In 1948, BBC radio aired a debate between Lord Bertrand Russell and Father Frederick Coppleston on the existence of God. Russell points out the problem with Coppleston's notion of a necessary being (God):
Russell: "...I think that, perhaps, in answering your argument, the best point with which to begin is the question of a Necessary Being. The word "necessary" I should maintain, can only be applied significantly to propositions. And, in fact, only to such as are analytic -- that is to say -- such as it is self-contradictory to deny. I could only admit a Necessary Being if there were a being whose existence it is self-contradictory to deny. I should like to know whether you would accept Leibniz's division of propositions into truths of reason and truths of fact. The former -- the truths of reason -- being necessary. [continued]...I will say that what you have been saying brings it seems to me, to the Ontological Argument that there is a being whose essence involves existence, so that his existence is analytic. That seems to me to be impossible, and it raises, of course, the question what one means by existence, and as to this, I think a subject named can never be significantly said to exist but only a subject described. And that existence, in fact, quite definitely is not a predicate."
You can find the complete transcript here: http://www.bringyou.to/apologetics/p20.htm
What does it mean to say that a proposition is analytic? There are classically two salient categories of proposition in logic: analytic and synthetic. The distinction is an important one. Analytic statements are true by definition, the predicate is embedded in the subject. This includes mathematical statements, where the truth of a statement is contained in the terms and follows the law of non-contradiction. Synthetic statements however are meaningful only if you know (or can imagine) what observations would verify them and what observations would falsify them.
In other words, statements are either
(1) Analytic a priori — like statements of math, which are meaningful but tell us nothing about the external world; or
(2) synthetic a posteriori — empirical statements -- statements about the world of the senses, meaningful and supportable by actual or possible observations, or
(3) nonsense (not meaningful at all).
We can doubtless apply these criteria to religious assertions. For example, religious people usually hold that the statement “God exists” expresses a fact about reality. If the statement expresses a fact, then the statement “God exists” is not analytic. Thus it must be either synthetic or nonsense. If the statement “God exists” is synthetic, then it can be verified or falsified empirically, i.e., there are observations that lend support to the notion or refute it.
But empirical observation does not verify or falsify the claim “God exists." If no observations verify or falsify the claim “God exists,” then the claim is simply nonsense.
Caveat: I have borrowed heavily from Logical Empiricism here.