From Wo’s
Weblog:

Argument
Z

1. If the conclusion of argument
Z is true, then argument Z isn’t sound.

2. If the conclusion of argument
Z is not true, then argument Z isn’t sound.

Therefore: Argument Z isn’t
sound.

Is argument Z sound? (If not,
which premise is false?)

There is a paradox here, but maybe this
question isn’t the best way to get at it. After all, the paradox can be
tightened up a little. Premise 2 is an analytic truth, so it can be dropped
from the argument. Hence the following should be just as paradoxical.

Argument
Z´

1. If the conclusion of argument
Z´ is true, then argument Z´ isn’t sound.

Therefore: Argument Z isn’t
sound.

But now it’s clear what the untrue premise
must be, it’s premise 1. So I think premise 1 is also untrue in argument Z.
That may be paradoxical, but at least we’ve located
the paradox.