10/15 blog post:

After encountering his father's ghost and learning that he (Hamlet Sr.) did not die by the bite of the serpent, but rather by the hand of his own brother.  He most likely was killed because his brother was tired of playing second fiddle and saw murder as the only way to clear the path for himself.  Hamlet knew from the start that something was off about his uncle and stepfather from the moment when Claudius said that he could call him "dad".  Hamlet's father's obsession with the term incest and incestuous stems from the fact that his former wife is now "in love" with his brother and that every smile in which Claudius sports is artificial and should not be taken seriously.