First Strategy: There is a difference between a regular and an irregular argument, and Philo accepts the irregular inference (but not the regular one, which he has been criticizing).
Second Strategy: Philo affirms the premises of the regular argument, but draws a conclusion that is so attenuated it avoids the objections he had raised.
Third Strategy: Philo accepts the existence of an intelligent designer on a different regular argument than the one he criticized.
Bednar, who thinks all three of these fails, proposed a fourth strategy, which takes elements from the first two strategies, and argued that Philo balances arguments for and against the intelligent designer, and finds that the arguments for, although very weak, slightly overbalance the arguments against, which are also weak.
Since I am a solid Second Strategy man, I'll be defending the Second Strategy from its rivals. I'll start with the claim that Philo accepts an irregular design argument.
The distinction between a regular and an irregular design argument derives from a statement made by Cleanthes in Part III:
Some beauties in writing we may meet with which seem contrary to rules, and which gain the affections and animate the imagination in opposition to all the precepts of criticism and to the authority of the established masters of art. And if the argument for theism be, as you pretend, contradictory to the principles of logic, its universal, its irresistible influence proves clearly that there may be arguments of a like irregular nature. Whatever cavils may be urged, an orderly world, as well as a coherent, articulate speech, will still be received as an incontestable proof of design and intention.
So Cleanthes here suggests that even if the design inference violates the rules of argument (and thus is 'irregular'), its psychological role is still such that pretending one can simply eliminate it is absurd. He has in mind the skeptic in particular. A true skeptic on Cleanthes's (and Philo's, and Hume's) view is not one who excludes all argument or reasoning (which, Cleanthes notes, is "either affectation or madness") but rather someone who rejects abstruse and metaphysical arguments, preferring instead to adhere to common sense and instincts of nature. Cleanthes points out that the skeptic on this point should therefore accept the design inference, which is a sort of instinct of nature. Even if the skeptic is right and the inference is not in perfect logical order, it is still the natural inference, and thus not something the skeptic can just reject (on the view of skepticism shared by Cleanthes, Philo, and Hume). Note that Cleanthes does not say the skeptic is right, nor even that the skeptic could possibly be right. What he is doing is putting the principles in a particular order. If a firm opponent in determinism were to say, for instance, "If we are determined, we are nevertheless morally responsible," it does not follow that he is admitting the truth of compatibilism. What he is more likely doing is insisting on the primacy of the principle of moral responsibility (e.g., as a first principle or axiom). It could very well be the case that he thinks the falsity of determinism follows with logical necessity from this principle; what he is doing, however, is putting the principle of moral responsibility forward as somehow more undeniable. I think this is what Cleanthes is doing here: he is not admitting that the argument is irregular; he is insisting that even if it is irregular, Philo still would have to accept it.
But the issue isn't whether Cleanthes accepts that it is irregular, but whether Philo does. And we need to be clear here. What we need to ask is not whether Philo accepts "the irregular argument" but whether he holds that the design argument is irregular. There aren't two different design arguments (or two sets of design arguments) on the table, one of which is regular and one of which is irregular; there is one design argument (or one set of design arguments) on the table, and the question is whether Philo takes that argument to be regular or irregular. There is no question, also, as to whether Cleanthes is right. If the argument is irregular, given that Philo shares Cleanthes's characterization of the skeptic he professes to be, Philo must accept the argument. And this is confirmed by the fact that Philo, shortly after Cleanthes finishes, is "a little embarrassed and confounded". But it does not follow from this that Philo in Part XII thinks the argument irregular; it only follows that up to Part III, Philo over-extended his argument, and was resoundingly trounced by Cleanthes because he was inconsistent. After Part III, of course, there are quite a few more parts, in which Philo resumes his argument and (presumably) stays within its bounds. Whether the argument is regular or irregular, it will have the same force, so Part III doesn't actually tell us what Philo's view is. So the question needs to be: in Part XII, does Philo say anything that clarifies whether he regards the argument as regular or irregular?
It is fairly clear in Part XII that Philo treats the argument as regular. In fact, he says:
Now, according to all rules of just reasoning, every fact must pass for undisputed when it is supported by all the arguments which its nature admits of, even though these arguments be not, in themselves, very numerous or forcible: How much more in the present case where no human imagination can compute their number, and no understanding estimate their cogency.
This seems to me as much as an admission that Philo regards the argument as a regular argument. And this is confirmed by what Philo says later: "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" (my emphasis). (There is one possible counter-indication, which I will discuss below.) It is worth noting, too, that these passages cut against Bednar's strategy as well: Bednar's strategy requires us to conclude that Philo regards the design argument as weak, whereas here he very clearly says it is very strong. Indeed, this is not surprising, because Philo closely connects the design argument with scientific progress:
A purpose, an intention, a design strikes everywhere 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.
This is a strong passage; but it is even stronger than it might look. That nature does nothing in vain is the foundation for Newton's First Rule of Reasoning; the reference to the Copernican system seems to be (as suggested by elsewhere in the Dialogues) a reference at least in part to Galileo; the reference to the anatomist may well be a reference to Harvey. Newton, Galileo, Harvey: what Philo is saying is that modern science rationally presupposes the design inference. (And, indeed, this is but one of many passages in the Dialogues that makes clear that Hume's primary interest in the Dialogues is not so much philosophy of religion as philosophy of science. This isn't particularly surprising, either; in the seventeenth and eighteenth century, almost all philosophical inquiry about the ultimate foundations of scientific inquiry would have taken place while discussing 'natural religion'.) I will get to the way in which it presupposes the design inference in a moment. What I wish to make clear right now is that there can be no question that Philo sees the design argument as a very strong argument indeed, and there doesn't seem any way to say he regards it as a weak argument without violating the text.
This is all confirmed by the Humean analysis of analogy, which I have previously discussed. After Part III, all Philo's efforts are concentrated not on rejecting the analogy itself (which on Humean principles is impossible and on which ground Philo becomes confounded) but on arguing that the conclusion is obscure and uncertain. In essence, the argument is something like this: "Given (as we must admit) that the order of the world is in some way analogous to the products of intelligence, the order of the world must have a principle of order that is in some way analogous to intelligence. OK, but what do we get when we get this conclusion? Given our starting point, what do we know about this 'principle in some way analogous to intelligence'? Not much." Much of Philo's argument, in fact, is devoted to arguing that this label, 'principle in some way analogous to intelligence' can fit all sorts of scenarios; and that, given the limits of the origin, we can say nothing whatsoever about whether this principle has something in some way analogous to our virtue and benevolence (and indeed, Philo argues, all the evidence is that it does not). The existence of the intelligent-like principle of order is taken as certain; its nature, however, could be any number of things, because lots and lots of things are analogous to intelligence (pretty much everything is in some way analogous to it, in fact).
So the conclusion is 'attenuated' in the sense that it is little more than an existence argument: it argues for the existence of something under a very vague description, and Philo wishes to insist (and at great length) on just how vague that description is. Nonetheless, he clearly considers it a good argument, if we keep within its (very, very limited) bounds. For it is nothing else than an argument that there is some reason to think that the way the world works is amenable to intelligent inquiry. It allows us to say (without cant and without mere guess) that nature does nothing in vain, that nature operates according to general laws, and things like this. There is a natural principle of order, analogous in some way to intelligence, that makes the world to be ordered in a way that intelligence can to some extent understand. The world doesn't just happen to be this way (on Humean principles one could never say that something 'just happens' to be this way, because chance is not a cause but a word indicating that we do not know the cause yet); there is a cause of its being so. Analogy is extremely important to Hume's entire philosophical project (as I noted when I discussed his account of analogy) because it defines a base level of intelligibility. And the inference that Philo accepts defines the most general and fundamental base level of intelligibility, because it is about that intelligibility itself.
So on the one hand Philo insists that the inference is significant. On the other hand, he insists that some theists make too much of it. We see this in his claims that there is only a verbal dispute between the rational atheist and the rational theist (like Cleanthes):
I ask the theist if he does not allow that there is a great and immeasurable, because incomprehensible, difference between the human and the divine mind: the more pious he is, the more readily will he assent to the affirmative, and the more will he be disposed to magnify the dfference: He will even assert that the difference is of a nature which cannot be too much magnified.
This has to do with the vagueness of the conclusion that can be drawn from the argument. He goes on to discuss the atheist:
I next turn to the atheist, who, I assert, is only nominally so and can never possibly be in earnest; and I ask him whether, from the coherence and apparent sympathy in all the parts of this world, there be not a certain degree of analogy among all the operations of nature, in every situation and in every age; whether the rotting of a turnip, the generation of an animal, and the structure of human thought, be not energies that probably bear some remote analogy to each other: It is impossible he can deny it: He will readily acknowledge it. Having obtained this concession, I push him still further in his retreat, and I ask him if it be not probably that the principle which first aranged and still maintains order in this universe bears not also some remote inconceivable analogy to the other operations of nature and, among the rest, to the economy of human mind and though. However, reluctant, he must give his assent.
The rational atheist must give his assent because he cannot (while being rational and while operating on Humean principles) allow that there is no principle grounding the intelligibility of the world at all; and since there is going to some analogy, however small, to intelligence, he essentially must accept that the theist is right, to the extent that he claims that there is some natural principle of order in some ways analogous to intelligence and in some ways disanalogous. So they both accept this and cannot rationally go any farther on the subject. Their dispute, therefore, is merely verbal:
Where then, cry I to both these antagonists, is the subject of your dispute? 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.
The difference here, Hume makes clear in a footnote, is similar to the verbal disputes between rational dogmatists and rational skeptics about the foundations of science:
No philosophical dogmatists denies that there are difficulties both with regard to the senses and to all science, and that these difficulties are, in a regular, logical method, absolutely insolvable. No skeptic denies that we lie under an absolute necessity, notwithstanding these difficulties, of thinking, and believing, and reasoning, with regard to all kinds of subjects, and even of frequently assenting with confidence and security.
The atheist, like the skeptic, emphasizes the difficulties that are raised by the inference; while the theist, like the dogmatist, emphasizes the necessity of the inference itself. Other than that, if they are sticking to what they can actually argue about the inference, they are arguing over words. (The perceptive reader will notice that this is the one possible counterindication to my conclusion that Philo accepts the argument as regular rather than irregular. Whether one regards it as a counterindication, however, depends on how one relates it to the subject at hand. Is the dispute between the atheist and the theist just the dispute between the skeptic and the dogmatist in disguise? Then the argument must be irregular. Is the irregularity of the dispute over skepticism something that results from the fact that this is over the issue of reasoning in general, as I think it is? Then the two disputes are only analogous, and there is no reason to think the irregularity of the one implies the irregularlity of the other.)
To recap: The argument Philo accepts is regular (and thus the First Strategy fails), strong (and thus Bednar's strategy fails), and is the same argument all the way through (and thus the Third Strategy fails - I didn't devote as much attention to this strategy because Cleanthes and Philo both seem to treat the argument as being the same all the way through); it is a strong, regular argument, with a very, very, very vague conclusion. Philo's objections after Part III are merely meant to establish the vagueness of this conclusion; he gives up trying to attack the inference itself when Cleanthes points out in Part III that on his own principles he would still have to accept it even if the inference violated the principles of reasoning. Philo is confounded and embarrassed. Demea then immediately starts complaining about the conclusion Cleanthes would have to get from his inference, and thus saves Philo by turning the discussion to whether the conclusion of the inference is everything the theist (whether Demea or Cleanthes) really wants - and the result is that it doesn't get them very far even on the issue of intelligence (beyond proving that some principle of order in some way analogous to intelligence exists), and doesn't get them anywhere at all on the issue of the divine moral nature. This result is effectively what Philo affirms in Part XII, and (although I've only looked at one part of the evidence here) is entirely consistent with what Hume says elsewhere. The Second Strategy, then, is the best interpretation of the text.