I've been formulating this in my head for a while now, and it makes sense in there...
God is defined traditionally as all powerful, all knowing, wholly good and responsible for creation. Indeed, it seems hard to define God as anything else other than at least one of these concepts
If we can prove that no being can possess these attributes we can say that God, as traditionally defined, does not exist. I aim to do this.
Firstly we should define what we mean by each term.
All powerful - God can do anything which is logically possible.
All knowing - He knows all that has been, all that is and all that will be
Wholly good - By good I take to mean maximising good in so far as to eliminate evil, so by wholly good I mean to maximise good in so far as to eliminate evil.
All powerful
Given the definition the fact He can't make a circle a square is no limit to His power. The fact He couldn't make a tree fall down would be. When we ask the following question however, we can see that no being can be all powerful. Can God create beings which, once created He can no longer control? If He can, then once He has created them, He is no longer all powerful, as He cannot control His creations. If He can't, then He is not all powerful as there is something which He cannot do.
There is nothing illogical about the question, indeed it is suggested by most theist to have already happened, therefore to say He can't do it as it falls outside the realm of logic isn't a valid excuse. So either way you look at it, God can't be all powerful.
All knowing
So we have concluded that God isn't all powerful, but He still is all knowing and wholly good. Now clearly God still has some power if he can create the universe, just not ultimate power. So God creates the universe, and being a wholly good God he would not want evil to befall his creation. Clearly it does, in both natural form; hurricanes, tsunamis, disease etc... and in moral form; murder, rape, theft etc... Now one might clear God from responsibility by saying, well if He were all powerful He wouldn't allow this, as He isn't there is not much He can do. However being all knowing God should realise that the creation of the universe will result in evil. Being wholly good, God would not want this, in fact a wholly good God would not create a universe where evil occurred. So as it stands, God creates the universe, but being wholly good doesn't want evil. However He knows He cannot prevent it as He isn't all powerful, and He knows that it will occur. So in this situation a wholly good God would not create the universe. But the universe has been created, evident in the fact that I'm here writing this. So the only conclusion, given that God is wholly good, is to say He must not know about the evil, otherwise He wouldn't have allowed it by creating the universe. So God is not all knowing.
Wholly good
Now we have established that God isn't all powerful, nor all knowing. But He still created the universe. And the evil that exists is either due to His lack of knowledge of it, or given his knowledge of it his lack of power to remove it. In creating the universe it is obvious God must have both some knowledge, i.e. of how to create a universe, and some power, i.e. the power to do so. Now as previously claimed a wholly good God would not create the universe if he knew it would cause evil. For this to be true we have to contend that eliminating evil or the lack of evil is a good in itself. I think this is true, as most people admit that it is good when a society is free from crime, or good when an evil is eliminated. So given this, if God knew of one single instance of evil in the universe he would have to abstain from creating this universe as it would go against his wholly good nature. So we have to contend that God knows of no evils that happen in the world. So God is still wholly good, although ignorant and powerless to all evil. I don't think its unreasonable to suggest that if God wasn't all knowing, he wouldn't know He had limitations. For instance you can't claim to know everything when you don't, you would always know that there were things you didn't know. So God knows his knowledge is limited. Hence He knows that in this world He has created the possibility of evil is real, even if he doesn't have conclusive proof of it. Now a wholly good God would not even allow the possibility of evil to befall His creations, as this would possibly go against His wholly good nature, and He wouldn't take that chance. So a wholly good God would not create the universe. But again clearly the universe has been created, so God cannot be wholly good.
The first argument holds true, regardless. The second argument suggests that God is wholly good, a claim the third argument refutes, but is not reliant upon this. All it relies upon is that God is more in favour of good than evil. For if this is so, then he will prefer good over evil at least most of the time, so even if He did prefer evil when He created the universe, hence not caring that its creation would entail evil, He would, when preferring good again, see his mistake in creation and destroy the universe, which would be good in the sense it prevented all possible evils. The third claim is reliant on the fact that we attribute creation to God. This claim is essential to theism, and if theists drop it, their whole concept of God loses all meaning as He is essentially a spectator in the game of life.
Writing this out in full, I am suspicious of its completeness. I am not claiming this 'theory' to be true, but instead by posting it inviting criticisms, amendments and responses. Even if only to establish I'm spouting a load of mince...