Professor of Philosophy Bradley Monton wrote a very interesting paper a few years ago, Design Inferences in an Infinite Universe. I brought it up and discussed it a few times at TelicThoughts (here, for example), but never came up with a satisfactory way of defending ID in an infinite universe. But I think I finally stumbled across a reasonable defense.
Normally, ID proponents rely upon a finite universe in order to make their arguments: Given a finite universe of about 13.7 billion years, and composed of about 1080 atoms, there simply hasn't been enough time (or so they argue) to generate the biological information that we see on Earth.
In his paper, Prof. Monton first points to empirical data that suggest that our universe is probably infinite in size. (From what I've come across, Monton's conclusion that our universe is probably infinite may not be that accurate. See here, for example. But it still leads to an interesting philosophical question.) In an infinite universe, the probability resources for generating the biological information on Earth would be more than sufficient, as are all sorts of improbable events, such as people walking on water.
Nevertheless, Monton maintains that there would still be ways, based on Bayesian probability theory, to persuasively argue for intelligently caused events or miracles. As an example, take the case of a man walking on water. Given the proper background information, such as, the man seems to be of high moral character and claims to be God's son, the probability that his walking on water was an act of God is higher than the probability that it is one of those improbable, but fully natural events that are bound to happen in an infinite universe. (We could contrast the case of this man walking on water, with a case where a man walks on water, but is not of particularly high moral character, or does not make any claims to a special relationship with God, and just happened to be out for a walk that day. In that situation, we would be less likely to take it as evidence of a divine miracle, and more likely to attribute it to one of those fluke things that happens in an infinite universe).
Monton goes on to compare this with the case of the origin of life, which he is willing to grant (at least for the sake of argument) as a highly improbable event:
"Here is one key difference. In explaining why one can infer design on the basis of the seeming miracle [a man walking on water], I pointed out that the seeming miracle would be more likely to occur under the supposition that God exists than it would under the supposition that there is no designer. This is what leads to the probability shift in favor of the designer hypothesis. In the existence of life case, though, it would be reasonable to think that there would be no more life in the universe under the supposition that God exists than under the supposition that there is no God. After all, even under the supposition that there is no God, we would expect there to be life in an infinite number of places in the universe. I see nothing in Christian theology, for example, which suggests that the density of life in the spatially infinite universe would be greater than it would be if there were no God.8
And in the footnote, he adds:
8There is still the question of why life exists on this planet. Before taking into account our knowledge that we’re here, that event is highly implausible under the chance hypothesis. But it is also highly implausible under the design hypothesis – we have no antecedent reason to think that God would create life on this planet, out of the infinite pool of planets in existence.
The thing I stumbled across has to do with something called the Rare Earth hypothesis (which I think was first proposed in the book Rare Earth; Why Complex Life is Uncommon in the Universe.) The authors, Peter D. Ward and Donald Brownlee, argue that animal life (non-unicellular life) "is exceedingly rare in our galaxy and in the Universe," and that it is only because of the very special and rare conditions that we find on our own planet that animal life is able to exist and thrive here.
If Ward and Brownlee are correct, then we do indeed have an "antecedent reason to think that God would create life on this planet, out of the infinite pool of planets in existence." It is because this is one of the few planets in our galaxy, or even in our universe, that has the properties necessary for complex life to thrive, and thus for creatures "created in God's image" to live.
What's interesting is that Ward and Brownlee believe that "simple" (unicellular) life is abundant in the universe. Of course it must be. For if simple life were as rare as they think our type of planet is, then how incredibly lucky it would have been for it to appear in just the right place, so that eventually it could evolve into animals.
So yes, even in an infinite universe there would appear to be good reason to believe that life on our planet was designed.
What might change this conclusion is if we do indeed find simple life on neighboring planets or moons. That, I think, would tend to support Ward and Brownlee's claim that simple life is abundant. In that case in an infinite universe, we would find simple life nearly everywhere, and therefore simple and complex life on rare planets such as ours. In such a case, this wouldn't mean that God hadn't designed both the simple and complex life. Merely that probability arguments for that conclusion wouldn't be very compelling.
Maybe that will be an impetus for exploration of our solar system.