Some define atheism in terms of the absence of the belief that God exists. This won't do, obviously, since then we would have to count cabbages and sparkplugs as atheists given the absence in these humble entities of the belief that God exists. But the following could be proffered with some show of plausibility: An atheist is a person whose psychological makeup is such as to permit his standing in the propositional atttude of belief toward the proposition that God exists, but who as a matter of fact does not stand in this relation, nor is disposed to stand in this relation were he to be queried about the existence of God. Note that it does not suffice to say that an atheist is a person in whom the belief that God exists is lacking for then the neonatal and the senile would count as atheists, which is surely a bit of a stretch.
But I now turn to some remarks of David Gordon which I find illuminating and helpful. My comments are in blue. Gordon's remarks are from his review of George H. Smith, Atheism, Ayn Rand, and Other Heresies (The Journal of Libertarian Studies, Fall 1992):
. . . Smith places great stress on the proper definition of atheism. An atheist, in his usage, need not deny that God exists: The absence of belief is sufficient. "An atheist is a person who does not believe in the existence of a god'' (p. 35). The issue to Smith is much more than semantic; he thinks a crucial philosophical issue is at stake. Since an atheist need make no claims about God, it is up to the believer to prove his case. "The theist, or god-believer, asserts the existence of a god and must prove the claim. If the theist fails in this task, reasonable people will reject the belief as groundless" (p. 63).
Yet this will not do, for the following reason. Suppose one defines an "antitheist" as someone who denies that God exists. A theist is then someone who lacks this belief. He need not believe that God exist: He need only fail to have the antitheistic belief that it is not the case that God exists. The burden of proof here is on the antitheist -- the theist is within his intellectual rights in refusing to become an antitheist. If Smith's argument works, so does this one.
Gordon's point is that the atheist cannot shift the burden of proof onto the theist by providing a negative definition of 'atheist' for the simple reason that the theist can avail himself of the very same definitional strategem. He can introduce the term 'antitheist' and then demand that the antitheist -- one who denies that God exists -- prove his antitheistic contention. If the atheist can be defined as one who is devoid of theistic belief, then by parity of reasoning the theist can be defined as one who is devoid of antitheistic belief.
What has happened? I suggest that the statement "S does not believe in God" is ambiguous. It may mean that on the list of all S's beliefs--his "belief set"-- "God exists" is not included. Taken this way, "S does not believe in God makes no substantive claim about God; it instead reveals something about S.
The proposition may, however, he construed differently. In this interpretation, S does have some belief about the existence of God; for example, "God does not exist," or "It is unlikely that God exists." If the proposition is taken this way, then the atheist, just as the theist, has made a claim about the world. To the extent some one who makes an assertion has a burden of proof, he bears it as much as someone who asserts that God exists. Smith's claim of a difference between theist and atheist, as regards the burden of proof, is plausible only if an atheist makes no claim whatever about God. Since he has said nothing about God, he of course has no obligation to prove anything about Him.
Furthermore, as usual in philosophy, there is a complication. A belief that mentions God need not be about Him. Suppose that S has this belief: "I do not know whether God exists." This seems best taken as a claim that S makes about himself. Aside from this and similar examples, however, the point made earlier holds. If an atheist makes a claim about God, he is under no less a burden of proof than the theist. Nothing that has been said so far implies that there is an obligation of proof on either the theist or atheist: The claim made above is that there is no difference in burden of proof.
Smith's definition of atheism will not gain for him the epistemological advantage he wants. But how does it stand strictly as a definition? Here the verdict is mixed. Smith is quite rightly alert to the objection that he has advanced a "stipulative" definition. A stipulative definition deviates from standard usage in order to characterize a concept in a question-begging manner. Many socialists, for example, refuse to count oppressive regimes as truly socialist. By definition, a centrally planned economy will promote liberty; counterexamples have been ruled out by a stroke of the pen.
Gordon tells us that "A stipulative definition deviates from standard usage in order to characterize a concept in a question-begging manner." If Gordon's definition of 'stipulative definition' is purely stipulative, then I cannot argue with him. But I don't think he intends it to be purely stipulative, in which case I beg to differ. One sort of stipulative definition is purely stipulative and involves no deviation from standard usage. Suppose I introduce the common noun 'fred' to cover anything that is both fat and red. I have not deviated from standard usage since there is no usage, standard or otherwise, for 'fred' as a common noun. Another sort of definition is precisifying: it takes a word in ordinary use and attaches a precise meaning to it. 'Valid' and 'sound' are words taken from ordinary English and given precise meanings in logic, meanings which to some extent run athwart the linguistic sensibilities of ordinary people. These precisifying definitions are partly stipulative and partly lexical. And then there are lexical definitions which record how a word is used at a certain time and place by a certain class of people.
My point against Gordon is that, while some stipulative definitions question-beggingly deviate from ordinary usage, some do not deviate from standard usage, and some others, though they deviate from standard usage are not question-begging. I would say that 'atheist' as used by Smith is a precisifying definition which takes a word in ordinary use and gives it a precise meaning. He is free to do that. In an argument with Smith I would give him his use of 'atheist' but then formulate the real question as follows: Is antitheism (as defined by Gordon above) true or not? I would insist that that is the real question since atheism (as the absence in many people of the belief that God exists) is trivially true.
Smith relies on his vast knowledge of the free-thought movement to show that his definition of atheism is not aberrant. Though this is good evidence that his definition is not stipulative, a more important question remains: Is his definition of atheism worthy of adoption? I do not think it is, at least in unmodified form. If someone has never thought at all about God, it seems to me odd to characterize such a person as an atheist. Further, think of someone with this view: "I am not sure whether God exists, but I certainly hope so." It strikes me as quite unusual to term this person an atheist. But both are atheists on Smith's definition.
Suppose, however, that I am mistaken, that Smith's definition of atheism is plausible, and that he is also correct that the theist bears a burden of proof the atheist does not. It is unclear how helpful this is to him, as against his more circumspect atheist colleagues. Smith does deny that God exists: The burden of proof argument will not help him. I wonder why he has made such a fuss about the definition of atheism.