The Pragmatic Inconsistency of Responding to Nihilism with Despair

(1) Necessarily, if metaethical nihilism is true, then nothing matters.

(2) Responding with despair to the (supposed) truth of metaethical nihilism presupposes the falsity of metaethical nihilism.

Therefore:

(3) If one responds with despair to the (supposed) truth of metaethical nihilism, then it is true that nothing matters and it is false that nothing matters. [From 1-2]

Therefore:

(4) It is impossible to consistently respond with despair to metaethical nihilism. [From 3 and LNC]

They key insight of this argument is that if metaethical nihilism is true, then literally nothing, including metaethical nihilism itself, matters.