Note: an updated version of this argument is available at here.
It is not uncommon, in interactions with atheists, for an atheist to claim that Christians and atheists aren't that different, for the reason that atheists only believe in one fewer deity than Christians. "We're both atheists with respect to the Homeric gods," the argument goes. This then implies that Christians and atheists are really much the same, except for one small detail - belief in one fewer deity. Perhaps it is even suggested that if the Christian were more consistent with his fundamental atheism, that he would become a full atheist as well. Unfortunately, for the atheist, this line of argumentation is fallacious, as will be demonstrated below.
In making this argument, the atheist is asserting that the atheist and the Christian are fundamentally similar, differing only in a minor detail. The Christian is told: "You're an atheist too. You just believe in one more deity than we do." Thus, atheists and Christians are both atheists, though they differ in the scope of that atheism. The fundamental characteristic that supposedly unites the Christian and the atheist, then, is unbelief in a number of deities. The argument is as follows:
P1. Unbelief in a number of deities is sufficient for fundamental similarity.
P2. Christians have unbelief in a number of deities.
P3. Atheists have unbelief in a number of deities.
P4. Relative to P1, belief in one deity is not sufficient for fundamental dissimilarity.
C1. Therefore, the atheist and the Christian are fundamentally similar.
Problems with the Argument
It should first be noted that P4 is not well-founded. How many deities does one have to believe in, before this becomes sufficient for a fundamental dissimilarity, relative to P1? Two deities? Five? Ten? Hundreds? Thousands? An infinite regress of deities? After all, a believer in the Norse pantheon is an atheist with respect to the Greek pantheon, and vice versa. Is a believer in the Norse pantheon then not so dissimilar from an atheist? Is such a person more dissimilar than a Christian? Is he dissimilar enough to be not fundamentally similar? Where is this boundary to be defined? Even a person who believes in an infinite regress of deities (such as a mormon) would not necessarily believe in the Greek pantheon. Is such a person an atheist with respect to the Greek pantheon? Is such a person fundamentally similar to an atheist? It seems hardly likely that this would be the case, given that such a person would believe in infinitely more gods than the atheist. Of course, an atheist is welcome to try to set a limit on this issue, but it is inconceivable how such a limit would not be purely subjective and arbitrary.
But to the main point, P1 is unacceptable, because it ignores the fundamental reasons as to why an atheist is an atheist, and a Christian a Christian. In general, a principle p is not sufficient for fundamental similarity if there are two other principles, p1 and p2 that are 1) more fundamental than p, 2) different, and 3) both imply p. In this case, the atheist proposes the Numerical Atheism Principle (NAP) as a sufficient criterion for fundamental similarity.
NAP: I do not believe in the existence of a number of given deities.
Of, course, NAP does not eliminate belief in one deity, or a few deities, but only requires that one does not believe in the existence of some number of given deities. Both the atheist and the Christian accept NAP. However, both the atheist and the Christian believe that the sky is blue, and that doesn't make them similar in any relevant ideological sense. NAP is not a sufficient criterion for fundamental similarity because there are two other principles that are more fundamental that explain why the Christian accepts NAP and why the atheist accepts NAP, but also demonstrate a more fundamental difference between the atheist and the Christian. If a more fundamental difference exists that demonstrates why two people believe something similar, then that similarity is not a fundamental similarity, since it is caused by an even more fundamental dissimilarity. These two principles are the General Atheism Principle (GAP) and the Christian Monotheism Principle (CMP).
GAP: I do not believe in the existence of any deity.
CMP: I believe in the existence of the God of the Bible.
Now, it should be evident to all that GAP and CMP are different. Beyond being different, they are categorically different. One is a categorical denial of the existence of any thing that is a deity, while the other is a fundamental commitment to the existence of one such being. The principles can be formally stated as follows, if we take E(x) to mean that "x exists," B(x) to mean "I believe that x" and Deity(x) to mean that "x is known as a deity":
GAP: (∀x)(Deity(x) → ~B(E(x)))
CMP: B(E("The God of the Bible"))
As one can easily see, GAP is a universal principle, whereas CMP is an specific, existential principle. Hence the difference.
To believe in the God of the Bible is to accept the Bible as God's authoritative and true revelation. This revelation states that no other deities besides the God of the Bible exist (e.g. Is. 45:5-6). Hence, the Christian, who holds to CMP (by definition, being a Christian), arrives at NAP. Similarly, the atheist holds to GAP (by definition, being an atheist), and NAP follows naturally from GAP - if one does not believe in the existence of any deities whatsoever, then given some specific deities, one will not believe in their existence.
It is thus obvious that the further suggestion that the Christian is a person who is inconsistent with his fundamental atheism is also thus refuted, since the Christian is not an atheist at all (not holding to GAP, but rather to CMP).
The fundamental error that the atheist makes in this kind of argument is asserting that because both the Christian and the atheist accept NAP, that the Christian and the atheist are fundamentally similar in atheism, differing only in the scope of their respective atheism. This is fallacious, because the Christian and the Atheist arrive at NAP for fundamentally different reasons.