Can we prove deities don't exist?
If deities existed we could empirically verify them. We could set up an experiment that could be falsified if somebody claimed that they could show or prove that deities exist. There is a long-standing unclaimed prize of $1 million dollars  that will be rewarded to anybody who can show under controlled scientific conditions any evidence for supernatural phenomena.
If we can't detect deities as they exist beyond the realm of our sense experience then no such experiment is possible.
There is not any credible evidence that I have seen or am aware of that could be used to demonstrate the high probability of the existence of the Western monotheistic, intervening, male God. The father of Jesus Christ. Nor the God of the old testament or for Allah of the Koran. If there was empirical evidence (not anecdotal evidence or personal psychological accounts of the presence of the divine) for deities then we should believe or think that they exist just like anything else we can scientifically verify exists.
There are many other religions on this earth polytheistic and deistic and so on. Not to mention the thousands of religions that have existed in the past that now have virtually zero adherents. The Greek gods, Wotan, Thor, Ra, etc.
If you see there is the same amount of evidence for other deities existing that you do for the prominent deity of your culture and time then you should give an equal probability that any of them exist.
How much evidence is there for deities?
Since those who believe in the divine do not usually do so based on empirical evidence, it is more-so based on their faith or a feeling that deities exist rather than basing their beliefs on much scientific reasoning. Why should we attribute more evidence for deities existing that we do for golden mountains, purple cows, unicorns, etc.? Coming up with a calculus as to why you think golden mountains have a lower likelihood of existing than a deity is very problematic. Intuitively you'd think that there is a lower chance of a golden mountain existing, but what evidence are you using to base this claim on? Just because many people believe in something that we can't know the true nature of (a paradox in itself), why should we think there is more reason to believe it? If you are trying to be objective, you'd see that this is a fallacy and we shouldn't think there is a higher chance of something being the case just because more people think it is so.
You could claim that you are equally an agnostic towards unicorns than you are towards other deities.
Most people don't take this position. An atheist or agnostic-atheist would mostly have a specific deity in mind when they say that they are atheists or agnostics.
Which deities and other metaphysical beings or entities should we be agnostic with respect to?
Agnosticism towards all deities and other possible metaphysical entities is the most defensible position. You cannot prove there is no evidence for golden mountains existing, so how could you similarly prove there is no evidence for deities existing?
Many would think there is more evidence for the deity of their culture because they have been heavily exposed to ideas related to this deity. It is the minority position amongst all of the stances towards deities that we should ascribe an equal probability that all deities exist. But why should you ascribe a higher probability to one deity existing as opposed to another just because it is the one that your culture most strongly believes or identifies with? Again this is the argumentum ad populum fallacy.
What do famous atheists think?
Most atheists such as Dawkins, Krauss, Hitchens, etc. (who have spoken along these lines) would be agnostic at the level where they are not going to say they can prove the non-existence of deities. But their belief in deities they think would be akin to their belief in unicorns — but perhaps NOT identical in probability. As trivial and condescending as that may sound.
Dawkins has said this in the past:
If you were brought up in classical Greece you'd be believing in, in
Zeus. If you were brought up in central Africa you'd be believing in
the great Juju up the mountain. There's no particular reason to pick
on the Judeo-Christian god, in which by the sheerest accident you
happen to have been brought up and, and ask me the question, "What if
I'm wrong?" What if you're wrong about the great Juju at the bottom of
It's not clear if that means he certainly thinks there is an equal chance of all types of other types of divine beings existing, but it does sound like it.
However, it appears he thinks there is still a chance that deities exist but he can't be sure or know which deities he had in mind (from an article about an interview with Dawkins):
There was surprise when Prof Dawkins acknowledged that he was less
than 100 percent certain of his conviction that there is no creator.
The philosopher Sir Anthony Kenny, who chaired the discussion,
interjected: “Why don’t you call yourself an agnostic?” Prof Dawkins
answered that he did. An incredulous Sir Anthony replied: “You are
described as the world’s most famous atheist.” Prof Dawkins said that
he was “6.9 out of seven” sure of his beliefs. “I think the
probability of a supernatural creator existing is very very low,” he
How could you prove a negative or prove the non-existence of anything that could possibly exist?
So, it's clear that even the most famous atheists still don't think they can prove with certainty that deities don't exist. Claims that assert the non-existence of deities should follow a similar line of reasoning. Otherwise, you are making claims that cannot be supported. But usually when we are talking about how reality is through the lens of science the "absence of evidence is evidence of absence". As in, we've seen no evidence for deities existing, so we can't say that they do. But I'm fine with saying that there is no more evidence for deities existing than other possible metaphysical entities. If there was scientific evidence for deities or for unicorns existing I'd believe this is so. Any probability I hold in mind for deities existing isn't based on scientifically verifiable facts. This sort of induction would be independent of what science has revealed about the universe. There hasn't been any evidence shown by science that deities exist. However, there are many questions science has not yet or maybe it will never be able to answer.
This is perhaps the god-of-the-gaps argument. But this is an area where many people invoke faith. They have faith that there is a higher power who can answer the questions science currently can't. Whether this is a good justification for believing in deities is contentious.
Furthermore, having a "lack of belief" in deities is a word game — this means you are an agnostic, many atheists say they "lack belief". But this is the same as being agnostic — you don't know, don't care, don't think it is possible to answer such questions, etc.
If you had to make a bet, what you bet that deities exist or do not exist?
What the chances of there being a theistic God who can cause wars, natural disasters, intervene in your personal matters, etc.? Could you be 100% certain or very sure that this isn't the case? Maybe you may sometimes feel a different way about this but don't rationally or logically think this is the case. If you had to make a bet as to whether a theistic god exists, would you bet against this? What about the austere beauty and order in the universe (the laws physics etc.)? Does this provide a rationale and a basis for something more that we cannot know? Is this nothing more than just a feeling? Although, asserting there is a creator adds an additional hypothesis to be explained on top of the already complex, undissolvable problem as to why there is a universe in the first place as opposed to no universe with the properties that it does have.
: One Million Dollar Paranormal Challenge
Edit: (One Million Dollar Paranormal Challenge ended in 2015, after being established in 1964)