Axioms of choice

“We hold these truths to be self-evident,” wrote Thomas Jefferson. By which he implicitly admitted that he couldn't prove what he was about to assert. The claim of a political philosopher that something is self-evident is equivalent to the fallback position of a beleaguered parent: “Because I said so.”

Jefferson's self-evident truths were that all men are created equal and that they have inalienable rights to life, liberty and the pursuit of happiness. 

Mathematicians call self-evident concepts axioms. For many centuries, the axioms of geometry were thought to be obvious statements about the physical world. Two points determine a line. That is, there is a unique line that passes through two points. From the axioms, geometers like Euclid proved all manner of interesting and useful theorems, including the famous theorem named for Pythagoras.

In time, however, the mathematicians realized that their axioms were agreed-upon conventions rather than irrefutable descriptions of reality. New geometries could be conjured by starting with different axioms. At first the new geometries were thought to be idle curiosities. But they came to have uses, for example in Einstein's theory of relativity.

Many people treat Jefferson's axioms as though they were handed down from on high—by the god of Moses, by Jefferson's “nature’s god,” or by some other deity. Humans tamper with equality, life, and liberty at their peril. George III of Britain and Louis XVI of France were slow to learn.

The appeal to a higher power is understandable. Patrick Henry wouldn't have said “Give me liberty or give me death” with such conviction if he thought liberty was merely one value among many that might have been chosen by the Continental Congress as a starting point for the American republic. Nathan Hale would have had to come up with different last words than “I regret that I have but one life to give for my country." Revolution is serious business, not to be undertaken on shaky principles.

For theists and deists, divine revelation might be sufficient justification for building societies on certain values. For others, societal axioms have to prove their worth. For example, societies that prioritize liberty ought to deliver better lives to their people than those that emphasize order, say. Equality ought to deliver a similar payoff.

What constitutes better life is often open to debate. Likewise how the values themselves are to be defined. Americans are more attached to political equality than to economic equality. Some countries of Europe and many traditional societies reverse that preference.

John Locke made the right to property foundational. Americans have generally agreed. But Karl Marx, various religious orders, and most American Indian tribes considered property rights derivative at best.

The Marxists lost the argument on property rights with the collapse of the Soviet Union and the abandonment of socialism by China. The Russians and the Chinese didn't become principled Lockeans but rather functional ones. Socialism failed the test of practice.

Yet aspects of socialism exist even in mainstream America. Taxes represent a taking of private property for public use. Anarchists aside, everyone acknowledges that some government is necessary, and so there must be some taxes. Libertarians want as little government and as little taxation as necessary. Conservatives allow more. Liberals still more.

What’s the right level of taxation? Once the principle of taxation is granted, the details are a matter of negotiation. And what kind of taxes? Americans in the 21st century are accustomed to income taxes, sales taxes, property taxes and excise taxes. Most pay import taxes without realizing it, since tariffs are baked into the price of goods they buy. Americans might have to get used to higher import taxes if the trade war with China continues.

Americans have largely rejected wealth taxes, aside from property taxes. And they blow hot and cold on estate taxes. These last are a good test of the dueling approaches to social norms. If people own property by right—if property is axiomatic—they presumably have a right to pass their property to their heirs. But if property is a social construct, then they don’t have that right. In the latter case, experiment will determine the optimal level of the estate tax. Set it low to encourage individual initiative. Set it high to reduce economic inequality.

Something similar applies to other so-called rights. How free should speech be? Americans insist on freer speech than most other people. But we allow all sorts of restrictions on speech, including laws against libel and slander, laws against child pornography, and laws protecting intellectual property. As with taxes, once you allow any restrictions, the rest is up for negotiation. What level of free speech works best? For whom?

Likewise the right to bear arms. It's not part of natural law. Or if it is, America is one of the few countries to have discovered it there. It's something that seemed advisable to write into the Constitution in the 1790s. Many people would like to write it out of the Constitution today. Nothing prevents them, except lack of the numbers required by the Constitution for doing so.

More than a few mathematicians have professed amazement that mathematics describes the physical world as well as it does. Much of this fit reflects a prudent choice of axioms.

The axioms of politics have been harder to agree upon. It doesn't help matters when advocates of certain axioms insist on their supernatural provenance, to the exclusion of others. Maybe they do reflect some particular ordering of the cosmos, but they still have to pass the test of human fallibility.