I have previously said that U of R economist Steve Landsburg is a very religious atheist, and I mean that sincerely. Steve derives his sense of the universe from mathematics, as opposed to his belief in a personal God. If it turned out that arithmetic contained a contradiction, I really think we would find Steve in a drunken stupor living under a bridge in a few years.
Anyway, in a recent post about mathematician Stanley Tennenbaum Steve writes:
I write as one who believes (like most mathematicians) that the system of natural numbers (including the operations of addition and multiplication) exists in an objective sense. By that I mean precisely this: Statements about the set of natural numbers (such as “Every natural number is the sum of four squares”) have objective meanings; they are not just strings of words. I take it that a thing exists if one can speak meaningfully about its properties. The facts that every natural number is a sum of four squares, that every number can be factored into primes, and that an odd prime number is a sum of two squares if and only if it leaves a remainder of 1 when divided by 4, are all properties of the system of natural numbers. Because it has these properties, the natural number system exists.
It would be nice to give a succinct definition of the system of natural numbers. That turns out to be quite impossible. …This means, in effect, that there’s no way to uniquely specify the natural numbers….
That’s where Tennebaum’s Theorem comes in. What Stanley proved (and of course I’m paraphrasing a bit here, because this is a nontechnical forum) is that in any nonstandard model of arithmetic, the rules of addition and multiplication are so complicated that no computer can be programmed to carry them out. In other words, you and I, whose brains are computers, have no hope of really understanding those addition and multiplication rules.
It seems to me, then, that our only hope for picking out the honest natural numbers from among a sea of impostors is a direct appeal to intuition. Fortunately, almost all of us have that intuition. We’ve known what numbers are since we were three….
So I contend that 1) the natural numbers exist because we can make meaningful statements about their properties, and that’s what existence consists of, and 2) the natural numbers are unfathomably complicated in the sense that there is no hope of pinning them down by any sort of description, even if we allow ourselves to incorporate sophisticated ideas like Tennenbaum’s into our description.
As many of you know, I’ve argued more than once (some of you might say more than necessary) that the existence of an unfathomably complex structure that was neither designed nor the product of evolution is a definitive counterexample both to the “intelligent design” argument that says a complex structure needs a designer and to Richard Dawkins’s position that all complexity is a product of evolution. It also settles (for me) the question of why the physical Universe exists — once you’ve explained the existence of something as complex as the natural numbers, explaining the existence of something as relatively simple as the Universe becomes a mere exercise. [Bold added.]
Steve has been an outspoken critic of people who claim to believe in the popular monotheistic faiths. And yet, if you stand back and look at what Steve is doing in the quotation above (especially the parts I put in bold), you will see his own position is pretty incredible itself.
First, Steve says that something exists if we can describe its properties. OK, watch this:
(1) God is omniscient.
(2) God is omnipotent.
(3) God is omnibenevolent.
These aren’t properties I dreamed up; these are standard attributes of the personal God about which mainstream theologians have written for centuries. So did I just prove that such a God exists?
Steve is going to have to say no–since he can hardly believe that people nowadays actually still believe in the God of the Christian Bible–and yet, that’s what pops out of his own framework. Now maybe Steve will say, “Well, your purported principles contradict each other. A being can’t be omniscient and omnipotent at the same time; even Mises has an argument about that in Human Action.” We can all have that discussion in the comments–I fallibly predict we will–but that’s beside the point. I could easily come up with a list of properties describing God that are consistent, and I wouldn’t have thereby proved that God exists, in Steve’s book.
So right off the bat, Steve is in trouble. A principle that he thought was beautiful and elegant when used to support his own belief system, for some reason will have all sorts of caveats when a Christian tries to use it. (In fairness, Steve does take on the ontological argument in his book. I really don’t see how Steve thinks he gets around his own critique, and neither does frequent Free Advice peanut-thrower Ken B. in the comments at Steve’s post. Thanks to Silas Barta for bringing this to my attention.)
But beyond that problem, there’s another with Steve’s commentary above: Look at the part again where he says, “[O]nce you’ve explained the existence of something as complex as the natural numbers, explaining the existence of something as relatively simple as the Universe becomes a mere exercise.”
Come again? I think I missed the part where Steve explained the existence of the natural numbers. Especially if you click on the link and read the whole thing, you’ll see that most of Steve’s time is spent explaining problems with previous attempts to characterize the natural numbers.
Indeed, this is truly the “explanation” Steve offers: “It seems to me, then, that our only hope for picking out the honest natural numbers from among a sea of impostors is a direct appeal to intuition. Fortunately, almost all of us have that intuition. We’ve known what numbers are since we were three.”
Sorry Steve, that’s not an explanation. If I said, “We know God exists because I have direct intuition, and most humans from history–though the percentage has gone down in the last 200 years, I grant you–have the intuition that there is a greater force than themselves in the universe, they think there should be a ‘meaning’ to life to make sense of everything,” I’m pretty sure the atheists would get medieval on me in the comments.
A few weeks ago Brian Shelley sent me this NYT review of a book (The Righteous Mind) that discussed how people deploy their reason to justify whatever views they already hold, on other grounds. I think there is an important point here. I hesitated to bring it up, lest exposing myself to accusations of, “Aha! Murphy finally admits it, Christians don’t trust reason!!”
We can all easily use our minds to spin out all sorts of justifications for what we believe in, or to blow up the intellectual edifices constructed by our rivals. I’ve run into this problem even in my normal work, where (say) I’ll come upon a Krugman piece or something from a think tank pushing federal subsidies for wind power, and it is expected that I’m going to poke holes in them.
It would be silly of me to say that this isn’t a biased structure. The one thing I try to do, to maintain my intellectual honesty and integrity, is to say I can never use an argument to attack my opponents, that I simultaneously would reject if my opponents used it against “my side.” (Well, there are other, obvious things too, like not making up statistics, not using graphs that are misleading, not deliberately taking someone’s remarks out of context, etc.)
But I’ve noticed that even here, things aren’t so cut and dry. If you’re a clever guy like Krugman or me, we can come up with “refinements” of the principles involved, so that really the two things aren’t analogous, and it’s fine for me to use the Principle-Version-A when blowing up the bad guys, but when they try to use something similar on my allies, nope it’s illegitimate because it’s actually Principle-Version-A-Prime.
To be clear, I honestly think I’m on the side of truth and that my conclusions would lead to a better society than what Krugman et al. are pushing, but my point is that I have recognized that my own rational introspection on the matter isn’t a disinterested bystander. And by the same token, I try not to get as outraged at Krugman et al. as I used to, because he presumably thinks the same thing.
Coming full circle back to Landsburg: To me it is laughably obvious that he is using principles to defend his worldview, that he would mock if I were to adopt them in defense of Christianity. This doesn’t underline that reason is useless, it rather shows that our opinions as to what constitutes a “good argument” depends not just on pure reason itself.