An argument for beheading or against lethal injection

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

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