A syllogism is a logical argument in which one conclusion is derived from two or more propositions. For example,
All humans breathe oxygen. (All A is B)
Truman is a human. (All C is A)
Truman breathes oxygen. (All C is B)
In "To His Coy Mistress," the three propositions of the syllogism are divided presented in the three stanzas. In the first stanza, the speaker supposes that he and his mistress could love each other indefinitely. His mistress is so wonderful that he would praise her for an incredibly long or maybe even infinite amount of time.
An hundred years should go to praise
Thine eyes, and on thy forehead gaze;
Two hundred to adore each breast,
But thirty thousand to the rest;
An age at least to every part,
In the second stanza, the speaker realizes that humans don't live forever and although the grave is a private (intimate) place, it is a place where "none I think do there embrace." In other words, there love will end when their lives do.
In the third stanza, the speaker concludes that since he and his mistress are mortal, they will make the most of their time.
And now, like am'rous birds of prey,
Rather at once our time devour,
Than languish in his slow-chapp'd power.
The syllogism could be stated as follows:
If time stood still, we could love each other forever.
But time flies, and we will not live that long.
Therefore, we must make the most of the fleeting time that we do have.
Note how the key words "had," "but," and "now" introduce each of the propositions.
"Had we but world enough, and time,"
"But at my back I always hear
Time's winged chariot hurrying near;"
"Now, therefore . . . let us sport us while we may;"