One of the most famous paradoxes in Macbeth is proclaimed by the witches in Act 1, Scene 1:
Fair is foul, and foul is fair. (I.i.11)
This statement by the witches is also a premonition or a foreshadowing of things to come. That which seems good (fair) is actually bad (foul). And that which seems foul is actually good. Moving forward in the play, when the witches give Macbeth the indication that he will be promoted (and eventually to king), this seems good ("fair"), but in the end this turns out to be foul.
Macbeth echoes this idea of the foul/fair paradox in Scene 3:
So foul and fair a day I have not seen. (I.iii.39)
Paradoxes continue in riddle form with the witches' premonitions about Banquo. "Lesser than Macbeth and greater" and then "Not so happy, yet much happier" (I.iii.68-69). They clarify these paradoxes by saying that Banquo will never be king but his sons will. Macbeth is unsure about these premonitions, stating in an aside that "This supernatural soliciting cannot be ill, cannot be good." (I.iii.141-42)
In Scene 5, Lady Macbeth asks the spirits to "unsex" her, thus making her (figuratively) more masculine, more (traditionally) one with power, authority, and the ambition to do what it takes to reach a position of power.