Take a system - say, throwing two dice. The set of all possible results of that action is the 'phase space' of that system - in the case of throwing two dice, it's the numbers 2 through 12. This definition is a little simplistic, but it'll do for the purposes to which I'm putting the concept. Wikipedia has a more precise definition.

So, phase space is simply the set of all states of a system - take every variable that can change, stick it on an axis, and that's your space. Obviously, for a reasonably complicated system, that's going to be massive - a set of N particles has a phase space with 6N axes.

Let's consider the most massive phase space of all - the phase space of universes. Take any variable that a universe could conceivably vary upon - say, the value of G, or the existence of gravity - and stick it on an axis. In short, imagine the set of all possible universes.

You know something about the world when we can narrow down which bit of that phase space we exist in. If you can say "Our world appears to have gravity", you've immediately cut out the infinitely many universes which do /not/ have gravity. When you can say "Our universe has gravity, and it works like this", you've cut out all the universes that have gravity that works like that.

Unfortunately, certainty with these statements is very difficult. There's a whole set of universes that /appear/ to have gravity that works like this, but actually don't.

Science sidesteps that issue - instead of saying "The universe is definitely in this set, we can ignore everything else", science says "The universe is definitely not in that set, we can ignore it". There are less universes that appear not to have gravity that works like this that have gravity that works like this than the opposite. You gain some explanatory power.

There is, however, a catch - science can never eradicate that universe in which you are the only being that exists and everything is a figment of your imagination, because that variable is unobservable. The concept is unfalsifiable.

But we don't worry too much about that, because it also means that that concept - solipsism - has no explanatory power.

Let me explain further - if you know that we are in a universe without slood, we also know that we are not in a universe with slood that works like this, that, or the other. In short, there is a constraint on the possible universes in phase space - they must be consistent. That means that we can derive further information about the universe from simple observations. If we know via deductive argument that in a universe where the strong nuclear force works like this, the weak nuclear force works like that, and we show that the weak nuclear force doesn't act like that at all, we have excluded some of the points on the strong-nuclear-force axis from the set of universes that we could be in. That is because phase space is not completely full - there are 'empty' points, where a combination of variables cannot possibly exist.

Solipsism has no such 'empty' points that we can observe - it must not, or we could determine whether or not solipsism is in the set of universes we might live in by observing the empty point. For all possible universes, there is another possible universe which is exactly the same, except that it's got a different value on the solipsism axis. Solipsism is a concept which cannot help us further understand the world, because it does not cut out anything from phase space.

I would allege that god, as a general concept, is the same as solipsism - it is unfalsifiable, and, therefore, it has no explanatory power - it does not remove any points in phase space from the set of universes we might exist in.

Consider the phase space of gods. It's pretty big. Certainly, some of these gods are falsifiable - if Zeus exists, for example, Mount Olympus must have certain properties. We can observe that Mount Olympus does not have the properties suggested, and, thus, conclude that Zeus does not exist. The concept of Zeus also, therefore, has explanatory power - if Zeus exists, we know Mount Olympus must be in a given state - some part of phase space is excised.

Consider the Christian god. He/she/it certainly doesn't require Mount Olympus be in a certain state, but I would allege that the combination of some of his claimed properties requires the world to be in a certain state - that would be the problem of evil - regardless, I think we can agree that the Christian god is, also, falsifiable, and thus has explanatory power - his/her/its existence makes a difference to the world.

But consider god as a general concept. Consider all of god-space. Is there anything in common between all gods that could feasibly be observable?

I do not think so. I can certainly come up with a deity that exists, but cannot be detected by any means. God is, at its most general, unfalsifiable.

And thus, this general concept of god has zero explanatory power - alleging that a god of some sort exists tells us nothing about the universe, unless you add additional properties that make that god falsifiable.

I would argue that as the existence of an unfalsifiable god has no impact on the world - much like the truth or falsity of solipsism - then I should pay no attention to the concept.

Of course, that does not mean that, say, the Christian god should be implicitly ignored. But then, I think he's been falsified.