The God traditionally believed in under philosophical theism must be all-virtuous, but certain virtues (like courage) can only be developed in the context of flawed, fallible creatures. Ergo, a perfect God cannot be all-virtuous. One or the other attribute must give way and if theists insist on ascribing both to God, then God is logically impossible.
Heres a formal statement of his argument offered by Douglas Walton offers in the book The Impossibility of God:
- God is (by definition) a being than which no greater being can be thought. (premise)
- Greatness includes greatness of virtue. (premise)
- Therefore, God is a being than which no being could be more virtuous. (from 1, 2)
- But virtue involves overcoming pains and dangers. (premise)
- Indeed, a being can only be properly said to be virtuous if it can suffer pain or be destroyed. (premise)
- A God that can suffer pain or is destructible is not one than which no greater being can be thought. (premise)
- For you can think of a greater being, that is, one that is nonsuffering and indestructible. (premise)
- Therefore, God does not exist. (from 3, 5)
Put more simply: If God exists, God should more virtuous than any other being in the universe. Virtue, however, requires attributes like being able to experience pain, fear, or even destruction attributes that God does not have. We must conclude, then, one of the following: God does not exist, God exists but is not the most virtuous being in existence, or God is the most virtuous being in existence but virtue does not require attributes like experiencing pain, fear, suffering, or destruction.
In the first two cases, the God traditionally believed in does not exist. In the last case, something very interesting in relation to the Argument from Evil occurs. Many theists attempt to refute the Argument from Evil by claiming that things like suffering, privation, destruction, etc. exist in the world because without them, we would never be able to develop important virtues like courage and charity.
These theists grant that the evil in the world is very bad, but they argue that the development of virtue is worth all that evil. These same theists also believe that God is all-virtuous but their perfect God is, by their own definition, incapable of developing virtues like courage.
There are a number of possible conclusions we could draw form this, none of them very good from the theists perspective. Perhaps we humans possess good attributes that God cant have but that would make us better than God on certain levels. Perhaps these virtues really arent so great after all, and thus we arent better than God but that would undermine the above theodicy which argues that these virtues are so wonderful they make all the evil worthwhile. Or, perhaps, God does have these virtues because God isnt perfect either but an imperfect God wouldnt be as worthy of worship as believers claim.
However we look at it, it appears unreasonable to conclude that the God of traditional, philosophical theism can exist. If God is perfect, God cannot be virtuous; if God is virtuous, God cannot be perfect. One or the other attribute must give way and if theists insist on ascribing both to God, then God is logically impossible.

