What evidence indicates that "To His Coy Mistress" is a carpe diem poem?
The Latin phrase carpe diem is most often translated into English as "seize the day." In other words, live life to the fullest; stop and smell the roses; make the best of every day. Don't wait for tomorrow--do it today. So a carpe diem poem would be one that expresses these ideas.
Most scholars would say that "To His Coy Mistress" is the best example of a carpe diem poem. In it, the speaker is telling his lady love that if they had all the time in the world, her coyness (or shyness or reluctance) would be okay. But time is slipping away. They will not be young forever, so now is the time to express their love. As he says:
Let us roll all our strength and all
Our sweetness up into one ball,
And tear our pleasures with rough strife
Thorough the iron gates of life:
Thus, though we cannot make our sun
Stand still, yet we will make him run.
Many elements in the poem indicate that the speaker is urging his beloved to seize the day. Look, for example, at the first two lines:
"Had we but world enough, and time,
This coyness, lady, were no crime."
This says IF we had all the time, you could be coy.
Then look at the start of the second stanza:
"But at my back I always hear
Time's winged chariot hurrying near…"
But we don’t have all the time, he's saying. Not only is our time limited, he feels and hears it rushing on. Therefore, the third stanza says, let's make love while we're still alive.
This part of the poem tells the lady what will happen to both of them before too long. Soon they will be no more, just ashes in a tomb. If she holds onto to her honor for too long, it will die with her, therefore, she should embrace his love and submit.
Seize the day before it is too late!
"Thy beauty shall no more be found, Nor, in thy marble vault, shall sound My echoing song: then worms shall try That long preserved virginity, And your quaint honour turn to dust, And into ashes all my lust"
This poem is a carpe diam poem. As it begins he says to coy mistress, if they have enough time, they can make love slowly and take a long time to be united. But in the next stanza, he says they have not enough time because time is rushing away and he is seeing the vast eternity lying infront of them.
For that reason, he is hurrying to make love. Because he does not want to loss the chance of making love. Here he uses a fine syllogism to show carpe diam theory.