Let's begin with Hamlet's dilemma in Act 4: he is the heir apparent (second only to Claudius) and at the same time a murderer to be exiled. Faced with this paradoxical situation, Hamlet spews out ghoulish and misanthropic conceits about life and death. For example,
"The body is with the king, but the king is not with the body" (4.2.25)
In this line, Hamlet argues that Polonius's body shares the same fate as the ultimate fate of King Claudius's body even though Claudius, still alive, cannot join the fate of the dead Polonius.
"The king is a thing--of nothing" (4.2.26-27)
This is a very succinct example of a paradox even though this seems to reveal how low and abject Hamlet feels about life.
Hamlet implies that Claudius is alive for the time being but he is to be reduced to nothing eventually. When dead, all humans--"the fat king and lean beggar"--are subjected to be food for maggots according to Hamlet. This is a truly nihilistic worldview and we witness the nadir of Hamlet's soul (the rock bottom of his soul).
He was a scholar at the University of Wittenberg, the "mould of the [perfect] form" (3.1.153); however, he now wags his tongue at humanity saying "you are all food for maggots and no more." Hamlet's soul is so dark and bleak and a statement like this will surely guarantee a prison cell in Alcatraz or the Tower of London. Whew, this stuff is too explosive.
"Not where he eats, but where he is eaten. A certain convocation of politic worms are e'en at him. your worm is your only emperor for diet. We fat all creatures else to fat us, and we fat ourselves for maggots. Your fat king and your lean beggar is but variable service--two dishes, but to one table. That's the end." (4.3.21-26)
In this gruesome conceit, Hamlet does not lose a beat in making fun of Polonius: due to his political ambition, Polonius turns out to be the best food for political maggots. Hamlet continues to claim that maggots are on the top of food chain because they can choose to eat either the king or a common beggar. In a way, humans fatten themselves only to fatten maggots and nobody can avoid this common end. How "jangled, out of tune, and harsh" the former "rose of the fair state" has become (3.1. 158,152)!
On a different note, the phrase "[a] certain convocation of politic worms" utilizes a pun on "the Diet of Worms," a politico-religious assembly that was held in Worms, Germany, in 1521 to deal with Martin Luther's Reformation movement. "A certain convocation of politic worms" is not only a pun but also a historical allusion. In addition, "fat" as opposed to "lean" and "king" as opposed to "beggar" constitute an antithesis.
"Father and mother is man and wife, man and wife is one flesh, and so, my mother." (4.3.54-55)
Hamlet insists that Claudius is Gertrude because the marriage vow makes the husband and wife one flesh. One plus one is one according to the bible. So, this paradox is also a biblical allusion.
ghoulish: suggesting the horror of death and decay (a ghoul is an evil spirit that feeds on corpses)
misanthropic: hating mankind in general
conceit: a fanciful poetic image, especially an elaborate or exaggerated comparison
nihilism: the philosophical belief that nothing actually exists or that existence is meaningless