Key lines to look at: 9.164-180, 9.882, and Blamires’ summary is extremely helpful.
It takes a great deal of explanation to get to Hamnet Shakespeare, and it is almost certain I will get some of this wrong. Essentially, understanding who Hamnet is, and the timeline of William Shakespeare’s own life is integral to understanding Stephen’s argument that Hamlet is his own father. This explains why I wasn’t able to follow the argument before.
First, Hamnet Shakespeare was William Shakespeare’s only son, who died in 1596 at the age of 11 of unknown causes, and Hamlet was written after Hamnet’s death, which is important for the purposes of Dedalus’ argument. Also, William Shakespeare’s own father had died at the time of his writing Hamlet. More background is that Stephen states at one point that William Shakespeare played the ghost of Hamlet’s father in his own production of the play. Now, forward to Stephen’s theory. Stephen argues that Hamlet in the play is at once both Hamnet and William. While it’s pretty clear that Hamnet can be Hamlet just by the names, the latter is the less obvious, but Stephen’s theory rests on the fact that William is at the time of writing the play a fatherless son. So, with Stephen having established Hamlet as both Hamnet and William, we see the first way in which Hamlet is his own father. Then, there is the point that Stephen brings up that William plays the ghost of Hamlet’s father in a production of the play, and since William put himself into the character of Hamlet, Hamlet is once again his own father by way of the transitive property. Additionally, William as creator of the play itself takes on the role of Creator, which means he is a Father (in a Christian sense as well) to all the characters in the play, including Hamlet and the ghost. Finally, when William’s father died, William took up the role of Father to all the generations of his family past and to come (thus Shakespeare is his own father as well). Key to this last very confusing part is the question: if a father with no son cannot be a father (by definition), is a son without a father (Hamlet, William after their respective father’s deaths) truly a son? William is in limbo when he writes Hamlet – he is neither father (Hamnet is dead) nor son (his own father is dead), and so he assumes the role of father to his whole lineage. So confusing, no wonder even Dedalus doesn’t believe in his own argument.