Millican provides some interesting textual evidence to support the contention that Hume was an atheist rather than, as sometimes claimed, an agnostic (or even some kind of deist). His key point is that the famous phrase that Hume puts in the mouth of Philo:
"that the cause or causes of order in the universe probably bear some remote analogy to human intelligence"
is echoed by an earlier comment in the Dialogues Concerning Natural Religion:
"a certain degree of analogy among all the operations of nature ... the rotting of a turnip, the generation of an animal, and the structure of human thought [are] energies that probably bear some remote analogy to each other".
And this phrase 'remote analogy' occurs nowhere else in Hume's writings. If they were meant to be read together, as seems very likely, then it would be very hard to conclude that this is evidence for Hume being a theist!
Millican is a top-notch Hume scholar, and in the comments thread linked to above he brings up a great many points. But this particular argument will not bear much weight. For one thing, Philo also says:
That the works of Nature bear a great analogy to the productions of art, is evident; and according to all the rules of good reasoning, we ought to infer, if we argue at all concerning them, that their causes have a proportional analogy. But as there are also considerable differences, we have reason to suppose a proportional difference in the causes; and in particular, ought to attribute a much higher degree of power and energy to the supreme cause, than any we have ever observed in mankind. Here then the existence of a DEITY is plainly ascertained by reason: and if we make it a question, whether, on account of these analogies, we can properly call him a mind or intelligence, notwithstanding the vast difference which may reasonably be supposed between him and human minds; what is this but a mere verbal controversy? No man can deny the analogies between the effects: to restrain ourselves from enquiring concerning the causes is scarcely possible. From this enquiry, the legitimate conclusion is, that the causes have also an analogy: and if we are not contented with calling the first and supreme cause a GOD or DEITY, but desire to vary the expression; what can we call him but MIND or THOUGHT, to which he is justly supposed to bear a considerable resemblance?
Which, if we take Philo to be articulating Hume (I'm not sure we should do so naively), would have to be a pretty massive bit of what Millican calls "theological lying". Further, if you recall the actual context of the rotting turnip argument, it's part of an argument that atheists can only be nominally atheists, because no reasonable person can deny that the universe is in some way like an artifact and therefore that its cause is in some way like an intelligent mind, which in turn is part of a larger argument that reasonable theists and reasonable atheists are only nominally distinct, because the former recognize that the cause must be radically unlike a human mind, whatever its similarities, and the latter recognize that the cause must have some likeness to a human mind, however different it may be. That is, the reasonable atheist has to admit that there is something orderly and artifact-like, at least to some extent, even in the rotting of a turnip. This in turn is part of a larger argument that they should lay aside their disputes and curb their animosity toward each other. Thus the whole passage is an argument that there is no difference of any importance between theists and atheists, because, with regard to their dispute, they each are able to know, or at least reasonably infer, one and only one thing about the matter (at all!), and it turns out that it's the same thing, with slightly different emphasis. In effect, Hume's view is that the theist shouts "The cause of the world is like a mind to the extent the world, as discovered by science, is intelligibly ordered!" and whispers "But must be so very different from any sort of mind we know that we can hardly grasp the difference." But the atheist shouts, "The cause of the world must be so very different from any sort of mind we know that we can hardly grasp the difference!" and whispers, "But it is like a mind to the extent that the world, as discovered by science, is intelligibly ordered."
Warburton also jumps the gun a bit in concluding that the "remote analogy" comments can't be read as (weakly) theistic. On the account of analogy that Hume gives in the Treatise, it doesn't matter whether the analogy is remote, or whether there are other, alternative analogies: neither of these affects the legitimacy of the analogy as a ground for inference. Every analogy is a foundation for probabilistic inference. Of course, they aren't necessarily all equal; some may be more "firm and certain" than others, in which case they overbalance the probabilities of the others. But the very context here rules that out: all analogies are fair game because we have no way of knowing how much the cause of the universe resembles anything in the universe. All we have to go on are analogies based on the fact that the universe in some way resembles an animal, a plant, a rotting turnip, an artifact, etc. It's conceivable that Hume has modified his view of analogy between the Treatise and the Dialogues; but the Dialogues actually fit the Treatise account of analogy very, very well. (Indeed, you can explain some old puzzles about the structure of the Dialogues by considering the Treatise account of analogy.)
So the "remote analogy" doesn't, I would argue, give us much, if any, insight into the matter: in fact, it muddies the waters, since the logical implication of the passage is that there is some genuine probability that the cause of the universe is like a mind, just as the theist says -- but it's an extremely small probability, as the atheist says -- but we have no way of checking in any case -- and thus all anyone knows is that you can make the analogy, which everyone agrees on -- so atheists and theists should set aside their disputes because they are not in any significant way different. That's what the argument says. Of course, that still raises the question of whether that's what the argument means.
Perhaps the way we should put it is to say that Hume probably bears some remote analogy to a theist....