### The Law Is Not a Mathematical Treatise

We often find people saying something like, "If Americans can serve in the military at age 18, it is contradictory not to let them drink at 18 as well." (An example of this sort of accusation.) But these complaints rest on a confusion.

When we want to build up a system of mathematics, such as geometry, we state propositions (theorems, axioms, lemmas, etc.) and work out their consequences. We should worry about the consistency of our propositions, because if two of them are contradictory, anything at all can be proven in our system.

But the law does not consist of propositions with logical consequences, from which we try to prove something further. It consists of rules of conduct, with consequences for the breaking thereof, which serve to help guide and improve our practical life. In general, the only important sort of proposition that laws contain is that X is illegal and Y is legal.* Therefore, in general, laws can be contradictory only in declaring X to be both legal and illegal at the same time. And the law is "incoherent" only when it makes the same actions both legal under one statute and illegal under another.

Since law exists to guide and improve our practical life, the justification for a law is not a logical demonstration, but an assertion of its practical efficacy: "Since we've passed the 'Pooper-Scooper' law, the sidewalks are so much cleaner, and we are not tracking dog poop into our apartments nearly as often!"

But, but... what about our rights?! Well, talk of abstract rights apart from a concrete set of social arrangements is a bunch of mularkey (a point even a libertarian icon like Mises agreed with), and the truth behind the assertion of rights is their practical efficacy: we'd all like to live in a society in which we can do what we'd like, in so far as "doing what we like" does not create social chaos. No one wants to have to check with the legal authorities to see if they can go for a walk, and since "going for a walk" does not generally produce social chaos, we generally should have no laws saying people can't go for a walk when they want. Similarly, the "right" to free speech is justified because we enjoy being able to say what we think without legal consequences, and that "right" is properly ignored when it creates social chaos, e.g., falsely shouting "Fire!" in a crowded theater. Consider: why don't Britons have the "right" to drive on the right-hand-side of the road, as Americans do? Or why don't Americans have the "right" to drive on the left-hand-side?

So the accusation that two laws, one of which sets the drinking age at 21, and the other of which allows 18-year-olds to serve in the military, are "contradictory" is:

1) False: there simply is no logical contradiction here, unless one ties several extraneous propositions to the laws, such as: "Anyone who can serve in the military is a legal adult. All legal adults must legally be able to perform the exact same set of actions." (The actual laws, not being propositions at all, do not imply or entail these propositions.)

2) Irrelevant: logical consistency is a virtue of a system of theoretical propositions, and is a notion that simply does not apply to practical life. In the world of practice, what is relevant is means-ends consistency, not logical consistency. We are being inconsistent, in practical life, if we, for instance, discourage our kids from drinking liquor while giving them bottles of vodka for their 13th birthday. And the problem with those two choices is not that they are illogical, in terms of formal logic (because there is no formal contradiction, first of all because these are not propositions), but that they work at counter-purposes.

(And by the way, I think that the drinking age should be lowered, but the reason we should lower it is that the actual outcome of lowering it would be better than the status quo, and not some alleged "contradiction.")

* A lawmaker may write some proposition into a bill, e.g., "Human life is sacred. Therefore, capital punishment will be illegal in Freedonia." The actual law is that "capital punishment will be illegal in Freedonia." The logical implication is a rhetorical flourish that has no legal impact: if someone should "discover" that human life is not sacred, capital punishment will still be illegal until the law is overturned.

1. But Mises was also a relativist. He thought any kind of talk about morality was "mularkey".