One of the central ways that Donne creates an argument against death in this powerful poem that is normally entitled "Sonnet X" in his Holy Sonnets, is through paradox. Remember, paradox is a statement that at first glance seems impossible or illogical, but when interrogated further, reveals a more profound truth or reality than was immediately obvious. What is interesting about paradoxes is that they grab our attention immediately and force us to consider issues more deeply that we otherwise would do.
In this poem, then, two key paradoxes are used to create Donne's argument against Death. The first is that Death doesn't actually "kill" its victims:
For those whom thou think'st thou dost overthrow,
Die not, poor Death, nor yet canst thou kill me.
This is because Death is shown throughout the poem to be nothing more than a transitional state, as some part of the person goes on living and there is an afterlife.
The second paradox that is used is at the very end of the poem:
One short sleep past, we wake eternally,
And death shall be no more; Death, thou shalt die.
Of course, this paradox is in many ways one of the strongest, which makes it a perfect way to finish the poem. However, Donne is suggesting that because Death lacks the power to really kill, because of the "eternal" waking we shall experience after our "short sleep," this shows that Death has no dominion over us and therefore metaphorically "dies."
Donne therefore establishes his argument very carefully through the use of paradox to demonstrate and illustrate that Death, although feared by many, actually does have no dominion over us.
Sonnet 10 begins famously with the opening line "Death, be not proud, though some have called thee" (1). This personification of death continues through the rest of the sonnet, as Donne basically calls out Death, as though to challenge him or to pick a fight with him. When reading the first two lines, Donne basically says that, although some people might consider Death to be "mighty and dreadful," he knows that Death is really not that scary (2). To further downplay Death's menace, Donne likens Death to "rest and sleep" which are really not frightening at all (5).
The end of the poem argues that Death's power over man is only temporary and fleeting, because God will resurrect His believers to "wake eternally" (15). Donne's "Sonnet 10" challenges Death, and through the poet's cleverly crafted argument, wins the fight! Donne's conclusion feels triumphant: "And Death shall be no more ; Death, thou shalt die" (16). Death, consider yourself 'poem-slapped' by John Donne...