What in Andrew Marvell's poetry establishes him as a metaphysical poet?

One example of Marvell's metaphysical approach is "To His
Coy Mistress". This poem expresses the metaphysical conceit which
is an attitude that comes across through a debate or argument.

In this poem, Marvell is essentially coming onto a woman
who has no speaking voice in the poem. He uses great hyperbole and a forward tone with
the intention of getting this woman that he is interested in to stop playing
hard-to-get. She has been coy, and he is trying to point out that there has been time
enough for that game, and now it is time to engage in a highly physical relationship.
Having been written in 1681, this is truly some forward and aggressive writing about
love.

So how does this fit the metaphysical poet
definition? As the great argument begins it's construction, Marvell presents the thesis
in the first stanza that if there was time, he would

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"Love you ten years before the Flood,

And you should, if you please,
refuse

Till the conversion of the
Jews."

Marvell is essentially
say that their courtship could go on forever, if they only had the
time.

But the next stanza, presents the antithesis: the
fact that life is limited and they only have so much time to
love.

"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 honor turned to
dust,

And into ashes all my
lust."

He is almost mocking
her. He lets her know that she will die a virgin if she doesn't accept his request here
pretty soon.

The final stanza marks the synthesis of the
two ideas already presented. This stanza likewise makes the great suggestion that they
take into account that time has been long enough for a flirting period, and now, it is
time to let the sporting begin. Marvell wants to Mistress to understand that a physical
relationship has to start at some point.

The structure of
the argument is what defines this as metaphysical: thesis, antithesis, and then
synthesis. Furthermore, the confidence in the argument that is marked by the hyperbole
further defines this as metaphysical.

Hope this
helps.