental argument is equivalent to the proposition, "There is no atheist in the world."[9]
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. I therefore conclude that Adler's a priori objection to negative existential propositions fails.
Hank Hanegraaff, Ron Rhodes, and Kenneth R. Samples
Hank Hanegraaff, Ron Rhodes, and Kenneth R. Samples take a slightly different approach.[10] 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.[11]
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.[12]
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 atheist is "dogmatic" for claiming that a god does not exist, is the theist also dogmatic for claiming that a god does exist? Of course not. 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.[13]
Bertrand Russell
Yet another objection to the possibility of an atheological proof 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.[14]
On Russell's view, while the agnostic 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 non-existence 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. 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.[15] 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.[16]
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.[17] Granted, there may be no way to 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.
Dallas Willard
A final objection 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![18]
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.
To put it another way, Willard's "general considerations" are the prerequisites 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.
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. Recent theistic scholarship on the argument from evil has not even questioned this consideration, much less deny it.[19] 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.[20]
Conclusion
In this paper, I have emphasized the possibility of disproving specific gods. I suspect that many people are under the false impression that the atheist is under some fictitious obligation to prove the non-existence of all possible gods in a single argument, in turn probably because many people conflate atheism with materialism.[21] I would be the first person to grant that there is probably not a single argument which proves the non-existence of all logically possible gods. But the existence of such an argument is not what the theism vs. atheism debate is all about. Rather, the issue is which, if any, logically possible gods exist. While some possible gods (e.g., the Greek Pantheon) do appear to be unfalsifiable, there does not appear to be any a priori reason why other possible gods cannot be disproved.
Acknowledgments
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.
Notes
[1] Bertrand Russell, "What Is an Agnostic?" The Basic Writings of Bertrand Russell (ed. Robert E. Egner and Lester E. Denonn, New York: Touchstone, 1961), p. 577.
[2] To my mind, the only atheist who has directly responded to this objection is Mark Vuletic. See his essay, "Is Atheism Logical?" (
http://www.infidels.org/library/modern/mark_vuletic/logical.html , 1996).
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 non-existence of God" need not depend on the soundness of such arguments. Even if all arguments for the non-existence of gods failed, that would still not prove the impossibility of a sound argument for the non-existence of a god.
[3] 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.
[4] On the former, see "Does the Atheist Bear a Burden of Proof? A Reply to Prof. Ralph McInerny" (
http://www.infidels.org/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. These arguments include divine incoherence arguments (see Michael Martin, Atheism: A Philosophical Justification [Philadelphia: Temple University Press, 1990], pp. 286-316), the atheistic teleological argument (Martin, pp. 317-333), the atheistic cosmological argument (see Quentin Smith, "Atheism, Theism, and Big Bang Cosmology" Theism, Atheism, and Big Bang Cosmology [by William Lane Craig and Quentin Smith, New York: Oxford University Press, pp. 195- 217]), the evidential argument from evil (see esp. The Evidential Argument from Evil [Ed. Daniel Howard-Snyder, Indianapolis, IN: Indiana University Press, 1996]), the transcendental argument for the non-existence of God (see Michael Martin, "The Transcendental Argument for the Non-Existence of God"
http://www.infidels.org/library/modern/michael_martin/martin-frame/tang.html , 1997), and the argument from nonbelief (see Theodore Drange, "The Arguments from Evil and Nonbelief" [
http://www.infidels.org/library/modern/theodore_drange/aeanb.html , 1996] and Nonbelief and Evil [Buffalo, NY: Prometheus, forthcoming]).
[5] Mortimer Adler, Truth in Religion (New York: Macmillan, 1990), p. 36.
[6] Adler, pp. 31-32.
[7] 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.
[8] Parsons 1989, p. 25.
[9] 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?" (
http://www.infidels.org/library/modern/michael_martin/no_atheists.html , 1996).
[10] Hank Hanegraaff, "The Folly of Denying God" Christian Research Newsletter (
http://iclnet93.iclnet.org/pub/resources/text/cri/cri-nwsl/crn0028a.txt , 1990); Ron Rhodes, "Strategies for Dialoguing with Atheists" (
http://home.earthlink.net/~ronrhodes/Atheism.html , 1989); and Kenneth R. Samples, "Putting The Atheist on The Defensive" Christian Research Journal (
http://www.iclnet.org/pub/resources/text/cri/cri-jrnl/crj0131a.txt , 1992).
[11] 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.
[12] Rhodes.
[13] I am grateful to Jim Lippard for this argument.
[14] Russell, p. 577.
[15] See Michael Martin, The Big Domino in the Sky and Other Atheistic Tales (Buffalo, NY: Prometheus, 1996), pp. 48-49.
[16] Bertrand Russell, "Am I an Atheist or an Agnostic?" Bertrand Russell on God and Religion (ed. Al Seckel, Buffalo, NY: Prometheus, 1986), p. 85. Italics are mine.
[17] 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.
[18] Dallas Willard, "Language, Being, God, & the Three Stages of Theistic Evidence" in J.P. Moreland and Kai Nielsen, Does God Exist? (Buffalo, NY: Prometheus, 1991), p. 198. Boldface mine.
[19] Instead, theists deny the existence of any actually pointless suffering. See Howard-Snyder, 1996.
[20] A point of clarification is in order. It is not necessarily true that the low prior probability of a particular god existing constitutes an argument for the non-existence of a particular god. There are certain gods -- what we might call "hidden" gods -- whose existence would entail the state of affairs in which their prior probability is low and in which there is no evidence of their existence. To use prior probability to prove the non-existence of those gods would be logically fallacious.
[21] Michael Martin, "Opening Statement by Michael Martin" The Fernandes-Martin Debate (
http://www.infidels.org/library/modern/michael_martin/fernandes-martin/martin1.html, 1997).
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"Is a Proof of the Non-Existence of a God Even Possible?" is copyright © 1998 by Jeffery Jay Lowder.
The electronic version is copyright © 1998 Internet Infidels with the written permission of Jeffery Jay Lowder.
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