Can we prove God does not exist?

It's a trite old maxim of folk logic that you cannot prove a negative. It's also a staple of religious apologetics to argue that belief in God need not be subject to methodological inquiry and verified evidentially. Combined, these two fallacies form a powerful weapon of perpetual ignorance among the faithful. Atheists themselves are fond of saying that atheism is a "lack of belief in gods", since that clears them of any sort of burden of disproof. Personally, while I think that atheism is at least in part a "lack of belief in gods", I think atheists who take the "weak" stance are to an extent selling themselves short. There are good reasons to say we can prove that God does not exist.

How should we go about this whole God thing?

First up to the plate is the contentious old question of whether the existence of God is a scientific question. I'd say that it depends on how one defines "God". If you simply mean some nebulous pantheistic-like super-intelligence that's intertwined with the universe, or you just want to say "a higher power" and leave it at that, well then no, it's not a scientific question because you've either left the being undefined (what does 'a higher power' even mean?) or made God semantically indistinguishable from the material universe. So, perhaps you define God as some incomprehensible being beyond the cosmic veil, or a deistic God who set everything in motion (or an Aquinian being who 'sustains' the universe in motion) but otherwise does not leave fingerprints of his actions. Same problem – you've defined God in such a way that in principle cannot be detected.

In all those cases, the theist has just failed to say anything worth considering. Saying you believe in an incomprehensible deistic God is about as interesting as me saying I believe in secretive extra-dimensional superintelligent alien overlords who, to us mere humans, would be indistinguishable from a God. There are an infinite number of such ideas, and they're essentially self-defeating – if something is incomprehensible, how can you know it exists? Even if such things do exist, it's like I always say (man, I really want this quote attributed to me!): the only thing worse than a God who does not exist is a God who might as well not exist.

Most theists, however, do not defined God as totally incomprehensible, mysterious or secretive. I mean heck, a cornerstone of Christianity is the concept of "revealed theology", the idea that God somehow let a few fortunate souls sneak a peak into the divine, then told them to spread the word. But that comes with a large caveat: as soon as one defines God as a being that interacts with the natural world in any way, then it stands to reason that the existence of God must be a scientific question. The reason for this was concisely illuminated by the physicist Lisa Randall in her outstanding book Knocking on Heaven's Door:
The problem is that in order to subscribe both to science and to a God— or any external spirit— who controls the universe or human activity, one has to address the question of at what point does the deity intervene and how does He do it. According to the materialist, mechanistic point of view of science, if genes that influence our behavior are a result of random mutations that allowed a species to evolve, God can be responsible for our behavior only if He physically intervened by producing that apparently random mutation. To guide our activities today, God had to influence the ostensibly random mutation that was critical to our development. If He did, how did He do that? Did He apply a force or transfer energy? Is God manipulating electrical processes in our brains? Is He pushing us to act in a certain way or creating a thunderstorm for any particular individual so he or she can’t get to their destination? On a larger level, if God gives purpose to the universe, how does He apply His will?
The problem is that not only does much of this seem silly, but that these questions seem to have no sensible answer that is consistent with science as we understand it. How could this “God magic” possibly work?
Clearly people who want to believe that God can intervene to help them or alter the world at some point have to invoke nonscientific thinking. Even if science doesn’t necessarily tell us why things happen, we do know how things move and interact. If God has no physical influence, things won’t move. Even our thoughts, which ultimately rely on electrical signals moving in our brains, won’t be affected.
If such external influences are intrinsic to religion, then logic and scientific thought dictate that there must be a mechanism by which this influence is transmitted. A religious or spiritual belief that involves an invisible undetectable force that nonetheless influences human actions and behavior or that of the world itself produces a situation in which a believer has no choice but to have faith and abandon logic— or simply not care.
I think Lisa Randall really nails it – I can think of nothing to add. Even a deistic God may not totally escape this conundrum, because how the universe began (or whether it began at all) most certainly is at least in principle a scientific question, even if it remains beyond the veil for the foreseeable future.

One person's proof is another person's not-really-proof

It's also worth considering what exactly we mean by proof. This is where philosopher types interject with a very precise meaning of the term – that of mathematics or deductive logic. Another physicist, Sean Carroll, often says that "Science is not in the business of proving things", and that's precisely the kind of "proof" he's talking about. To be philosophically precise, science uses inductive reasoning, not deductive reasoning.

Deductive reasoning and mathematics can be called "proof" because they tell us the consequences of axioms. If axiom x is true, then conclusion y must follow. But – again with a nod to Carroll here – we can't gleam from deductive logic or mathematics which axioms correspond to reality. For that, we must again use inductive reasoning. And when we use induction, we speak of things with varying degrees of reliability and probability, not absolute or irrefutable knowledge.

It's not hard to see why this is the case. If mathematics alone could tell us which axioms corresponded to reality, then physicists would never have to do experiments; they could simply solve their way to a complete understanding of the universe. But we can easily conjure up mathematical axioms that are contradictory or which can be found through experiment not to correspond to reality. Logical axioms are no different; a deductive argument may be valid, in that if the premises are unequivocally true then the conclusion must follow. But if the premises are not unequivocally true, the argument is nonetheless unsound. And to establish premises in deductive arguments as true (or, to be more precise, reliable), we are again left to inductive reasoning.

In the strict, deductive and mathematical sense, it's indeed true that you cannot prove a negative. But this is irrelevant for queries related to the existence of God, because that requires us to look at the world and establish the reliability of various propositions theists frequently espouse about the nature of God. If God answers prayers, orchestrates events in people's lives, heals people, causes natural disasters, etc. – then we are dealing with evidential claims that fall under the purview of the criteria Lisa Randall detailed. We're not talking about claims that can be deductively proved or disproved, but claims that are inductively reliable or unreliable.

Most people, when they are talking about whether we can "prove" anything about God, are not speaking with that kind of philosophical precision. They're speaking about "proof" more colloquially, in a more inductive sense – what we can reasonably, reliably know about the world around us. And to that extent, I think that we most certainly can prove that God does not exist. In this case the word "prove" is synonymous with "absolutely no rational reason whatsoever to assume the positive".

Absence of evidence and evidence of absence

Ironically, a pretty great critical summary of the old canard "absence of evidence is not evidence of absence" was written by none other than theologian William Lane Craig, in the book Philosophical Foundations for a Christian Worldview:
If someone were to assert that there is an elephant on the quad, then the failure to observe an elephant there would be good reason to think that there is no elephant there. But if someone were to assert that there is a flea on the quad, then one's failure to observe it there would not constitute good evidence that there is no flea on the quad. The salient difference between these two cases is that in the one, but not the other, we should expect to see some evidence of the entity if in fact it existed. Moreover, the justification conferred in such cases will be proportional to the ratio between the amount of evidence that we do have and the amount that we should expect to have if the entity existed. If the ratio is small, then little justification is conferred on the belief that the entity does not exist.
It might be more accurate to say that "absence of evidence is not proof of absence", because it's definitely evidence. Perhaps, to use Craig's example, a highly skilled team of forensically trained ninjas came in and removed all evidence of the elephant without being detected. But this is certainly far less plausible, and requires far more assumptions, than simply concluding – quite within the realm of reasonable doubt – that there was no elephant. Again, using that colloquial sense of the word "prove", there is absolutely no rational reason whatsoever to think there was an elephant on the quad unless there is evidence of one.

If indeed God does all the various things that believers attribute to him, then there is no question that there ought to be abundant inductive evidence of God's existence. When believers use the 'miracle' canard to imply that God's fingerprints in principle cannot be detected even though God totally does intervene in the natural world on a regular basis, they're trying to have their cake and eat it, too. And it's here where, in addition to Randall's excellent quote above, an old quote from PZ Myers is apt:
If something has an effect or influence, you can try to examine it using the tools of science — so when someone announces that gods cannot be detected by observation or experiment, they are saying they don't matter and don't do anything, which is exactly what this atheist has been saying all along.
Whenever theists try to escape this conundrum by positing a God beyond our purview of inquiry, they're falling right back into the trap of my own quote above: the only thing worse than a God who does not exist is a God who might as well not exist. They've simply posited a being that is utterly irrelevant to human existence. It's the theological equivalent of William Lane Craig's flea.

We can, then, through inductive evidence, prove (using the colloquial sense of the word) that God – as generally described in Western Monotheism – does not exist. There is absolutely no reliable evidence and hence no rational reason to think that there is a being who listens to prayers, orchestrates events in our lives, controls nature, creates and destroys at will, speaks prophetic words to his followers, or reveals himself selectively to a chosen few. The utter failure of theists to produce any sort of reliable evidence for any of these types of claims is indeed proof that God does not exist.

But obviously, the reason why the question remains contentious is because it is so semantically loaded and the philosophically precise usage of the words are often nonchalantly interchanged with the colloquial ones. So, perhaps this isn't an answer that can satisfy anyone, but I hope I've at least shed some light on the problem.


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