What does the line "A dagger of the mind, a false creation, proceeding for the heat oppressed brain" mean in Macbeth?

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What this line means is that Macbeth is wondering whether the dagger he sees before him is real or just a figment of his overheated imagination. Macbeth is about to kill Duncan, and the fact that he's wondering whether his eyes are playing tricks on him is a sign that he's not in the right frame of mind.

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When Macbeth is on his way to murder the king—a good man who is also his relative, friend, and house guest—he hallucinates a dagger hovering before him in the hallway, pointing in the very direction in which he is heading. It is very realistic and quite similar to the dagger that he plans to use to murder Duncan, and he reaches out his hand to try and grasp it; when he cannot, it occurs to him that it is just a "fatal vision" (2.1.48). He calls it a "dagger of the mind, a false creation," in recognition of the idea that it is a hallucination and not real. It is only in his mind's eye, not being seen with his literal sense of vision.

Further, Macbeth says that the hallucinated dagger proceeds, or comes, from his "heat-oppressed brain," indicating just how much tension and upset he feels about what he is about to do. Murder is not a comfortable action for him, especially not the murder of a kind and decent man who has recently rewarded Macbeth for his loyalty and service to the crown. Macbeth begins the play as an honorable man, and he even tries to back out of the plan to kill Duncan (before Lady Macbeth talks him back into it by telling him that he'd be a coward and weakling if he did not carry out their plot). This hallucination shows just how broken up Macbeth is before committing this heinous deed.

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Just before Macbeth makes his way to Duncan's chamber to commit the dastardly deed of regicide, he is struck by the vision of a dagger. Macbeth's first reaction is to ask himself if this is a dagger he sees before him. Of course it is; but the more important question is this: Is it actually real or just a figment of Macbeth's overheated imagination?

This is what Macbeth means when he asks if the dagger is simply

a dagger of the mind, a false creation,
Proceeding from the heat-oppressed brain?
(act 2, scene 1, lines 38–39)

In other words, Macbeth wants to know if the dagger he sees before him is just a hallucination, the product of a fevered brain. The very fact that Macbeth even has to ask such a question at such a vital moment indicates what kind of mental state he's in.

We know from previous scenes that he's not entirely comfortable with the prospect of murdering the man to whom he owes absolute loyalty. The feverish vision he sees before him could be seen as an additional confirmation of Macbeth's reservations about committing such a foul, ignoble deed.

And yet, the vision of the dagger appears as real to Macbeth as the dagger in his sheath, the one he's about to use to murder Duncan. It goads him on, leading him towards Duncan's chamber, where the murder will be committed. In that sense, the dagger's appearance could be seen as a manifestation of the supernatural forces to which Macbeth has succumbed.

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As Macbeth is walking towards Duncan's chamber to murder him, he speaks this famous soliloquy. He "sees" a dagger floating in the air pointing towards and leading the way to Duncan's room. He is wondering if this vision is real, or merely "a dagger of the mind," something created in his imagination - "a false creation."

He starts the monologue with one of the most famous lines from this play, "Is this a dagger which I see before me, The handle toward my hand? Come, let me clutch thee:--
I have thee not, and yet I see thee still."

The “heat oppressed brain” speaks to Macbeth’s confusion on which course of action to pursue. Duncan has been a fine king and has done Macbeth no harm. However, Macbeth’s own ambition (brought about by the witches prophecies), coupled with the insistence of his controlling wife, is telling him to kill the King and claim the throne. Macbeth has been forced to make a very difficult decision, to kill the king or disobey his wife and own desires.

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These lines are from Act 2.1. Here, Macbeth is experiencing what might be a moral crisis. He knows he is about to kill Duncan, but he is imagining what it will be like to actually hold the dagger and carry out the act.

Macbeth is properly horrified by his vision, but then a ringing bell snaps him back to reality and he feels new resolve to fulfill his plan.

Here is the soliloquy:Is this a dagger which I see before me,
The handle toward my hand? Come, let me clutch thee.
I have thee not, and yet I see thee still.
Art thou not, fatal vision, sensible
To feeling as to sight? or art thou but
A dagger of the mind, a false creation,
Proceeding from the heat-oppressed brain?
I see thee yet, in form as palpable
As this which now I draw.
Thou marshall'st me the way that I was going;
And such an instrument I was to use.
Mine eyes are made the fools o' the other senses,
Or else worth all the rest; I see thee still,
And on thy blade and dudgeon gouts of blood,
Which was not so before. There's no such thing:
It is the bloody business which informs
Thus to mine eyes. Now o'er the one halfworld
Nature seems dead, and wicked dreams abuse
The curtain'd sleep; witchcraft celebrates
Pale Hecate's offerings, and wither'd murder,
Alarum'd by his sentinel, the wolf,
Whose howl's his watch, thus with his stealthy pace.
With Tarquin's ravishing strides, towards his design
Moves like a ghost. Thou sure and firm-set earth,
Hear not my steps, which way they walk, for fear
Thy very stones prate of my whereabout,
And take the present horror from the time,
Which now suits with it. Whiles I threat, he lives:
Words to the heat of deeds too cold breath gives.

(A bell rings.)

I go, and it is done. The bell invites me.
Hear it not, Duncan; for it is a knell
That summons thee to heaven or hell.

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