"Paying Back" - Criminals should get their 'just deserts'- they deserve to be punished and society is morally entitled to take revenge. They should be made to suffer for breaching society's moral code.
May also act as a deterrent but its main purpose is to express moral outrage and therefore the punishment is good in itself even if it doesn't change the offender's behaviour. It punished crimes that have already been committed rather than preventing further ones.
Incapacitation removes the offender's capacity to offend again, e.g. execution, cutting off hands, chemical castration, banishment, travel bans, curfews/tagging