2266 The efforts of the state to curb the spread of behavior harmful to people's rights and to the basic rules of civil society correspond to the requirement of safeguarding the common good. Legitimate public authority has the right and duty to inflict punishment proportionate to the gravity of the offense. Punishment has the primary aim of redressing the disorder introduced by the offense. When it is willingly accepted by the guilty party, it assumes the value of expiation. Punishment then, in addition to defending public order and protecting people's safety, has a medicinal purpose: as far as possible, it must contribute to the correction of the guilty party
2267 Assuming that the guilty party's identity and responsibility have been fully determined, the traditional teaching of the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor.
If, however, non-lethal means are sufficient to defend and protect people's safety from the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common good and more in conformity to the dignity of the human person.-- Catechism of the Catholic Church
Today, in fact, as a consequence of the possibilities which the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm - without definitely taking away from him the possibility of redeeming himself - the cases in which the execution of the offender is an absolute necessity "are very rare, if not practically nonexistent."
First of all, the subject of this post is actually quite different from my other posts on the death penalty, which were about the death penalty as an idea, regardless of whether it were ever carried out or not. Here we are talking about executions that actually occurred. The question is, should they have?
First, let's look at this from the perspective of the operative virtues. Did the executions respect justice? That is, were the guilty parties really guilty of crimes so serious that they merited death? I don't think there can be any doubt that the answer is YES.
Was mercy operative in the executions? Although there will be some who think it is a mercy that the terrorists were not tortured the same way ISIS tortures its victims, again I think the answer is clear, and this time it is NO. However, the requirement for mercy is not of the same nature as the requirement for justice, and sometimes it will not be possible to be merciful.
The state must not show forbearance when the virtue of prudence shows that this would grossly violate its obligation to the public. Would it have been dangerously irresponsible for the Jordanian government to have simply continued to hold the terrorists in prison? That is hard to say. The main consideration is not what the individuals already in custody might do, but rather what their allies still under arms might do. Those allies are unlikely to be intimidated by the executions, and an escalation in the conflict between Jordan and ISIS seems unavoidable, but a failure of Jordan to (among other things) carry out the executions would likely have been taken as a sign of weakness promising future ISIS successes, and that could be very dangerous -- particularly regarding the ability of ISIS to attract and retain supporters and recruits.
In other words, this appears to be a case of achieving war aims by killing people who have in fact committed crimes meriting death. War is not inherently evil, particularly if you have expansionist psychopaths with stated plans of world domination on your border and they have already invaded a neighbor. If it is not necessarily wrong to effect the deaths of soldiers guilty of nothing but being on the opposite side, so long as the rules of a just war are observed and it is done to achieve important military goals, surely it is not necessarily wrong to achieve similar goals by killing those who actually deserve to die.
Interestingly enough, although both war and capital punishment are explicitly treated in the Catechism, this sort of overlap is not.