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What is the paradox in scene 3 of "Macbeth": "Lesser than Macbeth, and greater"?

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The paradox in Scene 3 of "Macbeth," "Lesser than Macbeth, and greater," highlights the contrasting fates of Macbeth and Banquo. Banquo is "lesser" in power and status since he never becomes king, but "greater" in moral integrity and legacy, as his descendants inherit the throne. This duality reflects Banquo's principled nature versus Macbeth's ambition-driven downfall, emphasizing that true greatness transcends immediate power.

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The paradoxical difference between Banquo and Macbeth extends beyond present circumstances. Macbeth's dearest wish is to gain the throne for not only himself but for his heirs as well. The idea of getting the throne merely to pass it on to someone else's family is infuriating to him--one of his motivations for murdering Banquo is that he does not wish to send himself to Hell just to benefit another's family line.

However, when Macbeth presses them, the witches tell him that this is exactly what he is going to do. The paradox is that Banquo will be "lesser" than Macbeth in that he will never himself be King of Scotland. In fact, Banquo is now nothing but a corpse in a ditch. However, his heirs are destined to become kings of not only Scotland but of the England of Shakespeare's time. Remember what the witches later show Macbeth in...

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Act IV, scene 1, Macbeth's second and last interview with them:

All Witches
Show his eyes, and grieve his heart;
Come like shadows, so depart!
[A show of Eight Kings, the last with a glass in his hand; GHOST OF BANQUO following]MACBETH
Thou art too like the spirit of Banquo: down!
Thy crown does sear mine eye-balls. ...
[...]
Another yet! A seventh! I'll see no more:
And yet the eighth appears, who bears a glass
Which shows me many more; and some I see
That two-fold balls and treble scepters carry:
Horrible sight! Now, I see, 'tis true;
For the blood-bolter'd Banquo smiles upon me,
And points at them for his. (IV.i)

The "two-fold balls and treble sceptres" are the sign of one monarch ruling both England and Scotland. 

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A paradox is a contradictory statement that expresses a truth.  The witches are contradicting themselves.  They say that Banquo is both lesser and greater than Macbeth.  How can both be true?  It would seem that they couldn't be - however, let me show you how they are.

Banquo is "lesser" than Macbeth in terms of power.  He does not have the political power that Macbeth has and will continue to get - Banquo is not a thane.  Also, there is every suggestion that while he is a powerful general, he is not as powerful as Macbeth.  King Duncan rewards Macbeth, not Banquo, for service.

However, Banquo is "greater" than Macbeth because he is both smarter and more grounded in his principles.  Banquo does not trust the witches or their prophecies, which turns out to be the better judgement - it is trust in the prophecies that brings Macbeth down.  Banquo immediately suspects Macbeth of the murder, knowing his friend well.  He does not rush to seek out his own power, like Macbeth did, when the prophecies seemed to be valid.  Finally, Banquo dies while trying to protect his son, encouraging Fleance to flee.  Macbeth pays little attention to Lady Macbeth as she slowly slids into insanity and dies - he is too focused on himself.

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This paradox is a reference to the fact that Banquo was the historical descendant of King James, who was the ruler of England at the time that William Shakespeare wrote and produced the play Macbeth. Although Banquo will never be king or rise above the position he already has (unlike Macbeth, who will become king of Scotland), his descendants will eventually become royalty. Macbeth and Lady Macbeth never have children, which is a huge problem for them and for noble society in general. There is at one point a reference to an infant that might have died, but besides that, Macbeth is fated to die childless. This means that his throne will not be passed on to those of his line/blood, which is a big deal. 

On the other hand, Banquo's bloodline will continue on, and prosper. Later in the play when Macbeth hires murderers to kill Banquo and his son, Banquo dies but his son Fleance escapes. The audience is to presume that Fleance's escape is a direct reference to King James's ancestry. Macbeth is upset by this because he fears that the prophecy will come true--that he will never have children to carry on his blood and name, but that Banquo's kin will become kings. 

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In Act 1, sc.3, Banquo and Macbeth, on their way home from battle, encounter the three weird sisters on the heath.  They hail Macbeth calling him Thane of Glamis, Thane of Cawdor, and King.  These are predictions of Macbeth's future.  Banquo tells them that if they can look into the future, then they should tell him what his future holds.  They hail him and say, "Lesser than Macbeth, and greater."  They go on to say that he won't be king (lesser than Macbeth), but he will be the father of kings (greater) - "Thou shalt get kings, though thou be none,".

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