Compare the works of art with those of nature. The one are but imitations of the other. The nearer art approaches to nature, the more perfect is it esteemed. But still, how wide are its nearest approaches, and what an immense interval may be observed between them? Art copies only the outside of nature, leaving the inward and more admirable springs and principles; as exceeding her imitation; as beyond her comprehension. Art copies only the minute productions of nature, despairing to reach that grandeur and magnificence, which are so astonishing in the masterly works of her original. Can we then be so blind as not to discover an intelligence and a design in the exquisite and most stupendous contrivance of the universe? Can we be so stupid as not to feel the warmest raptures of worship and adoration, upon the contemplation of that intelligent being, so infinitely good and wise?
From The Natural History of Religion in Four Dissertations (1757):
As every enquiry which regards religion is of the utmost importance, there are two questions in particular which challenge our principal attention, to wit, that concerning its foundation in reason, and that concerning its origin in human nature. Happily, the first question, which is the most important, admits of the most obvious, at least the clearest solution. The whole frame of nature bespeaks an intelligent author; and no rational enquirer can, after serious reflexion, suspend his belief a moment with regard to the primary principles of genuine Theism and Religion. But the other question, concerning the origin of religion in human nature, is exposed to some more difficulty.
From Part II, Dialogues Concerning Natural Religion (posthumously published in 1779 but finished just prior to Hume's death in 1776; the character Cleanthes is speaking):
Look round the world: contemplate the whole and every part of it: You will find it to be nothing but one great machine, subdivided into an infinite number of lesser machines, which again admit of subdivisions to a degree beyond what human senses and faculties can trace and explain. All these various machines, and even their most minute parts, are adjusted to each other with an accuracy which ravishes into admiration all men who have ever contemplated them. The curious adapting of means to ends, throughout all nature, resembles exactly, though it much exceeds, the productions of human contrivance; of human designs, thought, wisdom, and intelligence. Since, therefore, the effects resemble each other, we are led to infer, by all the rules of analogy, that the causes also resemble; and that the Author of Nature is somewhat similar to the mind of man, though possessed of much larger faculties, proportioned to the grandeur of the work which he has executed. By this argument a posteriori, and by this argument alone, do we prove at once the existence of a Deity, and his similarity to human mind and intelligence.
From Part XII, Dialogues Concerning Natural Religion (the character Philo is speaking):
You, in particular, CLEANTHES, with whom I live in unreserved intimacy; you are sensible, that notwithstanding the freedom of my conversation, and my love of singular arguments, no one has a deeper sense of religion impressed on his mind, or pays more profound adoration to the Divine Being, as he discovers himself to reason, in the inexplicable contrivance and artifice of nature. A purpose, an intention, a design, strikes every where the most careless, the most stupid thinker; and no man can be so hardened in absurd systems, as at all times to reject it. That Nature does nothing in vain, is a maxim established in all the schools, merely from the contemplation of the works of Nature, without any religious purpose; and, from a firm conviction of its truth, an anatomist, who had observed a new organ or canal, would never be satisfied till he had also discovered its use and intention. One great foundation of the Copernican system is the maxim, That Nature acts by the simplest methods, and chooses the most proper means to any end; and astronomers often, without thinking of it, lay this strong foundation of piety and religion. The same thing is observable in other parts of philosophy: And thus all the sciences almost lead us insensibly to acknowledge a first intelligent Author; and their authority is often so much the greater, as they do not directly profess that intention....
So little, replied PHILO, do I esteem this suspense of judgement in the present case to be possible, that I am apt to suspect there enters somewhat of a dispute of words into this controversy, more than is usually imagined. 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 inquiring concerning the causes is scarcely possible. From this inquiry, 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?
Every single one of these raises interpretive questions. "The Platonist" is a sketch of a philosophical perspective that is not Hume's, but that Hume seems to have some sympathy with. The design argument in The Natural History of Religion is only raised in order to distinguish sharply between an account of why human beings are religious and an account of what philosophical arguments can establish religious belief; much of NHR is filled with irony, so one might read it as ironic -- but it can't completely be removed without devastating one of Hume's key arguments, namely, that religion must originally be polytheistic, and could not be derived from "a contemplation of the works of nature" such as we find in the design argument, because then they would have been monotheists. (But, on the other hand, this argument also doesn't seem consistent with Hume's later views, as expressed in the Dialogues. Did he change his view? Or is the later expression a sign that this argument is not meant to be taken at face value? But how does one avoid taking it at face value while also not ruining the early argument of NHR?) In the passage from Part II of the Dialogues, Cleanthes gives the argument that will be criticized through most of the rest of the work. But, on the other hand, Philo repeatedly claims only to be criticizing Cleanthes's claim that this argument gives us insight into the nature of the deity; also repeatedly, he insists that he's not criticizing its ability to conclude to the existence of a deity. Yet Philo's summary of the argument in Part XII is clearly taken by him to give a very vague result -- he goes on to argue that the difference between the reasonable theist and the reasonable atheist is purely verbal! ("The Theist allows, that the original intelligence is very different from human reason: the Atheist allows, that the original principle of order bears some remote analogy to it.") Lots and lots of questions. But it's worth looking at Hume a bit on this point, because he is with Newton and Paley one of the three major architects of the design argument as we generally find it.