First of all, how does an atheist deny the existence of God? Well, he might just assertively utter
1. God does not exist.
But suppose our atheist is also a direct reference theorist, one who holds that the reference of a name is not routed through sense or mediated by a Russellian definite description that gives the sense of the name. The direct reference theorist denies the following tenet of (some) descriptivists:
The referent of a name N is whatever entity, if any, that satisfies or fits the descriptive content associated with N in the mind of the speaker of N.
For example, on the descriptivist approach there is associated with the name 'God' a certain concept in the mind of the person who uses the name, a concept which includes various subconcepts (immaterial, unchanging, omnibenevolent, etc.). The name has a referent only if this concept is instantiated. Further, nothing having a property inconsistent with this concept can be the referent of the name. Now if our atheist were a descriptivist, his denial of the existence of God could be expressed by an assertive utterance of
2. The concept of an immaterial, omniqualified, etc. being is not instantiated.
Clearly, if one's denial of the existence of God is to be true, the existence of God cannot be a presupposition of one's denial, as (1) seems to suggest; so (2) seems to be a well-nigh mandatory rewrite of (1) that avoids this well-known difficulty pertaining to negative existentials. Whether or not God exists, the concept God exists, and is available to be the subject of judgments. We cannot say of God that he does not exist without presupposing what we aim to deny; but we can say of the concept God that it is not instantiated.
But our atheist is a direct reference theorist, and so cannot avail himself of (2). He cannot say that the nonexistence of God is the noninstantiation of a certain concept. This is because the direct reference theory implies that the referent of a name can exist whether or not it instantiates any of the concepts associated with the use of the name. The theory implies that 'Socrates' names Socrates even if it should turn out to be false that Socrates was the teacher of Plato, the wife of the shrewish Xanthhippe, snubnosed, a stone-cutter by trade, etc., etc.
On the direct reference theory, for 'God' to have a referent it suffices that (i) there be an initial baptism of some being as 'God,' (ii) there be an historical chain whereby this name gets passed down to the present user; (iii) each user in the chain have the intention of using the name with the same reference as the one from whom he received it. Thus it is not necessary that the referent of 'God' fit any concept of God that the end-user might have.
Now the direct reference theory has an advantage I have already noted. It allows a Jew, a Christian, and a Muslim to be referring to the same being when they utter sentences containing 'God' despite the fact that their conceptions of God are quite different.
How then does the direct reference theorist deny the existence of God? Since his denial cannot be about a concept of God, it must be about the transmission of word 'God' anits equivalents in other languages. He must deny that the name 'God' was ever introduced in an initial baptism; or he must deny that the historical chain is unbroken; or he must deny that all the various users had the intention of using the name with the reference of the one from whom they received it.
But how can the nonexistence/existence of God hinge on such linguistic and historical facts? The nonexistence of God, if a fact, is an objective fact: it has nothing to do with the nonexistence of some initial baptism ceremony, or some break in a link of name transmission, or some failure of intention on the part of the name-users.
More fundamentally, is it not just absurd to hold, as direct reference theorists seems to hold, that it is not necessary that the referent of 'God' fit ANY concept of God that the end-user might have? For that seems to imply that anything could be God. Could God be Abraham's fear during a lightning storm on a high mountain? Obviously not. Why not? Because 'God' used intelligently encapsulates a certain descriptive content or sense that constrains what can count as God.
What am I failing to understand?