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I assume that there are also several atheists that recognize that their belief that "(2) No {A} does not exist" is based on faith and not logic.
I don't quite agree with this. The absence of evidence for an entity can be evidence for the absence of the entity if there is reason that evidence for its existence should exist if it does exist.
The arguments against atheism is rarely that a god exists, it is that a particular deity exists, and a particular religion is true. The assumptions of a fundamentalist Christian are:
1) A deity exists;
2) This deity has an interest in human affairs;
3) Lack of belief in this deity (or, more specifically, refusal to accept the sacrifice of the Christ for our sins) will result in eternal torment; and
4) This deity is perfectly just.
It is a reasonable assumption, then, that this deity would provide clear, unambiguous evidence that it exists. A portion of Christian apologetics attempts to resolve this, but these arguments are pretty unconvincing; remember, to avoid eternal torment it is not enough for me to say, well, yeah, maybe some god exists -- it is necessary for me to say, yes, the god Yahweh, as described in the Chistian Bible, definitely exists, and His Son came to earth to die for my sins.
For this reason, I maintain that the belief the evangelical Christian god does not exist is entirely reasonable; in fact, I would say that belief in the evangelical Christian god is entirely illogical and unreasonable.
Now, it is true that one can simply discuss the statement "The universe was created by an unimaginably powerful being at some point in the past, for some purpose of its own." If that is the statement, then I agree that this statement, by itself, without any qualifications, is perfectly logical consistent with the data. Although I do not believe the statement is true, I nonetheless cannot disprove it, and I admit that I could possibly be wrong. But I also find such a general statement uninteresting.
Sorry if this isn't exactly what you wanted to discuss.
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