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In Shakespeare's Macbeth, there are several quotes that refer to the "false face" theme, or what I call, "fair is foul..." (based upon the witches' quote"
In this, the idea is that you cannot always believe what your eyes may be telling you: what seems to be good may be bad, and what seems to be bad may be good. In this case, we are looking toward keeping the truth hidden in one's heart, and not where people can see it.
In Act I, scene iv, Duncan comments on the idea of the "false face," when referring to the former Thane of Cawdor.
There's no art
To find the mind's construction in the face;
He was a gentleman on whom I built
An absolute trust. (12-15)
(Ironically, although this quote refers to Cawdor, it could easily also describe Macbeth. In fact, the former Thane of Cawdor and Macbeth have a great deal in common by the end of the play.)
In Act I, scene v, Lady Macbeth offers her husband advice as to how he should hide his evil intent toward Duncan—beautiful on the surface, yet deadly underneath:
...look like the innocent flower,
But be the serpent under 't. (60-61)
Then in Act I, scene vii, Macbeth finally reconciles himself to murdering Duncan, and says:
False face must hide what the false heart doth know. (82)
We see the "false face" of Macbeth again when Duncan's murder has been discovered, and Macbeth murders the King's servants so they cannot cast doubt on the circumstances surrounding the assassination. He says he is sorry ("repent"), but he's really protecting himself and saying he has acted rashly out of his love for and loyalty to Duncan:
O, yet I do repent me of my fury
That I did kill them (II, iii, 87-88)
Who could refrain,
That had a heart to love, and in that heart
Courage to make 's love known? (II, iii, 97-99)
All of these quotes point to Macbeth's need to hide what is in his heart with a "false face:" a disguise that hides the evil within.