Locating the paradox

Brian Weatherson correctly argues that, since premise 2 of argument Z is analytically true, it can be simplified to

Argument Z':
1. If the conclusion of argument Z' is true, then argument Z' isn't sound.
Therefore: Argument Z' isn't sound.

The paradox then arises in two different ways. First, for premise 1 to be false, it must be the case that 'Argument Z isn't sound' is true and argument Z is sound.

Second, and more interestingly, the falseness of premise 1 analytically implies that argument Z is sound, which in turn analytically implies that all premises of argument Z are true, which implies that premise 1 is true.

This second paradox can be further simplified to:

Argument Z'':
1. Argument Z'' isn't sound.
Therefore: Snow is white or snow isn't white.

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