[Punishment] can deter crime and prevent the offender from committing further crimes.

I somewhat already addressed deterrence in one of my previous comments, however, I find that deterrence alone does not justify punishment. If the purpose of punishment is deterrence, and the point of deterrence is to prevent a future crime, either by the original aggressor or other potential aggressors, and the punishment can not do anything to make the victim whole, then it is in essence punishing for a crime that has not yet been committed. This alone is rather unjust, but the idea that punishing one party in attempt to deter other parties seems even more egregious. It essentially equates to punishing someone for the potential future actions of others.

Punishment can even rehabilitate some criminals, if it is not capital.

As a voluntaryist I advocate all human interactions need to be voluntary, lest they be immoral. If someone who has committed a crime and voluntarily agrees to submit to whatever ruling the arbitrator makes, retribution certainly could be a favorable outcome. However, rehabilitation that is not voluntary I would still argue is immoral.

It can satisfy a victim's longing for revenge, or his relative's desire to avenge.

I would argue that revenge and vengeance are a class of emotions that are sadistic in nature. While I agree that people do have sadistic thoughts and feelings, it is still wrong to act on them. While revenge and vengeance may be a far more understandable emotion, they are still sadistic. Deriving pleasure from the harm of others and acting on that pleasure against a person's will or preferences is not something I can justify as moral or just. If a sadist wants to act on these pleasures I am willing to posit that there is a function of the free market that will allow them to do so, but it definitely should not be the punishment of an unwilling party.

Punishment can also be used as a lever to gain restitution, recompense for some of the damage caused by the crime.

Punishment can be used this way, but it is unnecessary to consider it punishment, and there are other functions that work just as well in order to compensate damage and injury caused by the commission of a crime. Again, I bring up the distinction between punishment and consequence. If person A commits some trespass against person B, and the consequences of person A's trespass is a damaged front door, a missing tv, an injury to B which resulted in a visit to the doctor, costs of investigating the crime and finding A, and the costs of arbitration, and B is successful in meeting whatever burden of proof the arbitrator set to be convinced that A did commit and is liable for the trespass, then it would be reasonable to say that person A should be held liable for the consequences of his actions, not for retributive purposes, but simply because they are proximately related to A's own actions. Certainly B would not have gone to the doctor, replaced his front door and spent money on investigating and tracking down B if B had not committed this trespass. B certainly isn't likely to have spent money on an attorney or going to an arbitrator to hear the case against A had A not committed the trespass. All of these things could be said to have been consequences of A's actions, and it's reasonable to impose the costs of A's actions against him when he unjustly imposes costs against someone else. This is not something that falls within the scope of punishment or retribution. Simply calling punishment the consequences of one's actions are not sufficient to demonstrate that they are. Punishment occurring is completely independent to the action's of A and are imposed after the fact. The consequences of A's actions, however, are not independent of those actions, and occur regardless of whether A is caught. The idea that if A is caught and should be made to pay for the consequences of his actions comes down to the idea of liability, not punishment. Liability is a form of consequence because it manifests itself in the form of a responsibility that someone takes on. Liability can be implied or explicit, but none the less, inheriting liability is usually due to one's own actions (or the actions of another that you are charged with the responsibility of such as a child). Liability is a form of consequence because it is attached to the individual's actions and is dependent upon them. Punishment is not. If I ignore my responsibility to not break into your house, steal your TV and attack you in the process, it is reasonable to expect that I have imposed some level of damage against you. It is reasonable for me to expect that you will replace your door and tv and may visit the doctor to heal your wounds. These are costs that I have imposed against you. If I'm caught, repaying these costs are my liability and are justified. But forcing me to sit through some form of beating or imprisonment has no inherent attachment to my actions. There is nothing for you to gain by me getting assaulted or imprisoned other than to satisfy a sadistic urge. Also, imprisonment sold under the guise of safety is one I find hard to buy. Prisons usually tend to make people more violent and only more efficient criminals and should only be used to hold people who are there voluntarily. There are far more direct things that can be added in the name of safety. Perhaps compelling the criminal to pay for a level of safety that would have deterred him from committing the crime in the first place (eg, an alarm system, a dead bolt, et) yet still it would have to be after he agreed to appear to arbitration under no duress.

The whole idea of estoppel as applied by this book seems to be based on the subtle application of an ad hominem. The author claims that the legal idea of estoppel should embody the idea that actions and assertions should be consistent. This is a fine idea, but what are the conclusions in the context of enforcement? Someone can't claim to be the victim of assault if they have assaulted someone in the past? Someone can't claim to be the victim of rape if they have raped in the past? This seems to be a rather ridiculous basis for a legal theory (statists going to state I suppose). The idea that someone must live in perfect sync with their assertions lest their assertions be disregarded would mean that you probably couldn't take any reasonable or logical advice from anyone. An assertion should be judged only on the merits of its soundness in logic and the context in which it is being applied, regardless of the speaker. You can call a person a hypocrite for behaving in ways that are contrary to their assertions, but that does not poison the idea behind their assertion.

This does not discount the practicality of how estoppel is used, however. The idea of estoppel in the contexts of a lawsuit often are used for efficiency. If I cause $10,000 in damages to you, and you cause $10,000 in damages to me, certainly we can spend money on suits and counter suits to get a ruling that I owe you $10k and you owe me $10k, but in reality, the compensation of damages would simply cancel each other out. This does not mean that the damage done in total cancels out, however, it simply means that both parties have $10k less in overall wealth, leading to an aggregate loss of $20k. There is no need to add to these losses by pursuing a lengthy and expensive lawsuit, so courts use estoppel as a means by which to prevent such a lawsuit from occurring.

It becomes difficult to defend the idea of estoppel when it is interpreted as "You hit me, so I hit you and that makes us 'even'." It certainly does not make the parties even, it puts both of them worse off.

I define aggression in this context as "an initiation of violence or coercion against another person with the exception of force used as self-defense." I would define self-defense as "the immediate and necessary response to aggression that leads to the dissipation of that aggression." So when I say, "imposing aggression on the aggressor" I mean "using violence beyond the context of self-defense as a means to resolve an aggression that has already occurred." It wouldn't be a logical contradiction because any force that goes beyond the necessary means to end aggression would be defined as aggression itself. The extreme example would be if you slapped me 2 days ago, then I find and kill you, you wouldn't say that me killing you isn't aggression because it was in response to you slapping me, would you? Even if I simply hunted you down and slapped you back, doing so wasn't necessary to end your aggression, because you were no longer aggressing against me at that point. Since there was no immediate threat that you imposed against me at that time that justified me slapping you, it would be considered an additional initiation of force, therefore it would be additional aggression.

Unfortunately I don't really have any additional links to present to you. I find that I have a tendency to simply agree with a good idea that I read on mises and tend not to do a rigorous consideration of those ideas. Instead, I try to reason through things in the context of hypotheticals and discussion. I used to do quite a bit of reading on mises and find that it doesn't really give you the skills to convince other people of these ideas since most people don't consider it a credible resource (nor do they take the time to read the material anyway). I got frustrated by this. The idea that I was doing all of this reading to have the source's credibility disregarded. I realized that if I was going to convince someone I would have to take the time to build on the ideas that they already hold and show them to follow the natural conclusions of the opinions they already hold. Since most people already agree with the basis of the NAP, I find it is easy to convince them to at least extend the conclusions of their opinions to be more peaceful, if not full on voluntaryist.