Victor Stenger received his Ph.D. in Physics from UCLA in 1963. He has also made some criticisms of organized religion, and theistic belief in general. This entry will be the first of a series of posts responding to arguments that Dr. Stenger has defended in support of atheism. Summaries of his arguments can be found here: God: The Failed Hypothesis.
The first proof that Stenger offers contends that the very concept of God is incoherent. By "God" in this context, Stenger does not mean just any Creator or Supreme Being per se, but specifically the God of classical theism that possesses all possible perfections.
1. God is (by definition) a being than which no greater being can be thought.
This concept of God is what we will call "Anselmian theism" (named after St. Anselm, who defended the ontological argument).
2. Greatness includes the greatness of virtue.
Presumably, a maximally great being (God) must be maximally excellent in every possible world, or else God won't be maximally great to begin with. So far, so good.
3. Therefore, God is a being than which no being could be more virtuous.
(3) follows from (1) and (2).
4. But virtue involves overcoming pains and danger.
It is here that Stenger commits an equivocation. Classical theists have traditionally held that God's virtue is analogical, and not univocal, to human virtue. It is virtuous for a human being to overcome his/her fear of dying in order to fight in battle. This would be an instantiation of the virtue of courage. But, is courage required in order to be perfect in virtue? Consider a man who faces no threat of death, as is the case during a time of great tranquility. Is this person culpable for not fighting? If we take Stenger's argument to its logical conclusion, then we ought to say that the man in our analogy should go looking for a fight in order to prove his courage. Yet, this wouldn't be considered courage at all, but rashness.
I propose that Stenger needs to revise his definition of virtue. Otherwise, he is susceptible to the charge of question-begging. My own definition of "virtue" would be something like this: "a characteristic, or attribute, that results in the inclination to produce the best possible states of affairs."
If one is not satisfied with my own definition, let's take one from the Encarta Dictionary: "1. goodness: the quality of being morally good or righteous". 
5. Indeed, a being, can only be properly said to be virtuous if it can suffer pain or be destroyed.
Again, why? What is it about the ability to be destroyed, for example, that causes one to desire the best possible states of affairs?
6. A God that can suffer pain or is destructible is not one than which no greater being can be thought.
In other words, it is greater to exist necessarily than contingently. There's no difficulty here.
7. For you can think of a greater being, one that is nonsuffering and indestructible.
(7) seems to be more plausible than its negation.
8. Therefore, God does not exist.
The argument is logically valid, but we have seen that there are difficulties with (4) and (5). In fact, I would maintain that these two premises are patently false, and if nothing else, incapable of verification (as we will see, one of Stenger's own requirements for rational belief in a proposition is its ability to be empirically verified). With the denial of (4) and (5), his argument, though valid, is unsound.