February 01, 2004

Values vs. First Principles

I received a copy of C.S. Lewis' The Abolition of Man for Christmas; I'll be reviewing it eventually, but I want to re-read it first.

One of Lewis' points, though, is that the meaning of the word "reason" has shifted since the Middle Ages--indeed, since antiquity. Today what we mean by a reasonable or rational argument is one that follows the rules of logic. To the medievals, as to the ancients, the word meant something more--it meant logic, of course, but it also meant the recognition that certain truths were self-evident.

As, for example, that honesty is better than deceit; that integrity is better than corruption; that courage is better than cowardice; that sexual fidelity is better than promiscuity; that industry is better than sloth; i.e., that wisdom is better than foolishness.

The interesting thing about these kinds of self-evident values is that you can't really make a rational argument for them (in the modern sense of the word)--that is, from first principles. As Lewis shows in his book, any such attempt either fails at the outset or relies on some other standard of value that is to be taken as given. Try it--try to think of an argument in favor of honesty that doesn't involve an appeal to some other intangible value.

I'll have more to say about Lewis' argument, and the consequences that follow from it, when I actually review the book. In the meantime, I have some observations.

The first is that the primary lesson I draw from the history of philosophy is that you can't prove anything of interest about the real world from first principles. I'm thinking particularly of Mr. Hume; he began with the axiom that he should only believe what he saw, heard, tasted, smelled, or touched directly--and ended up with solipsism. In short, he proved that he couldn't prove that anything existed but his own mind. Some have regarded this as a profound result; I regard it is a reductio ad absurdum. His axioms were too few, and at least partially incorrect to boot.

It has long been my view that any philosophy that doesn't take objective reality--the world as it is--as its starting point is doomed to end in futility. Thus, the notion that any attempt to derive a worthwhile system of values from first principles is inherently flawed doesn't distress me; it's what I'd expect.

The second observation stems from the history of mathematics. Early in the 20th century there was an attempt to devise a set of axioms from which all of mathematics could be derived--a system in which every true statement of mathematics could be proven. Then Kurt Goedel came along and proved that you can't do it--that if your system is powerful enough to describe all of mathematics, then necessarily there will be true propositions within that system that cannot be proved. That is to say, there will be mathematical statements whose truth will be evident to the mathematician but for which no proof exists.

Now bear in mind that formal mathematics is all about proving things from first principles, and that it has nothing to do with contingent reality--and yet, even in this confined system, there are truths which must be seen to be self-evident.
It's improper, of course, to generalize from Goedel's theorem to the wider world...but it seems to me that objective reality is far more wild and complex and rich than mathematics, and that any formal philosophical system (like Hume's) that attempts to encompass it must likewise be larger and richer and more complex than mathematics. (And isn't that a thought to give one pause! As if math wasn't hard enough!) I don't think anyone is likely to accomplish it; mathematical reasoning is difficult enough, and one could argue that math is simply that branch of philosophy in which it's straightforward to tell whether or not you've made an error in your reasoning.

From this point of view, it once again doesn't surprise me that attempts to describe the nature of the world through formal reasoning from first principles have failed to capture its richness. And further, it doesn't surprise me that many important things about the nature of the world will be self-evident but unproveable--like the value of honesty, integrity, courage, compassion, and fidelity.

It's the attempt to dispose of our traditional values through logical argument that's unreasonable, not our acceptance of them.

Posted by Will Duquette at February 1, 2004 07:38 AM

Mindwarp said:

It's the attempt to dispose of our traditional values through logical argument that's unreasonable, not our acceptance of them.

I think you pretty much nailed what it is that turns people off about modern philosophy.

steveh said:

It's been awhile since I read "Abolition". It's definitely a heavy book (content-wise), even though it's one of Lewis's shorter ones.

As a math student, I do sometimes wonder about the difference between math and philosophy. Of course, math has always had the connection to some reality (we use exponentials to calculate interest, integrals to calculate force used to move an object, etc.), it has also always had an abstract, otherworldly side.

(Imaginary numbers...they exist, and are perfectly valid in certain mathematical situations...but I've yet to meet something in the real world that MUST be defined by the square root of negative 1.)

I also am sometimes surprised when I learn about how loosely mathematics was structured until a century and a half ago. (Newton's calculus worked fine, but it had no strict 'first-principles' definitions. Limits have been in use since the first attempt to estimate pi, but the strict definition is barely two centuries old.)

One idea which has been growing in the back of my mind is that modern mathematics has its moments--but the wonder of the study is too easily lost in the boring world of proofs, first principles, and strict logic.

And (probably like modern philosophy), it's rather hard to get people interested in something that so strict and complicated. A 'first-principles' definition of a thing that ignores its richness is hardly worth having.

(Come to think of it, that probably applies to theology also...)

J.W. Hastings said:

Will,

I just finished reading The Abolition of Man for the first time. As you can probably tell, it's influenced some of my recent postings on my blog. I'm interested to read your take on the book.

As for Goedel's theorem: I have no trouble generalizing from it, although I do recognize the limitations of such generalizations.

J.W.