What does it mean when Ophelia says, “Lord, we know what we are, but not what we may be." How do these ideas relate to theme? In what ways does Hamlet struggle with this very idea?
One should understand that Ophelia, at this point, is experiencing a mental breakdown. She has been confused by Hamlet's ambiguous words and actions and has been admonished by both her father and brother about pursuing relations with him. To crown it all, she has just learned that Hamlet has killed her father. All this trauma is enough to make even the most stable of individuals crack.
The question is: Does Ophelia say these words in a moment of brilliant intellectual enlightenment or are these just the ramblings of a mind gone astray? Whatever it may be, Ophelia is making a good point. Her statement is an accurate assessment of our being, our essence. We live in the present. What we know is what we know now and we respond to that; however, we do not know what we may become. We may guess or make assumptions about our futures or how we may respond to a situation, but we cannot be quite sure.
Ophelia, for example, knew that she had affection for Hamlet and that she was loyal to her father, but she did not know that Hamlet would mess around with her so much, confusing her -- telling her in one moment to "get thee to a nunnery" and in the next requesting to sit at her feet. She neither knew the extent of her father's meddling or that he would be killed by Hamlet. Finally, not knowing, she could hardly contemplate how she would react. It is certain that she never thought that she would lose her sanity, or later commit suicide.
It is this uncertainty which is a major theme of the play. Hamlet knows who he is: the son of a murdered king, rightful heir to the Danish throne. Furthermore, he knows what he suspects -- that his uncle had murdered his father and unlawfully usurped the throne, and that his mother may have been complicit in the murder. Hamlet also knows that he has to avenge his father's death, but he also knows that he is not a ruthless killer. After listening to his father's ghost, Hamlet sees his duty as a curse:
O cursed spite,
That ever I was born to set it right!
It is all this that sets Hamlet on the road of doubt and procrastination. He knows what he is, but is uncertain about what he may become. He rationalizes, considers and reconsiders. His intellectual perturbation does not allow him to act and his uncertainty is best expressed in his deep and moving soliloquy:
To be, or not to be: that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing end them? ...
It would be fair to say that, at this point, Hamlet does not even seem sure of what he is and is probably even more doubtful about what he may be. Poor Hamlet! If he had only known that his uncertainty would eventually lead to the tragic demise of so many, including him!
Hamlet relates this very idea in each of his soliloquies. Throughout the play, Hamlet is torn between his desire for revenge & his need to live up to his father's legacy, and his crippling inability to act on any impulse. Instead, he continually ruminates over who he is, what exactly is man, the meaning of life...essentially, anything and everything anyone has ever considered. Several times he works himself up to commit murder, steeling himself to kill Claudius. Yet each time he fails. He never can make the leap to actually, physically taking action.
So Hamlet is well aware of his self. He knows how others see him, & he knows how he himself considers his nature. Yet he cannot reconcile this knowledge with his behavior. Instead, he drifts into melancholy, fakes insanity, and eventually commits an inhonorable murder for really no reason, minutes after he failed to kill Claudius. He never knows "who he may be", because he never really makes an effort to be any different. He recognizes the potential, but can never act upon it.