Sometimes philosophy is a life and death matter. Let's say that time is continuous; i.e. that it can be represented by the real number line. The real number line is dense:
\[(\forall x \in \mathbb{R}) (\forall y \in \mathbb{R})(x <y \rightarrow (\exists z \in \mathbb{R}) (x < z <y))\]
For any two real numbers there is another real number on the line between them. This means that no two real numbers can be "touching"—there will always be another (in fact infinitely many) real numbers between them. And if time can be represented by the real number line then time is also like this; for any two points in time ti, tj such that ti < ti, there is another point in time tk such that ti < tk < tj. No two points in time can be touching—there will always be another (in fact infinitely many) points in time between them.
Now, at some time t1 a person S is alive and at some later time t2 S is dead. If no two points in time can be touching then there will be a period of time in which S is neither alive nor dead. This can be avoided by saying that life and death overlap; that there is a point at which S, in the manner of Schrödinger's cat, is both alive and dead, but both options seem like nonsense.
Is this a paradox? Perhaps not, or perhaps at least not a very deep one. I think the thing to say here is that the boundary between life and death is vague (though maybe there are reasons further down the line to think this could not be the case). If vagueness is the way out though, there is still a problem for those who hold an epistemic theory of vagueness. If vagueness is epistemic—if there is a definite boundary between life and death, but we just don't know exactly where it lies—then the problem just reappears.
