Dating back to the time of which Hamlet’s story took place, a King’s adviser was supposed to be a trustworthy figure. If the adviser was deceptive or misleading, he was killed.
Polonius, the King’s adviser in Hamlet, hires Reynaldo to spy on his son Laertes:
“By indirections find directions out: So, by my former lecture and advice, Shall you my son.”
Not only is Polonius giving the order to make up lies about his son, he clearly has no trust in his son and doesn’t respect his privacy. Is it possible to trust a man who is spying on you?
The very act of having Polonius as the King’s adviser in the play is paradoxical because of this. However, although paradoxical things are generally out of place, it seems to fit perfectly with the plot of Hamlet. The existence of a Ghost, based on the Elizabethan belief, indicated that something was fundamentally wrong with reality.
Why shouldn’t Polonius be anything but a normal adviser to the King?