On a New Argument for Agnosticism (2001)
In a recent Internet paper entitled "A Formal Justification of Agnosticism," Bill Schultz defends agnosticism by denying the universality of the Principle of Excluded Middle (P v ~P). In addition, he accuses me of using the Principle of Excluded Middle to try to "force agnostics into the atheists camp (p.5)." In this paper I argue that Schultz misunderstands my position and atheistic arguments in general. Furthermore, I maintain that his argument for agnosticism is weak.
Schultz's Characterization of the Atheistic Argument Against Agnosticism
According to Schultz:
The usual argument used by atheists to attempt to convince a nonatheist and nontheists to convert to atheism is that there are only two alternatives, either you believe that God exists or do not believe that God exists. If you believe that God exists, you are theist, and in the alternative, if you not believe that God exists, you are an atheist. The atheist assumes that those the only two options, and will sometimes badger an agnostic until and unless they assert their willingness to convert to atheism (p.1)
But what atheists argue in this way? Certainly I do not. Schultz seems to have confused epistemology and metaphysics. First of all, there is the metaphysical issue of possible states of the world. There is the possible state that God exists and the possible state that God does not exist. It is true that atheists believe either God exists or God does not exist. But so do most agnostics. Second, there is the epistemological issue: Are there good grounds to believe that God does not exist? Atheists answer in the affirmative. But agnostics answer in the negative. The issue between atheists and agnostics is not over whether it is true that either God exists or God does not but whether or not arguments such as those developed in Part 2 of Atheism are sound. In this part of my book I argue that there are good reasons for disbelieving in God.
Moreover, atheists need not maintain the claim that the Principle of Excluded Middle of classic logic is universally true. Of course, they need to maintain the much narrower logical thesis that either God exists or God does not exist. But their main point is epistemological--not logical. They must show that there is no good reason to believe God does exist and good reason to believe that He does not. Conversely, agnostics need not hold that the Principle of Excluded Middle is not universally true. They need only establish the epistemological thesis that there are no good grounds for believing that God does not exist. This combined with the establishing that the epistemological thesis that there are no good grounds for believing that God does exist--a thesis maintained by both atheists and agnostics--would establish agnosticism.
Schultz's Argument For Agnosticism
It is clear from the above that Schultz cannot argue for agnosticism by showing that the Principle of Excluded Middle is not universally true. Thus, even if the Principle of Excluded Middle must be given up in the context of subatomic physics this shows nothing about its applicability in the context of theology.
Moreover, Schultz cannot argue, as he seems to at times, that "any indeterminacy (p. 4)" is incompatible with the universal applicability of classical logic. There is after all epistemological indeterminacy, which is compatible with the metaphysical determinacy assumed by the Principle of Excluded Middle.
What then is Schultz's position? At times he seems to maintain that the Principle of Excluded Middle fails when the "underlying facts are unobserved (p. 5)." But this is highly implausible. At the present time extraterrestrial intelligent life has not been observed in the Universe but it would be absurd to deny that either there is such life or there is not. Suppose in the year 2101 extraterrestrial intelligent life was observed and on the basis of this new evidence that there was reason to think that this life was not new but had existed for thousands of years. Then we would have the following absurdity. In 2101 the statement "Extraterrestrial intelligent life existed in 1901" had a truth-value. But in 2001 the statement "Extraterrestrial intelligent life existed in 1901" had no truth-value. But how could this be? Surely, the plausible thing to say would be that in both 2001 and 2101 the statement has a truth-value but in 2101 we found out what this truth-value is. Before 2101 we did not know.
At other places in his paper Schultz's words suggests a more plausible position, namely, that that the Principle of Excluded Middle only holds for states that could possibly be experienced. Since it is possible in principle to observe extraterrestrial life the Principle of Excluded Middle does not fail in such a case. There are two questions that should be asked about this more plausible construal. First, is it too narrow? Second, does it show that the Principle of Excluded Middle fails in the case of God's existence?
First, there are many mathematical statements that describe states of affairs that are not in any obvious sense observable even in principle. To be sure, they are capable of a priori proof or disproof but this proof or disproof has nothing to with empirical evidence. But the Principle of Excluded Middle does not fail in these cases. I have argued that the same thing is true in theology. In Chapter 12 of Atheism I argued that there are many a priori disproofs of God, that is, disproofs that show that the concept of the theistic God is inconsistent. The Principle of Excluded Middle does not fail in such cases either. So Schultz's stipulation is too narrow.
But let us confine our questions to possible empirical evidence: Why does Schultz believe that the Principle of Excluded Middle when it is restricted in the way he suggests does not apply to God? Surely it begs the question to suppose that there can be no empirical evidence that is relevant to God's existence. Is it really so obvious that the statement that "God exists" is not disconfirmable by empirical evidence? To suppose that this statement is not disconfirmable must be shown by argument and not merely assumed. Indeed, atheists have argued that not only is the statement "God exists" disconfirmable, it has been disconfirmed. From the Argument from Evil to Ted Drange's Argument from Nonbelief to my Atheistic Teleological Arguments (Atheism, Chap. 13) atheists have used empirical evidence to argue that disbelieving in God is justified. To be sure, this disconfirmation is indirect and inferential. But Schultz seems to allow for this (pp. 4-5). So even granted the constraints Schultz requires for the application of the Principle of Excluded Middle agnosticism cannot be justified by his argument.
I have argued that Schultz has seriously misunderstood the import of atheists' arguments in general and my position in particular and his argument for agnosticism is weak. This does not mean that atheism is established or that agnosticism is refuted. But it does suggest that the tack of defending agnosticism against atheism via the alleged failure of the Principle of Excluded Middle is not a fruitful one.
 Bill Schultz, "A Formal Justification of Agnosticism," (2001), </library/modern/bill_schultz/justified.html>, spotted August 27, 2001.
 The Principle of Excluded Middle should be distinguished in many contexts from the Principle of Bivalence. In the context of the present discussion it is unclear whether making this distinction would serve any useful purpose. See Robert Audi, The Cambridge Dictionary of Philosophy, Second Edition. (Cambridge University Press, 1999), pp.737-738.
 To be sure, some intuitionist philosophers of mathematics have argued that the Principle of Excluded Middle does fail in certain areas of mathematics and argued that it holds only for mathematical statements capable of constructive proofs. See Stephen F. Barker, Philosophy of Mathematics (Prentice Hall, 1964) pp. 72-78. However, constructive proofs are far from being based on empirical evidence. In any case, intuitionism in mathematics is a very controversial position.