This is often cited as the main reason for having systems of punishment at all. There is a General theory of this and a Specific theory of this.
Deterrence
This is the place you go if you are found guilty of a crime and sentenced to incarceration
Prison
In Honor cultures, like that of the early Greeks, reputation is everything, so punishment has to have these characteristics.
You have to do it yourself, it has to be violent, and it has to be immediate.
Wergild was an early system for breaking up cycles of violence by doing this.
Paying money for a crime instead of directly avenging it
The 12 Tables were the name of the Criminal Law system of this civilization.
Rome
Plato said that this was also a valid reason for punishing people, particularly people who can't be reformed and remain dangerous. We still justify prison with this reason.
Incapacitation
This is the place you go if you are waiting for a trial but can't pay bail or are deemed too dangerous or too likely to run.
Jail
This retributive system from Babylon in 1700BC set specific penalties for specific crimes, including the famous "eye for an eye, tooth for a tooth".
Code of Hammurabi
The Wheel, the Iron Maiden, and the Rack are all methods of doing this in the Roman and Medieval era.
Execution
What was the purpose of the Spanish Inquisition?
Bonus 100 - Why were their prisons so nice?
To find heretics. Their prisons were so nice in part because they were inspected and found wanting but also because they tended to hold prisoners for long periods in the hopes they'd stop being heretics.
This type of punishment is meant to prevent revenge, which is sadistic, personal, and disproportionate, by being impersonal, measured, and proportionate, thus ending potential cycles of violence.
Retribution
If you include these two "p"s in addition to jail, prison, and community corrections, nearly 3% of the adult US population is regularly interacting with the corrections system at any given time.
Parole and probation
Modern legal systems are different from Honor cultures and also different from pre-modern legal systems because they make a habit of (in theory) carefully protecting these.
Human Rights
Why did early civilizations like the Romans, Greeks, and Medieval Europeans tend to employ such violent and frequently deadly forms of punishment as opposed to imprisonment?
They didn't have a system for paying for prison, they had no police, and they were obsessed with deterrence.
Egypt was very obsessed with having their criminals engage in this activity, to the point that escaping was seen as one of the worst possible crimes.
Making flour.
This reason for punishment was cited by Plato as the correct response to people who commit crimes because they haven't been properly educated on how to behave. The Parole system is based on the possibility that this will happen, but high recidivism rates call this into question.
Rehabilitation
Prison overcrowding has been seen as a serious problem. One way to address it is to use this strategy that achieves many of the same goals as prison without the same costs.
Home incarceration
A religious outlook on crime and punishment that believes that the world is fundamentally just because it is run by a just God tends to be skeptical of the need for a secular justice system, instead recommending this response to crime.
Forgiveness and prayer for the criminal
During this period, people like John Howard, Caesare Beccaria, and Jeremy Bentham radically changed the way crime was addressed.
The Enlightenment
Socrates of ancient Athens was forced to drink poison by the 11 (a group of judges) after being narrowly found guilty of corrupting young people. He could have been imprisoned or exiled but that didn't happen because...
He was allowed to pick his own punishment and refused everything except death
One purpose of "punishment" that is gaining popularity is "restorative justice". Restorative justice is not, however, strictly punishment, because its focus is on doing this:
Helping the victim of harm to become whole, often by having the offender take responsibility for the harm.
Philosopher Emile Durkheim argued that the system of corrections and incarceration is necessary because it is a key institution of this function
Social Control
Name 2 examples of ways the modern legal system tries to prevent people from being victimized by the law.
Jury trial, innocent until proven guilty, rules of evidence, right to confront accuser, immunity from testifying aginst self and relatives (I'll accept other things)
Benjamin Franklin got super angry about this form of punishment. He threatened to start sending buckets of snakes to England if they kept doing it.
Transportation of criminals
Rome didn't use long imprisonment as a punishment very often except for nobility. For example, the Greek king Perseus was held after his kingdom was conquered but died in prison in 166BC. The method they used to kill him was...
Keeping him awake