An argument for beheading or against lethal injection

This article is based on my 2013 article on state-beheading. Read the background here.

Beheading is intolerably cruel.
Beheading is less cruel than lethal injection.
Therefore, lethal injection is intolerably cruel.
If a mode of capital punishment is intolerably cruel then it ought to be illegal.
Therefore, lethal injection ought to be illegal.

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