According to Wikipedia, which I grant isn't always a reliable source, William James believed that truth is what is useful. To me that just sounds stupid. Certainly truth is not just whatever is useful. Should I be so dismissive or is there more to his theory of truth to be appreciated?

Oh, where to begin! Yes, James said this; no, it is not the case that James was stupid and it would be a travesty to dismiss James! But Lordy, have you stepped into a huge question- it is no wonder the Wiki-machine makes it sound so simplistic. Scholars of James, Peirce, and Royce (to name a few) make their livelihoods debating this particular question and I think it safe to say that you will not find consensus among them. Heck, at a table of four James scholars, there will be at least 5 opinions! [A great James scholar I know answers any question about James' thought with the caveat "Well, it's very complicated."] As a reader of classic American philosophy, with a deep regard for James, I confess I am at a loss to reply in simple terms - and will delight in the responses of others who go where I fear to tread. I am most familiar with Royce and therefore I offer this humble suggestion: if you wish to get a very quick course in James, you might start with his Lowell Lectures of 1907...

Hume stated that there is a gap between "is" and "ought." What about hypothetical imperatives? For example, it seems that, given a certain state of the material world, if I want to arrive on time for a certain meeting, then I ought to leave the house before, say, 8 AM. Did Hume's statement make room for such constructions, or does he not believe that the premises of hypothetical imperatives justify their normative conclusions?

A bit more information would help me in answering your question. The "gap" you mention between what is and what ought to be the case seems to permeate practical philosophy down to the ancients. Are you citing a particular passage in Hume? As for hypothetical imperatives Kant comes to mind; he suggests that the term "ought" in this sense is not normative language at all but addresses our freedom to let desire have a role in choices (hence the hypothetical part). The moral sense of "ought" for Kant is categorical, and he is well aware of the gap between the is and the ought. So I guess I'm needing to have a text - or a Hume expert to reply - before I can get the gist of your question.

According to the Stanford Encyclopedia of philosophy Schopenhauer was one of the first philosophers to advocate for the idea that the universe was not something "rational" What is an "irrational" universe then? Is there a difference between a universe being beyond the grasp of human reason and saying that the universe is "irrational"? Does he mean to say that the universe can do things that are illogical such as have square triangles?

It's been years since I've read Schopenhauer, so I cannot respond with his position as such. What I am noticing is that you seem to have excluded other possibilities by assuming that if the universe is not rational it must be irrational. What about non-rational, for example? No squared circles needed! If we posit that rationality is a capacity of human consciousness - and a mysterious thing consciousness is - what might it mean to call the universe "rational?" Are we saying it is conscious? Does the analogy to human consciousness hold sufficiently to apply to the vast universe? There might be human minds that see order and disorder and apply rational principles to their observations, but it is quite another thing to ascribe rationality to ... what? The universe is one of those concepts that is not a reality one can experience. Perhaps we can thank Schopenhauer (and his 19th century counterparts) for helping us see our anthropomorphizing for what it is. Does this help? -bjm