In act 4, explain the paradox of the apparitions.

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The apparitions further illustrate and emphasize the theme of equivocation and paradox. The witches use supernatural forces to further their purpose of misleading and deceiving Macbeth into committing further atrocities. They have been successful thus far and are intent on convincing the tyrant that he is invincible so that he...

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The apparitions further illustrate and emphasize the theme of equivocation and paradox. The witches use supernatural forces to further their purpose of misleading and deceiving Macbeth into committing further atrocities. They have been successful thus far and are intent on convincing the tyrant that he is invincible so that he may continue his evil.

When Macbeth visits them for further advice, they summon apparitions to advise him. The first spirit tells him to fear Macduff. This piece of information indicates nothing new since Macbeth knows that Macduff has turned against him. The witches' purpose is to show Macbeth that they know of what they are speaking. In the process, they further endear the gullible tyrant to them.

The second apparition, a bloody child, tells Macbeth to mock man's power for "none of woman born" shall harm him. At this, Macbeth sneers at Macduff's threat because he believes that the prophecy states that no human will be able to harm him for all humans are born of women. He realizes how foolish he had been when, in his confrontation with Macduff in Act 5, scene 8, the latter informs him that he was from his mother's womb "untimely ripp'd." It is clear that Macduff has not been born naturally but was cut from his mother's womb in a procedure now known as a Caesarean section. 

The third apparition, a child crowned, with a tree in his hand, informs Macbeth that:

Macbeth shall never vanquish'd be until
Great Birnam wood to high Dunsinane hill
Shall come against him.

This information further convinces the murderer that he is invincible. He interprets the prediction literally and believes that the trees will have to uproot themselves and march towards his castle physically. This is clearly impossible. Macbeth is shocked later when a messenger tells him in Act 5, scene 5, that the trees are marching towards his castle. Malcolm has instructed his troops to each cut down a branch from a tree and bear it in front of them as camouflage to hide their numbers. When Macbeth realizes this, he declares:

I pull in resolution, and begin
To doubt the equivocation of the fiend
That lies like truth:

He now grasps that the witches have deceived him with paradoxical statements.

The witches have achieved their purpose by fooling Macbeth into believing their prognostications and performing terrible acts of evil. Banquo warned Macbeth about their deceit and slyness, but he chose to ignore his advice deciding, instead, to assassinate his friend and confidante later. In the end, both he and his wife pay the ultimate price for their greed and gullibility. Sadly, though, many innocents also become victims of their malice.

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The paradox of the apparitions occurs in how Macbeth views what they show him and how the audience views their predictions. Macbeth needs to quell his fears that doom is upon him, so he takes the visions at face value. To the audience, the apparitions are symbols that foreshadow how the prophecies will be fulfilled. The armored head suggests war or rebellion, while the bloody child obscurely refers to Macduff's cesarean birth. Macbeth takes the comment at face value, and therein lies the irony. The crowned child is Malcolm and refers to the tree branches his soldiers will carry from Birnam Wood. The procession of kings reveals the future line of kings, all descended from Banquo.

Macbeth believes only what he feels will benefit him. He can no longer make rational judgments, and Hecate knows this. The contradictory nature of the apparitions will go right over Macbeth's head, and he will take from the apparitions only what he wants.

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When the apparitions (the weird sisters) reappear in Act IV, they come, unbeknownst to Macbeth, with more malevolent intentions. Hecate, the head of the witches, has appeared to the weird sisters since they delivered their prophecies to Macbeth. She has scolded them for treating a human being too kindly, telling them that Macbeth does not have the witches' interests at hearts. This time, therefore, they are under orders to deceive him, and they do so by making misleading and paradoxical prophecies.

For example, they tell him that no man born of woman can defeat him. Macbeth takes this to mean that he won't be defeated, as every man is inevitably born of a woman. However, the witches are defining birth more narrowly, excluding those born by Caeasarian section. The witches also prophecy that:

Macbeth shall never vanquished be until
Great Birnam Wood to high Dunsinane Hill
Shall come against him.
To Macbeth's mind that can't be because the trees can't uproot themselves and move to Dunsinane Hill. Of course, when the soldiers pull down branches from the trees at Birnam Wood as camouflage and take them to Dunsinane, the trees do, in a way, move.
Through paradoxical prophecies, the witches mislead Macbeth and help lead him to his doom.
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In Act IV, Scene I, when the apparitions appear before Macbeth, there are a couple of instances of paradox (a statement that seems silly or illogical but may, in fact, have some truth to it).

First of all, the second apparition tells Macbeth to laugh at the power of other men because nobody "of woman born shall harm" him. This statement seems illogical because everybody is, technically, "of woman born" since everyone has a mother. Macbeth takes this statement at face value, believing that he truly cannot be harmed by anyone. Later, it is discovered that this paradox has some latent truth when the reader learns that Macduff was not born naturally but was "ripped" from his mother's womb in a caesarean section. By taking this statement at face value, Macbeth fails to realize the danger posed by Macduff.

Another example of a paradox comes with the third apparition who tells Macbeth that he shall "never be vanquish'd" until Great Birnam Wood "comes against him." Again, this seems illogical because the woods cannot literally get up and march, and Macbeth comes to this same conclusion. This leads him to believe that his crown is safe. However, there is some truth to this statement since it is not the trees that march against him, but his enemies who congregate at Birnam Wood before marching on his castle at Dunsinane.

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The apparitions are paradoxical on a few levels. First of all, Macbeth projects all his fears and hopes into the apparitions. He is fearful of losing his crown; he is fearful of being overthrown; and he is fearful of his lineage not ruling Scotland. The apparations' predictions, paradoxically can never occur, yet they do. We know that the trees move up the hill because the soldiers use them for cover. Macduff defeats Macbeth as he is not naturally from woman born. Lastly, Banquo's line inherits the throne. So, what seems impossible becomes all too possible, and perhaps even more important, it is Macbeth's utter belief in the apparitions that leads to his death

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