Presupposition and Excluded Middle

If Socrates dies at time t, then Socrates was alive prior to t. If Socrates does not die at t, then Socrates was alive prior to t.  Since both 'Socrates dies at t' and 'Socrates does not die at t' entail 'Socrates was alive prior t,' we say that the latter is a semantic presupposition of 'Socrates dies at t.'

But wait a minute! Doesn't what I have written generate an inconsistent tetrad?

1) p entails q

2) Not-p entails q

3) Necessarily, for any p, either p or not-p (Law of Excluded Middle)

4) q is contingent.

The conjunction of the first three limbs entails the negation of the fourth. So something has to give.

It is a datum that q -- 'Socrates was alive prior to t' -- is contingent: true in some but not all possible worlds. So we either reject semantic presupposition (which requires the truth of both (1) and (2) ) or we reject Excluded Middle.

Why not reject Excluded Middle? Socrates dies at t and Socrates does not die at t are contradictories: each is the negation of the other.  There is no possible world in which both are true.  And yet there are possible worlds in which neither is true. Those are the worlds in which Socrates does not exist.