Truth, Beauty and Axioms

To be filed under "be careful what you ask for...," there were some amazing questions this weekend. Let me try to weigh in on as many as I can this week. Here are three.

Gwydion asked, " What's the joke that ends with the punchline "Rectum? I nearly killed him!"

Wish I knew, but worked it into the early sections of the Comedist Manifesto (the holy skripture of Comedism) with a new set-up here.

BeepBeep asked, " The difference between an axiom and a presupposition?"

The two are similar in being propositions whose truth is presumed by some other belief or set of beliefs. A set of beliefs is axiomatized if it is shown that there some basic set of logically independent statements from which the entire system can be derived. Each member of this basis set is an axiom of the system. The classic example, of course, is Euclid's Elements where he starts with 5 axioms, 5 common notions and derives all the complex theorems of plane geometry (yes, I know Hilbert showed the complete set of axioms, but we can talk about that later).

A presupposition may or may not be an axiom because for nearly any set of beliefs you give me, I could list a large number of statements that would also have to be true for your beliefs to be true, but they needn't be logically independent nor need the set of beliefs be axiomatizable. Philosophy is very good at teasing out presuppositions and challenging them, although few after the logical positivists have thought that all rational beliefs need to be axiomatized.

pm asked, " Keats once wrote: "truth is beauty and beauty truth"do agree with Keats? Why or Why not?"

The answer is yes and no. Keats' original sentiment is a shot in the war between rationalists and romantics. Philosophy is a reactive discipline -- only when the world changes in some significant way can we realize that there is a presupposition (or axiom, for that matter) which needs overturning and along comes a new worldview. After the scientific revolution, there was a strong turn towards a rationalistic view of the world, that the universe was comprehensible by the human mind through science and reason. To many, this view stunk of hubris, it deprived the universe and life of mystery, beauty, and deeper non-observable meaning. Keats was thumbing his nose at the idol of truth held high by the scientific and asserting the primacy beauty, the hallmark of the romantic.

As someone firmly in the offending camp, I do roll my eyes at the sentiment. The idea that a mathematized well-ordered universe is somehow without beauty, elegance, or mystery is to not at all understand the results of modern science. Reality is stranger, more gorgeous, more complex than any human dream could make it. What the romantics seek is more than present in the rational understanding.

In this light, we can reinterpret Keats to should a deep truth about the way science works -- there is an aesthetic criterion of theory choice. In an important way, we do think that scientific truth is based upon beauty. We have seen it in the writings of the greatest of scientific minds. Isaac Newton, in his masterwork, The Mathematical Principles of Natural Philosophy, sets out a primer on scientific reasoning, he tells us how we ought to rationally approach the world. These guidelines include this,

"We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes."

The idea here is that Nature is simple, elegant, beautiful and any scientific theory that will describe it must be poetic in its compact internal structure if it holds any hope of adequacy. Theories with ad hoc pieces stuck together in a fashion that is not intellectually streamlined and uniform will not do. The world is beautiful and so must also be its description. Clunky science is bad science.

Perhaps the best example of this attitude comes from Einstein. When the general theory of relativity came about in 1916, there were no ways of testing it aside from a hitch in the orbit of Mercury that it could describe. But in 1919, the British physicist A. E. Eddington undertook an excursion to West Africa where he could observe a total eclipse and test Einstein's prediction of light bending, an effect that was not present in Newton's theory. When word of Eddignton's observation returned to Europe confirming Einstein's theory, it seemed a big deal. Here was the first true experimental support, yet Einstein, upon being informed was unmoved. Shocked at his lack of jubilation, he was asked what he would have thought if the experiment had shown him to be be wrong. Einstein calmly replied, "I would have had pity for the dear Lord. The theory is correct." The idea is that the theory was too beautiful, too elegant to be anything other than true. Beauty, when you get to rational endeavors of the highest magnitude, indeed is a measure of truth.