There are two major understandings of law that are generally classified as legal positivism. The first, which was argued by
Thomas Hobbes,
Jeremy Bentham, and
John Austin, is a theory of law which is defined in terms of an
uncommanded commander, or
Sovereign. All law, as this first group of
positivists understands it, stems from the will of this uncommanded commander. For
Hobbes, this is in fact a moral imperative. The argument presented by Hobbes (in his most famous work,
Leviathan) goes something like this:
1) In a state of nature, all people (in fact he wrote "men", and, this having been written in 1651, it's a pretty safe bet that he meant men, but in any case) are functionally equal, in that just about anyone can kill just about anyone else, given the right circumstances, and, while almost everyone thinks themselves smarter than most other people, this is basically because people are full of themselves. This being the case, everyone has equal rights to everything that they survey, up to and including the lives of others. This is because the only way to ensure the safety of one's own person and property in a state of nature is to arm oneself against and dominate everyone who could possibly pose a threat.
2) Moreover, since there is no limit to anyone's rights, there is no context in which anything can be considered to be just or unjust, right or wrong, good or bad, etc., except in what agrees or disagrees with a person's own personal taste.
3) However, for fairly obvious reasons, this means that living in a state of nature tends to make life "solitary, poore, nasty, brutish, and short."
4) Therefore, whereas we would prefer, all things considered, not to be abruptly bludgeoned to death at any given moment, it is a law of nature (that is, a principle that should be intuitively obvious to anyone) that one should seek peace.
5) In order to achieve peace it is necessary for people to give up some of their rights; for example, the right to bludgeon others to death. If everyone gives up this right, then people can be reasonably certain that, on the whole, the number of violent bludgeoning deaths will decrease.
6) In the context of this kind of agreement, there is created a concept of justice; that is, it is unjust to break one's agreements. Moreover, breaking one's agreements goes against the laws of nature, because where there are no agreements, there is no peace; where there is no peace, there is a state of nature; where there is a state of nature, there is a good chance that you will be abruptly bludgeoned to death (this is more or less the point that all of Hobbes's arguments boil down to; in fact, possibly the simplest arguments for Hobbes's legal positivism is that it is, quite literally, better than a kick in the head).
7) As long as neither party has any assurance that the other party will respect the agreement, however, the agreement is functionally useless, since neither party has a strong enough reason to set aside their own rights. Therefore, there needs to be something that compels both sides to keep their ends of the bargain, on pain of some punishment that outweighs the benefits of breaking the agreement.
8) In order to give both parties an equal interest in maintaining the agreement, there must be some judge who has no reason to prefer one side over the other, and this judge must have the power to punish either party of that party breaks the agreement. In this specific case, the minds of all parties involved are not equal, unlike in the state of nature, because the parties bound by the agreement are biased, and therefore not qualified to mediate a dispute between them. Therefore, the reason of the judge, so long as that judge is impartial, is superior in this context.
9) In order for everyone to be bound under the same agreements, it is necessary for people to come together under a commonwealth. In order to ensure that everyone has an equal interest in maintaining the agreements of this commonwealth, there must be an impartial judge that settles disagreements that occur within the commonwealth. In particular, there must be a single clear source of authority; otherwise, there is controversy, and controversy eventually leads to (you guessed it) death by bludgeoning.
10) In order for this judge to be impartial, it cannot have any preference for one side or the other in any disagreement. In particular, then, the judge cannot be subject to the same agreements as the people that the judge presides over.
11) Finally, since the will of this judge is the only objective standard of justice that people have to rely on, it follows that obeying the commands of this judge is moral, and indeed not obeying them is contrary to the laws of nature. Therefore, in a long and complicated way, the laws of nature imply that there should be an uncommanded commander whose will should be obeyed by everyone.
Hobbes was a staunch royalist, and Leviathan is in many ways an argument against rebellion against the monarchy. However, the uncommanded commander does not necessarily have to be a single person, so long as whatever body holds power is not checked in any way.
While this kind of argument defined legal positivism for many years, a dissenting position was put forward much later by H.L.A. Hart. Hart argued that law cannot be understood in its entirety as a command; in particular, there are many laws that confer rights, which, rather than saying "You must do this (or abstain from doing this) on pain of punishment," instead say "You can do this, if you like, in the following way." Also, Hart argued that while the person or persons that constitute the governing body may change over time, people have a habit of obedience to the system that declares the governing body to be authoritative. This is the basis for Hart's "Rule of Recognition". This states that it is not the body of the Sovereign, as Hobbes and Austin argued, in which authority is vested. Rather, authority is vested in the means by which people recognize laws as being authoritative. For example, we recognize laws passed by duly constituted governments as being authoritative in a way that rules passed by the Boy Scouts of America are not.
There are two theses that have been used to define legal positivism; namely, the Identification Thesis and the Separation Thesis. The Identification Thesis states that morality should not play any part in applying the law to different circumstances - the law are the same in all cases. The Separation Thesis states that there is nothing inherently moral about the law - that is, obeying the law is not necessarily any more moral than disobeying the law. These theses help define the difference between the philosophies of Hobbes and Hart; Hobbes's philosophy incorporates only the Identification Thesis, while Hart accepts both.
For Hobbes, the identification thesis is a necessary result of having a single authoritative Sovereign. While the Sovereign may defer adjudication of its laws to lesser judges, it is the duty of the judge to enforce the will of the Sovereign. In particular, this means that the judge should not be using his/her own sense of morals when rendering judgments, as this would involve usurping the authority of the Sovereign. Instead, the judge should look to the written law to determine the will of the Sovereign. For Hart, the purpose of the Identification Thesis is to avoid confusion; specifically, it is of no help to anyone to confuse the law as it is with the law as it ought to be. If the law as it is proves to be unpalatable, then it should be changed, but the only thing that is accomplished by ruling contrary to the law as it is is to weaken the assurance of those governed by the law that the law will be applied consistently; a guarantee that is essential to a functional system of law.
The Separation Thesis, by contrast, makes no sense when viewed from Hobbes's perspective. It is only when we have a commonwealth, under the rule of a Sovereign, that we have any concept of morality. It is necessarily moral to follow the laws set out by the Sovereign, and immoral to break them, since the laws of nature mandate the existence of a uncommanded commander in order to stave off a state of nature. For Hart, on the other hand, the Separation Thesis is what makes positivism useful for people governed under laws. When we understand that law as it is is not the same as law as it ought to be, we can make for ourselves a moral decision about whether or not to obey the law. This is simply a more honest approach to law, as far as Hart is concerned; it is much better to say "This is the law, and I do not accept it," than to say "This cannot be the law, because I do not like it."
The approach to law that is most in conflict with this philosophy is the school of natural law, which holds that, if judges use their common sense in all cases, and establish precedents within the common law, the law will eventually work itself pure. In particular, this school rejects the thesis that morality can play no part in applying the law, and instead believes that there are certain moral principles to which the law must be accountable.