What is the paradoxical nature of The Tempest?

The Tempest is one of Shakespeare's most well-loved but also most unusual plays. Although classified in the First Folio as a comedy, it does not have the light hearted tone or the humorous situations apparent in most of Shakespeare's comedies, and also lacks the trademark situations (such as having women dressed as men) that are hallmark's of the playwright's comedic works. Neither is it a tragedy, for it is not full of battles, or political intrigue, or acts of violence or murder. The genre of the play is somewhat paradoxical, since it does not fit comfortably into any of Shakespeare's usual categories of comedy, tragedy or history. It is sometimes referred to as a "tragicomedy" as is another of the Bard's later plays, The Winter's Tale.

It's set in a place that appears to be far removed from the rest of the world. It is also described and portrayed as a kind of utopia, or idealized society characterized by justice, harmony and equality. In Thomas More's writings on Utopia, the idealized society is a place where wealth and resources are shared equally. What is paradoxical about this play's so-called utopian setting and its vaunted idealism is that one of the main characters, Caliban, is a slave who is shunned and ostracized for being an ugly monster. Ariel, too, the sprite who is a servant to Prospero, is also somewhat enslaved and wishes to be released from service. In an ideal society, there would be no slavery or indentured servitude. This forced service is one of the main paradoxes present in the play.

As for equality, women in this place are not treated as equal members of society. Prospero's daughter, Miranda, is kept sheltered from men by her father. In fact she has never seen young men prior to their arrival after the storm, upon which she says "O, brave new world, that has such people in it."

The novel Brave New World by Aldous Huxley, which takes its title from Miranda's words, is a story of a Utopian society as well, though Huxley refers to it as a "negative Utopia" also known as a dystopia--in this way, that book is also a paradox, ultimately portraying a world that is the opposite of what its title suggests.