When Euclid wrote Elements circa 300 B.C. he set down five axioms.
- A straight line can be made from any two points.
- A finite straight line can be extended continuously.
- A circle can be described by a line segment with a fixed point and the opposite point rotated continuously to its original position.
- All right angles are equal to one another.
- If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
There is no proof of these axioms. They are definitional as to a line, a circle, an angle, and parallel and intersecting.
There are two basic polygons of Euclidian geometry that are remarkable descriptors of phenomena: the triangle and the circle. A triangle is a polygon that can be made with the fewest number of sides. A circle is a polygon with an infinite number of sides.
All similar triangles have the same proportions regardless of scale. Any point on a circle can be described by a line descending from that point to intersect at a right angle with a radius. One can know the proportions of that triangle knowing only one other angle. All the trigonometric functions can be thus derived.
Euclid’s Elements is so well founded on these self-evident axioms that Euclidian geometry and derivations of it are used to describe with accuracy nearly all—it is subject to some exceptions that it is not necessary to discuss here—human experience of the physical world, from solid bodies to sound waves. Derivatives of Euclidian geometry describe (though not unqualifiedly) planetary motions adequately through Kepler and many quantum phenomena (e.g., spherical harmonics that govern electron shells which in turn govern quantum states of energy). The structure of Euclid’s Elements is similar to the structure of experience.
If you were to deny the axioms of Euclid’s elements—other than, to some extent, the fifth axiom (a discussion for another place)—you would destroy the descriptive and predictive character of Euclidian geometry and its derivatives.
Jefferson’s Declaration of Independence begins its argument justifying the revolution with “we hold these truths to be self-evident.” The first axiom of the American Revolution is “all men are created equal.”
This axiom is a rejection of the ground of government which had for so long dominated world opinion, the divine right of kings. The divine right of kings is a principle of inequality, culturally understood in the West from the paternity of Abraham, the authority of Saul, and the authority of Caesar. It is a mix of divine anointment, conquest, and heredity. Absent supernatural proofs, anointment is an inequality rooted in fraud. Conquest is an inequality rooted in force. Heredity is a mix of both, which Thomas Paine rebutted simply with if God intended hereditary government He would not “so frequently turn it into ridicule by giving mankind an ass for a lion.” The authority of kings is an authority based on a political geometry of fraud, force, and, not infrequently, farce.
Equality and free government are based on an opposite and superior political geometry of reason. The unique characteristic of a human being qua human being is reason. As all right angles are equal, all human beings, other than infants and imbeciles, possess reason.
“Nobody ever saw a dog make a fair and deliberate exchange of one bone for another with another dog.” —Adam Smith, Wealth of Nations
When Adam Smith wrote this he was speaking specifically of trade. But the principle is the same when applied to politics. Only human beings can—and persistently do—enter into agreements.
Reason is the power to distinguish between universals and particulars. A human being can see a chair and comprehend that it is at once a particular chair and one of an infinite number of possible chairs. This is true of the general manner of ideas and expression of human beings. We use speech constructed on mutual understanding of particular things participating in universal categories.
One dog fairly and deliberately exchanges one bone for another with another dog.
Each word in the above sentence represents a concept that is universal: oneness, otherness, fairness, deliberateness, what is a dog, what is exchanging, what is a bone. Each word is intelligible because it has a particular meaning as well.
Yet Adam Smith’s dogs do not have this “simple” power and as a result are incapable of making an agreement, a fair and deliberate exchange.
Human beings make agreements using words and remembering their meaning. The basis of these agreements is concurrence about the universal and particular meaning of words sufficient to form, in the parlance of common law, “a meeting of the minds.” Agreements, or contracts, are compilations of words which deliberately describe an exchange of one thing for another and to which the parties bind themselves in the future. Unique among animals that live in society, we use speech to exchange ideas about the just and the unjust. All human beings, infants and imbeciles excepted, are capable of making agreements about the just and the unjust. That is the basic geometry upon which our liberty is built.
- All men are created equal.
- They are endowed by their creator with certain inalienable rights,
- That among these are life, liberty and the pursuit of happiness.
- Governments are instituted among men to secure these rights, deriving their just powers from the consent of the governed.
The above might be called Jefferson’s Elements. They are axioms. No further proof of them is necessary. They can be examined and applied. And they can be denied. But they cannot be denied without destroying free government, just as Euclid’s axioms cannot be denied without destroying the remarkable descriptive predictive character of Euclidian geometry. The structure of Jefferson’s Elements is similar to the structure of experience.
Today, we are in the midst of a political defense of Jefferson’s Elements against a drift of political opinion that has slowly separated itself from these axioms.
Heredity has become an increasing part of our politics. It has been pointed out many times, but for the election of Trump we would have gone on to twenty-four of the last thirty-two years with one of the same two political families in office.
The agreement, the compact made by the People, the Constitution also has become routinely ignored, as both parties advance legal theories that do not require the words of the Constitution to have their plain meaning. Justice Gorsuch is a good first step in remedying this. Similar nominees upon the retirement of Kennedy and Ginsberg will also be essential.
The law with respect to immigration has been routinely ignored, with a view towards institutionalizing and making permanent that disregard as a prosecutorial discretion.
The Congress’ political will has been sapped by its preference for delegating legislative power to the bureaucracy, and the bureaucracy has correspondingly developed a political will independent of the process of elections.
These things and more are now at issue in the pitched battle over Trump’s presidency. There is an enormous effort afoot to convince you that the great issue of our time is the etiquette of tweeting on Twitter. This is an effort to focus on the small to take your attention off of the larger matter of Jefferson’s Elements.
Happy Fourth of July.