Why Punish? sounds like a straightforward enough question, but it could be answered in at least three different kinds of way.
First, answering Why punish? could be taken to involve an investigation into the origins, causes or mainsprings of punishment. In all known societies, there are more or less settled ways of responding to wrongdoing and this commonly (though not always) takes the form of repaying the wrong with some sort of hardship or infliction on the wrong-doer. Yet why is it that people do this? And why do we all recognise the power of these ‘retributive emotions’ that make us feel that punishment is fitting and that wrongdoers should not go unpunished? To understand this seems to involve a sociological investigation or perhaps an anthropological or psychological one. Maybe the urge to punish is just one aspect of the exchange and reciprocity that cements any community – just like (say) gratitude. Perhaps punishment gives people the occasion to denounce and repudiate the crime and thereby to affirm the values that bind them, making them into a community rather than just a collection of people living side by side. Or perhaps the origins of the urge to punish are to be found in our psychological needs and insecurities.
Second, Why punish? could be taken to call for an investigation into the purposes of punishment. ‘Punishment’ does not and could not have a ‘purpose’ apart from the purposes that people may set for it. And people may (do) set different purposes, not only for an imposition of punishment in a particular case, but for the institutions and practices of punishment in general. The legislator who sets the legal parameters, the judge who imposes the sentence, the personnel who put it into effect, the offender her / himself may all set different aims and purposes. For that matter, each of them may (is likely to) have more than one aim – for instance, to give the offender what he deserves, to bring it about that he does not offend again and to deter other people from offending – and it is an open question to what extent these several purposes are compatible. Perhaps many of the purposes that are avowed for punishment may well be unachievable or at least achievable to no more than a very limited extent.
Third, the question could be understood as a challenge to examine the justifications of punishment. This speaks more to the question ‘how could we (or why ought we to) punish?’ than ‘why do we?’. This is a search for justification rather than explanation. To justify something is to show that it is morally required or morally permissible or maybe morally better than alternatives. This is moral inquiry and is a distinct project in its own right. In some debates, aims and justifications are not always adequately distinguished, but it should be clear that setting an aim for punishment does not resolve the ethical question of whether this is justifiable.