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The intention to punish an organism must be understood as separate from the intention to deter a behavior. In the first sense, the implicit theory of justice suggests that an individual who goes against the law has a debt to be paid in pain of one kind or another. In the latter, the implicit theory is that the lawbreaker is to be negatively reinforced in order to produce a behavior that is in line with the set of behaviors that the law is attempting to produce. The pain is used as a means of communication, a part of the bargaining process with the lawbreaker. In the former debt of pain model, the pain itself is the objective, whereas in the latter the ideal set of behaviors is the objective. The pain is not a means, it is an end. It lacks no signal encoded in it other than the aesthetic judgement that it is correct for the recipient of the pain to be in pain, for their identity demands it.
Such aesthetics that arbitrarily inflict pain are best termed sadism, and cannot be understood to be prosocial, for they will inevitably eliminate some functionality of the population by gaining pleasure from damaging them. Pain without signal must be understood to be the essence of cruelty, and the term “cruel and unusual punishment” should be used only in the hopes that it does not become usual, for something cannot be in and of itself justified by the everydayness of custom if it otherwise consists of the infliction of pain with no other justification than the pain itself. To say that something is legitimized by custom is to say that it is legitimized by size, even less justified than the common fallacy of “two wrongs making a right.”
To explain further, cruelty cannot be understood to be justifiable unless one takes the repugnant perspective that the pleasure that the community takes in watching the punished suffer is greater justification than the negative justification of the suffering visited on the lawbreaker—something phenomenological, and thus impossible to compare. I must, from my own perspective, demand that such bloodsport be confined to the dust heap of history. Still, the concept of punishment as a debt of pain is embedded into many legal traditions, implying means that the legitimacy of such institutions must be called into question. Often sadism is disguised as negative reinforcement, often by suggesting that negative reinforcement is the only means that might work to avoid recidivism. Negative reinforcement should obviously not be the first choice of any justice system, for if one is able to correct a criminal behavior without any need to inflict pain, why not choose that option instead of the one that causes needless suffering in comparison?
In summary, it seems correct to take the final position that punishment as a debt of pain is never justifiable, that negative reinforcement is occasionally necessary for lack of other options for correcting a criminal behavior, and that these concepts are reliably confused. It seems worthwhile to think about, at some point in the future, why debt of pain and negative reinforcement models are reliably conflated, as the answer to that question is also the answer to why zero-sum behaviors are chosen in situations where they are of equal personal utility to positive-sum behaviors.