In Shakespeare's Hamlet, what is meant by "foil"?
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In Hamlet, Shakespeare provides information about Hamlet through his use of a foil, which serves a specific purpose in providing indirect and direct characterization of another [major] character, giving the reader a deeper insight into that character...using comparisons. A foil, then, is...
...[a] character that serves by contrast to highlight or emphasize opposing traits in another character.
The author, in this case, Shakespeare, allows us to better understand who Hamlet really is inside, by comparing him to other characters in the story. Hamlet also better understands himself and his "almost blunted purpose" (III.iv.122) of avenging his father's murder.
...in Hamlet, Laertes and Fortinbras, whose fathers have been killed, are foils for Hamlet.
In Act One, Hamlet is visited by his dead father's spirit (the Ghost); Hamlet learns that Claudius (Old Hamlet's brother and Hamlet's uncle) murdered Old Hamlet. The Ghost charges Hamlet with the task of avenging his father's death.
List, list, O, list!
If thou didst ever thy dear father love—…
Revenge his foul and most unnatural murder. (I.v.26-27, 29)
But know, thou noble youth,
The serpent that did sting thy father's life
Now wears his crown.
O my prophetic soul! My uncle! (43-46)
Once Hamlet learns of this, he promises to take his uncle's life. However, he is also concerned (as would be Elizabethans of that time) as to whether the ghost is honest (good) or evil—as they believed the powers of darkness did all they could to trick one into sacrificing his immortal soul. This may be the case with the Ghost: what if he is a manifestation of the Devil? So Hamlet looks for proof.
The foils draw his attention inward, showing him how slow he is to act based on the reactions of others in similar situations—and he questions why he hesitates.
Fortinbras lost his father—and wants revenge. But Old Fortinbras' death and loss of lands took place in battle with Old Hamlet—all was done honorably. Fortinbras accepts this. Traveling across Norway's land Hamlet finds that for honor, Fortinbras is fighting for a worthless piece of land. Hamlet compares himself to Fortinbras; Hamlet has many more reasons to act, and he curses his reticence:
How stand I then,
That have a father kill'd, a mother stain'd,
Excitements of my reason and my blood,
And let all sleep, while to my shame I see
The imminent death of twenty thousand men
That for a fantasy and trick of fame
Go to their graves like beds, fight for a plot... (IV.iv.58-64)
Laertes has also lost a father and seeks revenge:
And so have I a noble father lost;
A sister driven into desperate terms,
Whose worth, if praises may go back again,
Stood challenger on mount of all the age(30)
For her perfections. But my revenge will come. (IV.vii.27-31)
These foils present us with comparisons to Hamlet. Fortinbras and Laertes both take immediate steps to avenge their fathers. Fortinbras is honest, though misguided. Laertes is filled with hatred and anger (fed by Claudius). Fortinbras cannot honorably continue: he moves on to other things. Laertes will dishonorably seek to avenge Polonius' death.
By comparison, Hamlet lacks commitment to his purpose. His "indecision" is said to be the reason for his ultimate death—had he avenged his father's death earlier, he, Gertrude and perhaps the others would have been saved.