Does Hamlet have a preoccupation with philosophy, or does he just have an obsession with life and death turned into a philosophical form?
I don't think Hamlet is preoccupied with philosophy for philosophy's sake, he is just a thinker who contemplates his actions and the possible consequences of those actions. He contemplates fatal flaws, and looks inward and outward to assess those human weaknesses. He contemplates suicide and death because he is in circumstances that suggest those topics: his father's death/murder, his own thoughts of suicide, the need a avenge his father's death, his accidental murder of Polonius, and the death of Ophelia. There is no one philosophical truth or philosophy that Hamlet speaks of; he speaks in a thought-provoking (philosophical) way about the topics on his mind.
In my reading, there is little indication that Hamlet is at all interested in philosophy, although I'm not sure that we would all think of the same thing when using that word. He is obsessed with the fact that he KNOWS he should act, but that his personality, religious scruples (perhaps), and general character seem to make that impossible. He has many explanations about why he cannot act. For example, when he has a chance to kill Claudius at prayer, he comes up with the somewhat convoluted story that he doesn't want to kill him and send him to heaven (since he is at what appears to be prayer, but which isn't really prayer at all) because his father did not have the chance to repent before he was killed. He can't even bring himself to kill himself because of the "dreams that may come" after death ... another excuse (maybe a better one) for inactivity.
Again, in my reading there is no philosophy in this at all. I'll be interested in what other have to say.
The circumstances that Hamlet faces bring quite a few subjects before us. What philosophy or philosopher's work should we be looking for that Hamlet is not interested in? In Professor Greenblatt's widely noted book we find the suggestion that Hamlet is occupied with a spiritual crisis. Perhaps the perceived lack of interest on the part of Hamlet indicates that he simply doesn't like his job("Denmark's a prison") and that a kind of representative democracy would improve sanitation and spruce up the gardens in Denmark. The example noted in post #2 has been much referred to here lately("Now might I do it pat," Act 3, scene 3). One reason Hamlet passes up the opportunity is suggested in ROMEO AND JULIET: "God shield I should disturb devotion!"(ROM4.1). In the speech from the King that precedes Hamlet's we find an allusion to GENESIS and when Hamlet next encounters the King we find another: "Father and mother is man and wife, / Man and wife is one flesh"(4.3).