How do the first four lines in Shakespeare's Twelfth Night both show conceit and relay a paradox?
Conceit is typically understood as a feeling of being wrapped up in one's self. Either one has an overly high opinion of one's self or flatters one's self (Random House Dictionary). One way in which we can see Duke Orsino's opening four lines as being conceited is that they clearly show his obsession with his love for Olivia. He is so wrapped up in his love for her that he can't think of anything else. Plus, being wrapped up in one's own feelings rather than paying attention to other things going on in the world is certainly a form of conceit. Being completely wrapped up in your own emotions is the same as thinking that only your own emotions and thoughts are what's important, which is indeed self-flattery.
A paradox, similarly to an oxymoron, is two conflicting ideas or concepts that when put together actually make sense "on a deeper leve" (Dr. Wheeler, "Literary Terms and Definitions: P"). Dr. Wheeler gives us the example, "Without laws, we can have no freedom." Since laws can be seen as restraints, we can see how laws can be considered the exact opposite of freedom. However, it's true that without those constraints we would have total anarchy, and everyone's basic human rights of life, liberty, happiness, and even property would be jeopardized, and as the U.S. Declaration of Independence states, if these basic rights are not protected, we have no freedom. For example, if a thief is not restrained from thieving by a law, then the thief would be permitted to take away someone else's property, which would also be taking away that other person's freedom.
Duke Orsino's lines are paradoxical because what he is saying is that if music makes people fall in love, then he wants to hear too much music so that he'll get sick of both music and love, so sick of both things that he'll finally stop loving. Hence, the paradox is that on the one hand, he is asking for his appetite for love to be fed, but on the hand, he is only asking that because he no longer wants to be in love. It's a lot like the too-much-of-a-good-thing paradox. On the one hand, people like to consume what they enjoy, such as chocolate, but on the other hand, if a person eats too much chocolate, that person could become literally, physically sick, like having a sick stomach, and that person can also become absolutely "sick," or tired, of the flavor. Orsino is hoping that the music will feed his cravings for love until he becomes completely tired of his feeling of love, as we see in his lines:
If music be the food of love, play on;
Give me excess of it, that, surfeiting,
The appetite may sicken, and so die.
That strain again! it had a dying fall. (I.i.1-4)