Reason based on self-evident truths

One of the more well-known tenets of the Renaissance is its reliance on reason. This reliance has brought forth vast scientific advances, taking us from the Gutenberg Bible to CD-ROMS, from blood sticks and fleams to the eradication of smallpox. Much of the new knowledge has certainly been used for evil as well as for good, but science itself has vastly expanded through reason.

Moral/social philosophy, though, has had a rougher time. From supposedly well-reasoned analysis have come such jewels as Marxism and its cousin fascism. Today, we have gender feminism, multiculturalism, and the militant strains of atheism. These new moral theories, of course, must destroy the more traditional ones they seek to replace. A common attack is based on misuse or misunderstanding of a basic logical concept: the idea of the self-evident truth.

Such a truth, also called an axiom, is a basic starting point, something that seems obviously true beyond question. They are necessary because one has to start somewhere. If you want to make a reasoned argument, you first choose your axioms, which you state without proof. If you reason well enough, your argument will stand on the axioms like a skyscraper on bedrock.

Perhaps the most famous examples are in the Declaration of Independence. "We hold these Truths to be self-evident: that all Men are endowed by their Creator with certain inalienable Rights, that among these are Life, Liberty, and the Pursuit of Happiness..." Notice that Jefferson does not try to prove these statements. He merely states them, assumes them, and goes on from there.

A deeper axiom in the Declaration, of course, is the existence of God, and this is the one that draws fire so often these days. Those who base their positions on an understanding of God's laws, or even on similar principles like the existence of right and wrong, good and evil, and absolute truth, are attacked for "failing" to prove their axioms. For instance, "How dare you claim God loves us when you can't even prove He exists? You're basing your whole argument on something you can't prove. You're a mind-numbed robot," etc., etc.

Though this argument is used to good effect, there's a delicious irony in it. The very people who attack self-evident truths, claiming to be more "logical" than that, are using self-evident truths themselves. In using logic, they have no choice, and they can no more "prove" their axioms than anyone else can, since an axiom is so basic that it cannot be proven.

If you doubt it, state your favorite position ("Gay marriage should be legal," for instance) and have a friend ask "Why?" at every stage. You will reach a point beyond which you cannot proceed; you will throw up your hands and say, "Because it's obvious!" This is no failing on your part; it's just that reason can't do everything. A great 20th-century discovery is Godel's Incompleteness Theorem, which basically says that human reason is limited since we cannot ever prove that any logical system is self-consistent. Another way to say this is that reason itself is based on faith in things we can't prove. (Ever wanted to irritate an atheist? Just tell him that.)

This is not to say that truth does not exist, but only that reason can't prove all of it. (In fact, the rules of logic are themselves based on axioms. Can you prove that if A implies B and B implies C, then A implies C? I agree, it's obvious, but that's not a proof.) One of my own axioms is that absolute truth does exist, whether we mortals can ever know it through reason or not.

If reason ultimately rests upon self-evident truths, how can we tell which truths are truly self-evident? How can we agree on them? To some, for instance, it is self-evident that human lives are more valuable than the lives of any other mammals. Some, though, deny it, taking the axiom that all mammalian life has the same value. (How they feel about reptiles, insects, jellyfish, etc., is unclear.) These are huge questions, and part of the answer is that some such differences simply cannot be bridged.

Nonetheless, we can at least agree on the nature of reason. Reason is an extremely powerful tool, and everyone should be able to use it well. In the realms of metaphysics and morality, though, its limitations become clear. So know what your axioms are, and never be ashamed to base an argument on an "unprovable" self-evident truth. By the nature of logic, there's no other way.

John Keisling bids Pete Wilson "Goodbye and good riddance!" He (Keisling, not Wilson) is a math Ph.D. candidate whose column appears Wednesdays.

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