Which of the premises in this argument is
false?

P1. Everest is determinately a mountain

P2. Something is Everest

C. So, something is determinately a
mountain

There must be a false premise, since the
argument is valid, even if ‘Everest’ is a description rather than a proper
name, and the conclusion is obviously false. There is no thing such that it
rather than one of its mereological siblings is determinately a mountain. So
which is it?

It has to be P1, right? But isn’t it
determinately true that Everest is a mountain? Yes, but that doesn’t imply P1.
P0 does not imply P1, as we can tell by noting that P0 is true and P1 false.

P0. Determinately,
Everest is a mountain

P1. Everest
is determinately a mountain

Interesting to note how this compares to K0
and K1

K0. Jack
knows that Everest is a mountain

K1. Everest
is such that Jack knows it is a mountain

It is either an argument for or a
consequence of the theory that names are directly referential that K0 does entail
K1. (It could be both an argument for the theory and a consequence of it.)
Assuming there is a connection between ‘determinately’ and ‘knows that’ (a
connection that everyone on the ‘conservative’ end of the vagueness spectrum
endorses) then the failure of P0 to entail P1 suggests that perhaps K0 does not
entail K1.