Full Idea
We kill the irredeemably wicked, for three reasons: that they may no longer harm us; as a deterrent to others like them; and because it is actually better from their own point of view to die, when their souls are so damaged they cannot be improved.
Gist of Idea
We execute irredeemable people, to protect ourselves, as a deterrent, and ending a bad life
Source
Galen (The soul's dependence on the body [c.170], Kiv.11.816)
Book Reference
Galen: 'Selected Works of Galen', ed/tr. Singer,P.N. [OUP 1997], p.173
A Reaction
The third one sounds like a dubious rationalisation, given that the prisoner probably disagrees. Nowadays we are not so quick to judge someone as irredeemable. The first one works when they run wild, but not after their capture.