The problem is unsolvable in Hume's terms, not just for Epicurus but for everyone. There's nothing wrong with that--I actually think we're better off without absolute oughts, which is the same thing as saying that we're better off without absolute morality. If God commands you to sacrifice your firstborn, even allowing a God there is no absolute morality to say that you should follow his whims.
Why should we avoid things that cause pain? You might say, because Nature has given us pain a guide. Okay, why should we follow Nature? Because that is the surest road to the life of happiness. Okay, why should we pursue happiness? Because the happy life is the best of all possible lives. Okay, why do we want to live the best life? Because it's the most pleasant life. Why do we want the most pleasant life? Because it's the best life. Why--
--because I said so!
The problem is unsolvable in Hume's terms, not just for Epicurus but for everyone. There's nothing wrong with that--I actually think we're better off without absolute oughts, which is the same thing as saying that we're better off without absolute morality. If God commands you to sacrifice your firstborn, even allowing a God there is no absolute morality to say that you should follow his whims.
I think this is where I am personally happy to part ways with Hume, but before I travel down that road, the first question I always try to ask is "What did Epicurus think?" Not because I am automatically going to defer to Epicurus, but I am always extremely curious to know his position before I decide whether I am agreeing with it or not. I "think" that I can predict that Epicurus would part company with Hume, but I would be happy to entertain any suggestions that he would not.
But back to the personal part:
I personally am willing to go with an authority on something, like I go with a brain surgeon when I need brain surgery, IF I can first check out the thing in which I am placing my confidence and if I decide that it is worthy of confidence. In the case of "Nature" as a guide I tend to see Hume's infinite regression of "why's" as akin to Democritus' apparent infinite regression to "nothing truly exists except matter and void" and to me that way lies nihilism and despair and the abyss. [Thanks to the Sedley article which describes it better than I can] it appears to me that Epicurus rejected Democritus' radical atomic reductionism, and I am thinking he would reject Hume's reductionism for analogous reasons. At some point you have to make a practical decision to "live," and that point is where we "trust the senses," which amounts to "trusting what Nature gave to us" for survival.
Quote from David Sedley, Epicurus' Refutation of Determinism, p 33In confirmation of this, we can return to the close and apparently conscious parallelism between Epicurus' treatments of determinism and scepticism. The sceptics refuted in Lucretius IV must be, or prominently include, those fourth-century Detilocriteans like Metrodorus of Chios, Anaxarchus, and even Epicurus' own reviled teacher Nausiphanes, who had played up the sceptical side of Democritus' thought, and against whom Epicurus was eager to marshal the positive empiricist arguments which Democritus had also bequeathed.39 This scepticism was the result of what I shall call reductionist atomism. Because phenomenal objects and properties seemed to reduce to mere configurations of atoms and void, Democritus was inclined to suppose that the atoms and void were real while the phenomenal objects and properties were no more than arbitrary constructions placed upon them by human cognitive organs. In his more extreme moods Democritus was even inclined to doubt the power of human judgment, since judgment was itself no more than a realignment of atoms in the mind XXX. Epicurus' response to this is perhaps the least appreciated aspect of his thought. It was to reject reductionist atomism. Almost uniquely among Greek philosophers he arrived at what is nowadays the unreflective assumption of almost anyone with a smattering of science, that there are truths at the microscopic level of elementary particles, and further very different truths at the phenomenal level; that the former must be capable of explaining the latter; but that neither level of description has a monopoly of truth. (The truth that sugar is sweet is not straightforwardly reducible to the truth that it has such and such a molecular structure, even though the latter truth may be required in order to explain the former). By establishing that cognitive scepticism, the direct outcome of reductionist atomism, is self-refuting and untenable in practice, Epicurus justifies his non-reductionist alternative, according to which sensations are true and there are therefore bona fide truths at the phenomenal level accessible through them. The same will apply to the XXX, which Epicurus also held to be veridical. Pleasure, for example, is a direct datum of experience. It is commonly assumed that Epicurus must have equated pleasure with such and such a kind of movement of soul atoms; but although he will have taken it to have some explanation at the atomic level, I know of no evidence that he, any more than most moral philosophers or psychologists, would have held that an adequate analysis of it could be found at that level. Physics are strikingly absent from Epicurus' ethical writings, and it is curious that interpreters are so much readier to import them there than they are when it comes to the moral philosophy of Plato or Aristotle.
(I haven't gone back and got those pesky Greek letters in my computer yet, thus the "XXX's" )