What does Hamlet's quote "Doubt thou that stars..." to Ophelia mean?

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This statement in Hamlet's love letter to Ophelia is his way of telling her to never doubt his love, even if she doubts everything else. Some critics have focused on the possibly intentional ambiguity of the words, as if Hamlet could also mean "doubt" as another way to say "suspect," in which case, the statement would convey that he does not love her.

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The following lines are from the love letter Hamlet writes to Ophelia in Act 2 Scene 2 of William Shakespeare’s Hamlet. As a dutiful daughter, Ophelia passes this letter to her father Polonius who then reads it to the King and the Queen.

Doubt thou the stars are fire,

Doubt that the sun doth move,

Doubt truth to be a liar,

But never doubt I love.

It seems that Hamlet has been courting Ophelia who is unable to respond to his feelings because her father Polonius forbids her to do so. Polonius feels that this unrequited love is the reason behind Hamlet’s madness.

The most simplified and obvious interpretation of these lines is Hamlet’s hyperbolic assertion that Ophelia could doubt the most believable scientific phenomena and forces of the universe, but she should never doubt his love towards her.

Of course, the fact that the stars are only made of fire is questionable to astronomical sciences now, but at the time period of the play, it was treated with downright certainty. However, Copernicus challenged the fact of the movement of the sun and most of the Shakespearean audience would have suspected this anyway.

There is a possibility of semantic ambiguity in the poem if Shakespeare used the word "doubt" to mean "suspect". Hamlet's love poem, then, would ask Ophelia to go ahead and suspect all proven forces of the Universe but “never suspect that he loves (her)”.

This, confusingly,  generates complete semantic inversion of Hamlet’s use of language to express his feelings, which sounds more like a denial of love. Was Hamlet telling Ophelia to believe he loves her or to be sure that he doesn't? Is it a poem Hamlet wrote to express his love or to refute it? This ambiguity has garnered a lot of interest amongst literary scholars although Hamlet’s love to Ophelia isn’t the main focus of the play.

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This is a quote from a love letter Hamlet wrote to Ophelia, who dutifully passed it on to Polonius, for young women were not to receive letters from men they were not betrothed to. Polonius now reads it to the King and Queen, as is his duty to do: He wants to let them know that he forbids Ophelia to think of Prince Hamlet's love and that this forbidden love might be the cause of Hamlet's madness. 

Hamlet is hypothetically contemplating Ophelia's possible doubt of things that are fixed as a way of forming an analogy to the undoubtable truth of his love for her. 

Though the logical construction is more complex than this, one way to understand what Hamlet says is to think he suggests that if, in her heart ("In her excellent white bosom"), she ever doubts that the stars are made of fire, that the sun moves, that truth can lie, she must never doubt that he loves her.  He is posing the hypothetical situation in which Ophelia may doubt things that are clear facts and saying that, no matter what, she must not doubt his love.

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