What's a law?

In terms of speech acts, what kind of thing is a law? I'll suggest that it is a declaration (of a state's official position on some matter), an instruction (to various parts of the state on how to conduct themselves in specified situations), an assertion of fact, or some combination of these.

An example of a law that is just a declaration is found in Chapter 2, Section 28 of the Massachusetts General Laws: "The corn muffin shall be the official muffin of the commonwealth."

This is simply a declaration of a state's official position. By itself, it asserts no fact independent of the facts that it creates, and it carries no legal consequences. In conjunction with laws that contain instructions to the state, it could have consequences. For example, if the Commonwealth passed a law that required a representation of the official muffin on the state flag, then our law would result in a requirement that a corn muffin, and no other kind of muffin, be depicted. This requirement is created by the instruction to the state, combined with the fact created by the declaration in Chapter 2 Section 28, namely the fact that the corn muffin is the official muffin of the Commonwealth.

An example of a law that is an instruction without any explicit declaration or assertion of fact is the first amendment to the U.S. Constitution, which reads:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.

This is an instruction to Congress to not make certain laws; in combination with other laws that structure the relationship between the branches of the government, it is also an instruction to the courts to invalidate such laws if Congress creates them.

Although there is no explicit declaration, there is an implied declaration that it is the official policy of the United States to disapprove of the proscribed Congressional acts. In general, a proscription or punishment of an activity implies an official declaration of disapproval. This can be seen from the oddness of placing next to such a proscription or punishment an explicit declaration of support for the proscribed or punished activity. Such as:

It shall be the policy of the United States to promote witchcraft. Practitioners of witchcraft shall be put to death.

If this law makes no sense, it is because the implied declaration of the second sentence contradicts the explicit declaration in the first one. Many laws containing instructions will contain implied declarations within them, but not all. For example, a law setting fees for government services are not likely to contain such implications, unless the amount of the fee is meaningful. A law setting the fee for a fishing license at $25 is not likely to be an expression of one policy or another regarding fishing. But if the cost of the license was $5000, it might be seen as implying an anti-fishing declaration.

An example of an explicit factual assertion is the Second Amendment, where an assertion is adjoined to an instruction.

A well regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed.

The instruction appears to be aimed at Congress to not pass laws that infringe on the right to keep and bear arms, to the Executive to not take action that infringes on the right, and to the Judiciary to take actions such as invalidating Congressional enactments that infringe on the right, enjoining Executive actions that interfere with the right, and compensating citizens whose rights have been interfered with. There is also a factual assertion that a well regulated militia is necessary to the security of a free state. There may be a presupposed fact that there exists a right to keep and bear arms, if one takes a naturalistic view of rights. On the view that the state creates rights, it may be a veiled declaration of a right rather than an assertion of fact.

Could a law be a freestanding factual assertion ? Could there be a law, for example, that just asserts that the weakness of labor unions (at the time of the passing of the law) is economically harmful?

I don't know of the existence of any such laws, and people would find them odd. But there would be some sense to it. If courts are bound by the laws that the legislature passes, factual-assertion-type laws would have the effect of precluding courts, in their reasoning, from making use of a proposition that contradicts a factual assertion in a law. The exploration of this relationship between the courts and the legislature is an issue for another time.