I think that the argument as formulated relies heavily on the definition of "design," which probably needs to be stipulated. If "design" is used in a relatively weak sense, then 2 is clearly false; but if "design" simply means "deliberate arrangement," then 2 is trivially true and 3 is the dubious premiss. Proponents of "intelligent design" arguments typically try to establish objective criteria for "specified complexity" that is considered to be evidence of design in this stronger sense — aletheist

Yes, "design" seems to have two different meanings, and it is not clear which one Paley might mean, and he may be guilty of equivocating or begging the question. By "design" one might mean something like "observable complexity of patterns." However, by "design" one might also mean "intelligent design" or, as you put it, "deliberate arrangement." If by "design" Paley means "observable complexity of patterns," then he may be guilty of equivocating, since he seems to infer "deliberate arrangement" from "observable complexity of patterns," and it is just not clear that this inference is right. If by "design" Paley means "deliberate arrangement," then, I think, his claim is not trivially true, as you put it, but question-begging, as he is assuming what he is trying to prove.

Hume lived and worked a long time - about 100 years? - before Darwin. The objections you're attributing to David Hume are much more like those of Richard Dawkins who has devoted many books, such as Blind Watchmaker and Unweaving the Rainbow, to exactly this question — Wayfarer

Of course Hume lived one hundred years before Darwin. My point is that Hume seems to be arguing that the belief that "observable complexity of patterns," as I put it above, can only arise as a result of intelligent design is an unsupported assumption. To make his point, he seems to argue that, for all we know, "observable complexity of patterns" can arise through natural processes. I was just using natural selection as an example of such a natural process. I take it you realized later that is my point.

Where I think both Hume and Dawkin's argument fails, is that science itself presumes an order which it doesn't explain. Science itself is based on observation and inference - but it is created on the basis of existing order, namely, 'the order of nature'. I don't think there's any sense in which science explains that order. — Wayfarer

I don't understand this criticism. When we do science we look for "observable complexity of patterns," and we try to give explanations for them according to natural "laws." It seems to be a huge leap to say that we presume "deliberate arrangement." I would think that science is nothing if not the attempt to explain order, if by "order" we mean something like "observable complexity of patterns." Isn't one of Hume's points that to explain "order" in this sense, we simply do not need to appeal to an intelligent designer, because we can appeal to natural "laws," even if we can't justify the regularity of causal laws according to anything but custom or habit? It seems you're making the exact assumption that Hume denies as unsupported.