Retributive justice gets a bad rap. It is frequently stereotyped as a primitive (pre-Enlightenment, at least) desire for revenge writ large. That is not to say that there are not those who support retributive justice because of this very reason; there are. But that should not preclude a reasonable debate about its merits.
Punishment theory posits five somewhat distinct (I’ll come back to this later) justifications for penalties.
The first four, broadly speaking, are consequentialist and therefore teleological in nature while retribution is generally regarded as deontological. I do not wish to indulge in a debate over how hard and fast these categorizations are. There is an ample literature in moral philosophy engaging in just that debate. But for my purpose the general classification suffices.
To make this a bit more concrete- teleological reasons for punishment focus on the consequences of penalty. What matters to the consequentialist is that a particular goal is achieved, such as incapacitation or rehabilitation. This should not be construed to mean that consequentialists care not about the morality of the criminal act. (One might be able to find someone, somewhere who subscribes to such a view, but it is not within the mainstream.) But a discussion of the moral opprobrium is secondary to their aims.
Contrast this to a deontological perspective on punishment, which stresses retribution as moral desert. Where consequentialists are looking towards future ends, retributivists look back to the criminal act in order to determine the just punishment. As above, there may be someone, somewhere who is an absolutist with respect to retribution, but generally speaking notions of potential outcomes may play a role in retributive justice.
What’s Right With Retribution
Retributive justice exerts a strong emotional and intellectual appeal. Its focus on the morality of the actor in determining penalty seems both logical and right. The emotional appeal is based in our inherent morality. Humans are, by nature, moral beasts. It is why certain precepts of behavior enjoy near universal acceptance, despite near infinite differences in societies and religiosity (or lack thereof). It explains why both Richard Dawkins and Pope Benedict agree that murder is wrong.
And its intellectual appeal is actually quite similar to the consequentialist reasoning underlying teleological notions of punishment. Specifically, retribution relies on the notion of consequences for morally impermissible actions. And holds that those consequences/penalties are to be proportionate to the severity of the act committed.
Retributive justice is much more securely nested in notions of morality. And this is what makes it such a good fit for a criminal justice system. Crime is not only an offense against the direct victim, but an offense against society and its norms, mores and rules. Thus retributive justice is not seeking to make the victim whole by taking something from the offender. Rather, it is society showing its disapproval of the act in which the offender engaged. The notion of an eye for an eye is not to make the offender and the victim equal, but to ensure that the punishment is equal in severity to the offense.
It should be noted that retributive justice can be crude and even barbaric, in its extreme. Specifically, I would mention capital punishment here in the US or loss of limbs/appendages in some other parts of the world. But these are literal interpretations of an eye for an eye. I am not comfortable defending such systems.
In addition, retribution or any other rationales for punishment do not need to be mutually exclusive. I would argue that most criminal justice systems are hybrids. Each particular system may place different values on each of the rationales, and some may even leave one or more out. But, in practice (as opposed to discussions of theory) punishment serves many (competing) interests.