From Pope John Paul II's encyclical, Evangelium Vitae -- "The Gospel of Life", section 56. After a discussion of self defense, he says
This is the context in which to place the problem of the death penalty. On this matter there is a growing tendency, both in the Church and in civil society, to demand that it be applied in a very limited way or even that it be abolished completely. The problem must be viewed in the context of a system of penal justice ever more in line with human dignity and thus, in the end, with God's plan for man and society. The primary purpose of the punishment which society inflicts is "to redress the disorder caused by the offence." Public authority must redress the violation of personal and social rights by imposing on the offender an adequate punishment for the crime, as a condition for the offender to regain the exercise of his or her freedom. In this way authority also fulfills the purpose of defending public order and ensuring people's safety, while at the same time offering the offender an incentive and help to change his or her behaviour and be rehabilitated.
It is clear that, for these purposes to be achieved, the nature and extent of the punishment must be carefully evaluated and decided upon, and ought not go to the extreme of executing the offender except in cases of absolute necessity: in other words, when it would not be possible otherwise to defend society. Today however, as a result of steady improvements in the organization of the penal system, such cases are very rare, if not practically non-existent.
In any event, the principle set forth in the new Catechism of the Catholic Church remains valid: 'If bloodless means are sufficient to defend human lives against an aggressor and to protect public order and the safety of persons, public authority must limit itself to such means, because they better correspond to the concrete conditions of the common good and are more in conformity to the dignity of the human person.'
To sum this up, capital punishment is not intrinsically immoral, but there are essentially no situations in which it is morally acceptable.
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