Natural law theory exaggerates the relation of law and morality. Positive law is a reaction against particularly that aspect of Natural law theory. It insists on a distinction between human law, which they call positive law and moral and scientific laws. Human laws are posits of human society while scientific laws are independent of what we take them to be. (You will note, sometimes, that writers refer to what I call 'mores' as 'positive morality' in contrast to 'rational morality'.)
The Classical version of positive law theory is John Austin's (1797-1859)"command theory." His model was that of a definition and his goal was to give a definition of law that removed all evaluative language. We see some continuity with Aquinas' natural law. While he rejected the blurring of law and morality, he did give a similar "unified" definition of law: "A rule laid down for the guidance of an intelligent being by an intelligent being having power over him." God and men both make laws so his distinction is between the laws of God (reason) and those of historical human societies made by political "superiors." He insisted on distinguishing the theory of (concept of) law from the "science of legislation" which had to do with the criticism (evaluation) of the law (c.f. Dworkin's theory of legislative justice).
Austin is a prime example of a positivist in legal theory, but his was only one version which we call "command theory:" Law, Austin reasons, has the status of command. Austin then defines 'command" as any signification of a desire by the sovereign. He then defines the sovereign as "the determinate rational being or body that the other rational beings are in the habit of obeying." Each of these further definitions is an attempt to substitute a descriptive analysis of some prescriptive concept. The notion of a 'command', for example, includes a normative element of authority and imperative (as distinct from a presumptive request). Similarly 'sovereign' has a normative element of legitimacy. He tries to define these both away through the notion of shared habits. One of Austin's motives was to block moralistic theories of legitimacy such as those the USA used for forty years in refusing to recognize China. If a government is in stable effective control of a territory, then its writ just is the law of that land.
The rest of the definition of 'command' is important. Austin's analysis of a law is different from a normal command in the sense that a law must be logically general. The court makes particular judgments, but the legislation is always general in form. A direct, one-time command to an official is not law. Law is a command to "forbear a whole class of acts."
There is a further element that Austin thinks is inherent in the notion of law-namely that of punishment. However, 'punishment' also has a normative connotation, namely, of a harm that is "deserved" or results from violation of a valid law. This Austin tries to define away with the words "accompanied by the threat of evil in case he does not."
These once all the definition all illustrate how Austin tries to eliminate the notion of legal 'duty' or 'ought' in terms of the probability of punishment-the 'habit' or tendency of the system. Degree of obligation corresponds to probability and severity of harm. This raises serious problems for the command theory. Consider one serious crime that is difficult to prosecute: rape. The rate of arrest and conviction for rape is lower than that for most other serious crimes. Further, the punishments are relatively light because male judges frequently have a "boys will be boys" bias. Does this mean that a male's obligation or duty to avoid raping is not a strong duty?
The problem, simply, is that the definition doesn't capture our concept. The counter-attack on positivism focused mainly on the command aspect and its link to punishment. We distinguish laws from illegitimate commands. Rule by a criminal gang may be generalized and backed by threat of force, but it is not the rule of law. And many laws have no punishments attached to them.
Austin knew about and acknowledged some of these difficulties. You will notice his answers in the text. He addresses declaratory laws such as laws that repeal laws and laws with no penalties, laws merely creating rights for example and laws defining marriage. Other problems arise, especially for Austin, with English "customary" laws (The "Common law" includes decisions of judges made according to legal "principles" for which there is no written legislation. European states with a Roman law heritage do not have this element as strongly in their law.) Austin explains all of these away with his notion of tacit consent of the sovereign. Since the king does not object, he must have consented. However, they certainly require a very loose application of a "signification of desire."
Other problems concern international and primitive law. Most legal history recognizes laws of primitive tribes that have no writing, hence, no formal, legislated code. Austin's somewhat unsatisfactory response is primitive law is not law. A good theory could take that position, in principle, but not when we present it as a counter-example to the definition. We naturally judge that the definition fails if it does not explain our normal use of 'law'.
Another problem has to do with Austin's failure to recognize a kind of complexity in the law. In England and America, there are "layers" of law which Austin cannot easily make sense of. They treat the constitution and treaties as a "higher" law. Such a law "constrains" subsequent legislation and Austin's command theory makes little sense of that. It has equal trouble with the complex federal legal system where each state is sovereign and yet part of another state.
America poses other problems for the implicit political theory in Austin's definition. The American political system has an arrangement of "branches of government" with "checks and balances" so, in theory (current events to the contrary), no single branch is superior or has a free hand. How would we determine who, in that system, is "the determinate superior body"? The highest authority in their local theory is the "people" who contract or "hire" the government institutions through their constitution. Who, then, is the "bulk" of society who owes that body obedience?
The attempt to eliminate evaluative language fails. Austin tries to make law "closed on facts," but the effect is to make it mysterious how there could be any legal obligation or right.
Some of the most devastating criticisms of Austin's Command theory comes from other "positivists." One is H. L. A. Hart, whom we will read frequently in this class. He raised the problem alluded to above of the mob of gangsters on an island. Their demands on the local population seem to meet Austin's definition but we would call their's the opposite of a rule of law.
Hans Kelsen (1881-1973) developed an interesting modern version of positivism around this implicit criticism of Austin. He is still committed to the separation of law and morals, but tries to avoid Austin's mistake of reducing obligations to non-moral habits, probabilities, harms and expressions. Kelsen is still a positivist in that he agrees that law must be posits (social constructions) rather than derivations from reason. The key evidence for this is that public law is flexible and dynamic in contrast to God's law, which never changes. Natural law seems to imply that real law cannot change (except, remember, in the details).
However, Kelsen recognized that law must also have a normative base. Logically, he concludes, there must be a basic norm on which law rests. However, it does not need to rest on a moral norm. It is the prescriptive premise from which the obligation of law follows. Without that basic norm, we can't get the legal "ought" from the sociological or historical "is." There has to be such a norm or justification would never come to an end. Still, the normative grounding is different from the norms of morality-Kelsen preserves the separation. This yields a more subtle and defensible version of positive law.
He calls that basic norm "the logical constitution." It is the basic evaluative premise from which the legitimacy or validity of all the laws derive. An example of a basic law would be: One ought to obey all those acts of Legco which are signed by the chief executive and acceptable to the NPC." Laws can be created, but the basic norm specifies how they can be created and changed. Only those created in accordance with the basic norm will be valid laws. The notion of a valid (binding) law must be kept distinct from the notion of a good (just) law. Criticism of law is indeed a moral matter but a bad law may still be a valid law and create a legal (but not moral) obligation.
One feature of Kelsen's separation is that he thought of the basic norm as purely procedural. It specified how other laws could be made, but not what possible content they may have. If a law followed from the procedure, it could have any content at all. Further, the basic norm, unlike ordinary laws, does not "follow" from any other higher norm. It is not a component of God's natural law. What makes the basic norm "real"? (Notice the basic norm cannot be described as 'valid'-'valid' is defined only for ordinary laws.) What gives a basic norm its normative status--its ability to create other legal "oughts"?
This puzzle plagues all of positive law theory. How can they explain the legitimacy of the rule of law itself-of the basic norm of law? Kelsen wanted to avoid Austin's recourse to habit, but ends up facing a similar problem and giving a more complex but still inadequate solution. The basic norm, he says, is an accepted custom, or in Kelsen's full wording, "when the custom through which the constitution has come into existence or the constitution-creating act consciously performed by certain human beings, is objectively interpreted as a norm-creating fact. . ." then a basic norm exists. It is not created or justified by that "objective interpretation" or widespread, interpersonal acceptance. The acceptance comes in merely presupposing the norm. The basic norm is when the custom is consciously interpreted as being a norm creating fact.
This leads Kelsen to an interesting doctrine of revolution. Revolution is when the basic norm is changed by some procedure not specified in the basic norm. Would changes to the basic law and bill of rights by the provisional legislature constitute a revolution? The USA had such a "revolution" early in its history when the US constitution was written. Its adoption did not follow the rules of amendment contained in the old "constitution" (the Articles of Confederation). But the society "consciously interpreted" the ratification procedure as conferring legitimacy, so it constituted a change of basic norm.
The principle of legitimacy, Kelsen asserts, is limited by the principle of effectiveness. Some "fact of the matter" determines what is the legitimate government of a society and what are its laws. Validity is a matter of effectiveness only for the basic norm, however. If no one pays obeys the subsequent laws, then the regime is plagued by lawlessness. But as long as the people accept that they are laws (which they are disobeying, the basic law is still effective. However, that situation is clearly a borderline one. Normally, people will be guided by their recognition of an obligation to obey at least some of what they regard as valid laws. So even widespread disobedience to other "valid" laws is consistent with the claim that they are valid. The basic norm is still effective if the custom is "objectively interpreted" as validating or legitimizing law-making actions.
 This is not a fatal objection. Austin could retort that we misuse the concept when we talk of primitive tribes. He may be right even if he cannot convince native speakers of his account of the rule for use of the term. However, this does make it hard for him to prove his claim to those speakers.