I’m going to argue that we can’t. (This doesn’t entail that we can prove that God does exist, and I’m assuming we can’t do that, either.) I make no claim to originality in any of this. The underlying basis of proofs against God’s existence is that the use of logic is sound, so I am going to call this into question.
1. We all know that when we dream, we reason in ridiculous and absurd ways which we acknowledge once we wake up. Suppose that this life itself is nothing but a dream and that we will one day “wake up” from it into a higher level of existence and realize that all of our reasoning in this life was ridiculous and absurd. I say the atheist has no way to prove that this suggestion is wrong.
2. In order to prove that God doesn’t exist, the atheist assumes that reality is sufficiently rational that a logical proof will work. But we have no guarantee that reality is rational, and paradoxes like Russell’s Paradox suggest otherwise. Here the atheist is in a bind because the believer in a rational God will also believe that God orders the universe in a rational way. But the atheist has no such ground for believing that reality must be rational. And proving that reality is rational is a raising-yourself-by-your-bootstraps operation that won’t work, simply because any proof that reality is rational already requires reality to be rational.
3. Atheists often use the argument from evil to show that God doesn’t exist. It argues that if God exists, then God, being good all-knowing, knows that evil exists, and being powerful, can wipe out evil, and being good, wants to wipe out evil. Accordingly, evil shouldn’t exist, but it does exist, so God can’t exist. But as with (2) above, we have no guarantee that this argument works. If, as some philosophers like Quine believed in the last century, quantum mechanics shows that the law of excluded middle is wrong, then why can’t both God and evil exist? I admit that this isn’t an instance of the law of excluded middle, but my point is that once we begin doubting logical truths, there really is no stopping point. Everything can be doubted.
4. My point in the last two paragraphs was that there might be a general irrationality in reality. Now I simply want to cast doubt on God’s rationality. I happen to believe that God is rational, but I have no guarantee of that. If God is irrational, then the three conditions listed in the last paragraph may all be true at the same time that evil still exists. That is, God knows that evil exists, has the power to destroy evil, and wants to destroy evil, but being irrational, doesn’t destroy evil.
This post was inspired by this link which I was led to from Keith Burgess-Jackson’s blog (here).

The argument from evil fails for the same reason as the first one. It is also a bootstrap argument. You must assume that such a thing as good and evil exist and this cannot be done in a purely materialist universe. If all that exists is atoms and the void then all morals are only personal or group preferences and no metaphysical conclusions can follow.
Posted by: Louis Lamy | 01/07/2012 at 07:11 AM
Gratuitous correction:
You wrote, "God, being good, knows that evil exists". You probably meant to write, "God, being omniscient, knows that evil exists".
Posted by: Mark Spahn | 01/07/2012 at 02:46 PM
If I recall correctly, Stephen Hawking presented a program, perhaps on Discovery or some such channel, purporting to demonstrate that God does not exist. My recollection was that his final statement in the program was something on the order of 'Therefore I believe that God cannot exist" This struck me as more of a statement of faith than of proof.
Posted by: Steve Atchison | 01/07/2012 at 02:51 PM
Mark, you're right. I fixed it. Thanks.
Posted by: John Pepple | 01/08/2012 at 06:38 AM
"This doesn’t entail that we can prove that God does exist, and I’m assuming we can’t do that, either."
History may have just thrown the world a curve ball and it could very well hit the mark. Proof of God, in the theological sense, is of course a misnomer, a philosophical contrivance to avoid accepting our ignorance of such a reality. As a humanity, we have all been conditioned, seduced or indoctrinated, for all of history by 'theological' exegesis, particularly those with their own religious claims and agendas, to accept that a literal proof of God is not possible for faith. And thus all discussion of morality and apologists 'theodicy' is contained within this self limiting intellectual paradigm and bubble of presumption, especially evident in the frictions between science and religion. It would now appear that all sides squabbling over the God question, religious, atheist and history itself have it wrong! That bubble could now burst at any time!
The first wholly new interpretation for two thousand years of the moral teachings of Christ is published on the web. Radically different from anything else we know of from history, this new teaching is predicated upon a precise and predefined experience and called 'the first Resurrection'. A direct individual intervention into the natural world by omnipotent power to confirm divine will, command and covenant, "correcting human nature by a change in natural law, altering biology, consciousness and human ethical perception beyond all natural evolutionary boundaries." So like it or no, a new religious claim testable by faith, meeting all Enlightenment criteria of evidence based causation and definitive proof now exists. Nothing short of a religious revolution is getting under way. More info at http://www.energon.org.uk
http://soulgineering.com/2011/05/22/the-final-freedoms/
Posted by: goliah | 01/08/2012 at 11:33 AM
Steve Atchison: I commented on Hawking a while back:
http://iwantanewleft.typepad.com/i-want-a-new-left/2010/09/hawking-on-gods-nonexistence.html
Posted by: John Pepple | 01/08/2012 at 04:37 PM
Louis Lamy: The argument is a reductio ad absurdum aimed at theists, and they believe that good and evil exist, so it’s perfectly acceptable for the atheist who uses this argument to assume that they exist. Accordingly, I don’t see that there is any boostrapping going on.
One could argue that assuming that good and evil exist weakens the atheist’s conclusion, which ought to be “Either God doesn’t exist, or good and evil don’t exist.” But since most theists want both anyway, that isn’t much of a problem.
Posted by: John Pepple | 01/08/2012 at 04:48 PM
goliah, can you summarize this new religious claim?
Posted by: John Pepple | 01/08/2012 at 04:51 PM
John, I actually do not see a problem stating that "God, being good, knows that evil exists." I have long thought that it is entirely consistent that God could be good, and yet divine that the world is a better place with some evil in it than none. Ultimately, men are capable of correcting evil and creating even greater good.
I am an agnostic. Yet, I've long thought that if God exists as He is supposed to be, then why does man think he could possibly know all there is to know about God? On some level, being God - wouldn't he be "unknowable" in full to man?
I might add that those who are believers tell me that you really cannot rationally explain God. That is, to some degree, the definition of faith.
Posted by: Peg | 01/12/2012 at 10:10 AM
Well, the problem with “God, being good, knows that evil exists” was that it was part of a logical argument, and the logic wouldn’t work if I had left it like that.
Anyway, most theists will agree that God was willing to have some evil in the world because it was better for people to have free will, even if they do evil, than it was to deny them free will and have no evil (because then we’d be automatons). I tend to agree with this, except that not all the evil in the world is caused by our free will, so something is left unexplained.
As for God’s being unknowable, yes, we aren’t in a position to deny that. On the other hand, much of what people find mysterious about God comes from the assumption that God intervenes on occasion in our world. Then one has to explain why God performed a miracle on one occasion, but not on another, similar occasion. I prefer the deist position, in which God never intervenes. It makes God much more understandable.
Posted by: John Pepple | 01/14/2012 at 06:42 PM