This is going to be a bit off-topic, at least in the context of my previous posts.
I was watching a production of Ambroise Thomas’ opera, Hamlet, recently.  It called to mind the first essay I was assigned to write after starting CEGEP.  I was taking a class on Shakespearean tragedies, and we were asked to take and defend a position on the question, “was Hamlet insane?”
I recall being a bit perplexed by the question itself, but I did write something.  I don’t recall now what position I took, that isn’t really the point of this posting.  However, when I ponder the question itself, now, many years later, I really don’t think I’d be able to write on this topic without a lot of research.  If I were posed this question now, it would be a much more involved assignment, and would take a lot longer to answer.  I might, in fact, have to answer with the substance of this posting, rather than taking a position on the question of Hamlet’s sanity.
Before continuing, I’ll say that phrasing a question so broadly is a bit awkward.  What, precisely, does one mean by “insane”?  Are we talking about a specific psychiatric diagnosis, or something less well-defined?  In what follows I will assume that we have settled on a particular meaning for the word as used in the question posed by my professor.
So, why is this question difficult for me to answer now, when I was able, as a teenager, to produce several pages of arguments?  No doubt my outlook on the world has changed, it’s been a long time, and people change.  I’ll describe the way I look at this problem now, as a no-longer-teenager.
First of all, I do enjoy works of fiction.  Books, movies, television shows, they keep my attention, and I focus on them while watching/reading.  However, I do always know that such things are fiction.  One or more writers sat in a room and created the story out of whole cloth.  I am more likely to be affected by the sight of somebody’s cut finger in the real world than a traumatic injury in a fictional television show, because I know that the latter is not a real event, an actor is portraying the injury with the help of a special effects team, and at the end of the day that actor will return home having suffered no harm.  In that respect, I somewhat sympathize with the position of the character Chandler on the show “Friends”, who said, somewhat indignantly, that Bambi’s mother didn’t die, they simply stopped drawing her.
So, with that introduction, we come to the issue that I think was perplexing my younger self, but which I couldn’t really pin down in words at the time.  The character of Hamlet is a fictional creation, whose actions and behaviours were imposed by William Shakespeare.  The actions of the characters in the play are not those of sentient creatures, but are driven by the dictates of the plot and the historical setting that Shakespeare is trying to present in the play.
Every year or two there will be a newspaper story about some group of researchers who declare that a certain historical figure, dead a thousand years or more, suffered from this or that undiagnosed malady, and they offer as evidence some small set of collected descriptions or writings that they assert proves their claim.  While one may find issue with specific instances of these announcements, the researchers are writing about real people, who interacted with other people in the world, and left traces.  There are objective facts about these people, from which one might be able to draw conclusions.
Fictional characters, such as those in the play “Hamlet”, don’t have those interactions with reality.  When they are not on stage, they don’t exist, except as required by the logical continuity of the plot in which they find themselves.  If nothing in the story hinges on what Polonius had for breakfast a week before the opening scene, then one cannot reasonably expect to “discover” what he had for breakfast, because the character is in a sort of limbo, existing only as dictated by the logic of the story.  We know that, years earlier, he had a daughter, because she exists in the play, but we don’t know about things that are not explicitly derived from the text of the play.
So, we come to the question of Hamlet’s sanity.  There are three possible positions one can take.  He was sane, he was not sane, or his sanity is unknowable.  The answer lies, first and last, in the mind of William Shakespeare.  When he was writing the story, he knew the answer to that question.  He could then choose to write the story to communicate the idea that Hamlet was sane or insane, or he could choose to make the story deliberately ambiguous on that point, allowing the audience to ponder the question but not supplying enough information to allow a definite determination.  Think of the end of the Arnold Schwarzenegger version of “Total Recall”.  There was chatter on the SF Usenet groups discussing the question of whether or not the entire story was an implanted memory, where the character in the story never went to Mars, and in fact never got out of the fancy chair.  My position on this question is that the filmmakers deliberately left it an open question.  There’s no way to determine which is the “actual” answer, because there is nothing outside of the screenplay, and the writers want the answer to be “I don’t know”.
To my thinking, then, the question of “was Hamlet insane?” comes down to asking to know the mind of the author.  We have to read the text, and take our cues not from the actions of the characters but in the way the author chose to depict them.  Don’t think “why did Ophelia say that?”, she didn’t.  Think, instead, “why did Shakespeare choose to have Ophelia say that?”  The play underwent several revisions, we can assume that the rewrites would at least have allowed Shakespeare to communicate the most important points of the story to his satisfaction, and the question of the sanity of Hamlet certainly would be one of those important points, as it is raised several times by characters within the play.  If characters are wandering around asking each other if Hamlet is insane, one hopes that the playwright pondered the issue himself, and that the text of the play communicated, to his satisfaction, the answer that he wanted to convey to the audience.
Fine, so how does one go about knowing the mind of the author, as he is currently unavailable for interviews?  This is where this stops being a CEGEP homework assignment and becomes something more like an English major’s university project.
We have a playwright, and we have his contemporary audience.  Shakespeare was not writing for the modern audience, of course, so the way he wrote was to communicate his thoughts to those living in the same time.  Shakespeare’s depiction has to be examined in the culture of the time.  To begin, the play is based on a story, already hundreds of years old by Shakespeare’s time, of “Amleth”.  How much did the Elizabethan theatre-going audience know about that story?  Was the title character in there famously known to be insane?  If so, Shakespeare need do little more than demonstrate questionable behaviour by Hamlet, and the audience would fill in that yes, the character of Hamlet was insane.  But if that was not the popular understanding of the time, then it does little to illuminate the question.  There may be other cultural cues that I haven’t thought of, but I’m a physicist and not an English major, and I haven’t done this research, I merely point out where I think the research has to go in order properly to address the question.
After looking at the cultural context, we go on to the play itself.  The characters were written around the end of the 16th century, but one imagines they might have behaved anachronistically, saying things or behaving in ways that were not appropriate for Denmark of hundreds of years earlier.  The story was written for the Elizabethan audience, the members of which had their own cultural cues defining eccentricity and insanity as they would have experienced it and talked of it in England of the time.  Certain phrases, gestures, or reactions of the character might have communicated sanity or insanity quite unambiguously to the audience of the time, but a modern reader, not steeped in the culture, might miss those cues entirely, introducing ambiguity where none was intended.  To address this question, one would have to perform a quite lengthy examination of the popular perception of insanity at the time, both in reality, the pub gossip of the time, and in popular fiction of the era, to look for any literary shorthand that might have commonly been used to convey the concept of insanity.  After this research was performed (I hesitate to say “completed” because this sounds like a project that one could never truly decide was finished), the play would be re-examined in the context of this new understanding, to see if there were any unambiguous markers in the play.
Having examined the play, our journey into the mind of William Shakespeare would now go to his other works.  We would examine characters throughout his plays, ones in which insanity is unambiguously manifest, starting with Ophelia but not restricting ourselves just to the one play.  We would learn how Shakespeare developed his insane characters in his works, and how he depicted them as progressing.  We could then look at the character of Hamlet once again, and say that Shakespeare’s writing style strongly suggests that he was sane, or insane, or maybe progressing toward insanity, or, once again, we might decide that it was ambiguous, that Shakespeare has not given us a clear answer to the question.
There’s at least one more avenue of research that I believe ought to be followed.  One would have to research the reviews and discussions of the play Hamlet as it was being performed, while it was still susceptible to being edited by Shakespeare.  What did the reviewers say about the character of Hamlet?  What did people say about it at the pub?  Were there letters to the local newspapers that touched on the topic of Hamlet’s sanity?  Basically, what can we learn about what the contemporary audiences got out of the story?  If it was ambiguous to them, at a time when William Shakespeare would have known their reactions and been able to edit the play to better communicate his position, then I think we can say with some confidence that he deliberately wanted the character’s mental health to be ambiguous, and anything we might say, as modern teenagers in a CEGEP English class, has very little weight compared to that.
So, there we are.  If a professor asked me that question today, I don’t think I could submit any response I’d be happy to hand in without doing a lot of tedious research with dusty books in old libraries.  It’s not something I would throw together on a typewriter in the week before it was due.