A literary paradox is a seemingly contradictory statement or situation which, upon further thought or investigation, nevertheless makes sense or contains elements of truth in the context in which the statement or situation occurs.
The first paradox in act 1, scene 1 of Shakespeare's Macbeth is the appearance of witches themselves, who might or might not exist. In Shakespeare's time, witches and the supernatural were absolutely believed to exist, so the paradox isn't as pointed or apparent to the Elizabethan audience as it might be to a modern audience.
In this first scene of the play, in only twelve lines, Shakespeare establishes for the audience the "world of the play." The world of Macbeth is one which accepts witches and the supernatural as essential elements of the play. The witches often speak in enigmatic, contradictory terms, and events and characters in the play are not always as they appear.
SECOND WITCH. When the hurlyburly's done (1.1.3).
In terms of a singular, isolated instance of disorder, noise, confusion, chaos, or, in this frame of reference, a battle in a war, "hurlyburly" is a self-contained incident, with a beginning and an end. In terms of the continuing conflict and struggles of life, however—particularly the daily struggle for existence that most of the population experienced in Elizabethan times—the "hurlyburly" never seems to end.
In Henry IV, Part 2, Shakespeare uses word "hurly" to describe a storm at sea as a metaphor for a storm in his mind that won't let him sleep (3.1.25). In the context of the opening scene of Macbeth, "hurlyburly" can also mean a storm, which contains the elements of thunder, lightning, and rain to which the First Witch refers in the preceding line.
SECOND WITCH. When the battle's lost and won (1.1.4).
This statement seems contradictory in that a battle cannot be both lost and won, but only if applied to one or the other of the opposing forces. However, if applied to both forces, one force can be the winning force, and the other can be the losing force.
Also, one of the forces might win the battle, but the effects of the victory might be devastating to that force in terms of loss of life, or within the social, economic, or political context of the battle or the war.
"Fair is foul and foul is fair" (1.1.11) is the most famous paradox, if not the most famous line, in Macbeth. Many, many books and articles have been written about this single line. This enigmatic line, like everything else that happens in the first scene of the play, helps establish the world of the play, in which appearances can be deceiving, and nothing is as it seems.