Kalam, Infinities, and Intellectual Honesty

I was glancing around Adam Lee’s website and noticed his archive of foundational essays (some of which have been partially incorporated into his book). One is a very long, detailed response to the traditional arguments for the existence of God. Lee notes that,

In my experience, many of the people who present these arguments are under the impression that they are either new or irrefutable. Therefore, it may surprise them to learn that all the most commonly heard arguments for God’s existence have been around in one form or another literally for centuries, and all of them were refuted soon after they were first proposed.

These arguments include the ontological argument, the cosmological argument, the design argument, and so on.

And I happened to notice that one subsection concerns the version of the cosmological argument as advocated by… William Lane Craig, the Christian apologist who debated physicist Sean Carroll a couple months ago, during which this “Kalam argument” was addressed yet again.

As summarized by Lee, part of his argument hinges on the concept of infinity, which he claims cannot exist in reality, because the idea of infinity is self-contradictory. “For example, the set of all numbers is infinite in size, as is the set of even numbers, but if we subtract the latter from the former the resulting set is still infinite,” as Lee summarizes.

Heh. I studied this stuff in college – I was a math major. Yes indeed, it is counter-intuitive that, for example, the set of even natural numbers and the set of all natural numbers are, in fact, equivalently infinite. This is because you can state a rule to describe a one-to-one correspondence between members of both sets. Even more counter-intuitive is that there are infinities that are *not* equivalent — for example, the set of all “real numbers” (including all those numbers with infinite fractional components, like pi) is a higher order of infinity than the set of all natural numbers. This is because any proposed correspondence rule between those sets can be proved to miss infinitely many real numbers. (Aleph-naught) These concepts were invented by Georg Cantor in the 1880s. I’ve always thought this stuff was really cool.

But infinities are no more imaginary than negative numbers, and different orders of infinity are analogous to multiple dimensions — a geometric plane is, for example, more infinite in some sense than an infinite line. There’s nothing incoherent about the idea, as Craig claims. As Lee notes,

But this does not prove that such a thing is impossible, merely that the human mind cannot adequately conceive of it. There is no law that requires reality to conform to our expectations. Most people would also find the idea that light can behave both as a particle and as a wave to be counterintuitive or absurd, but nevertheless, quantum mechanics has taught us that it is so.

That a concept at first glance seems counter-intuitive does not mean it is self-contradictory, as Craig claims. A theme of this blog is how science fiction can suggest, if only by implication, many things that may be true about the universe but which are not intuitive to the human mind, or even conceivable to it at all. Keep in mind that our intuitive understanding of the world, how things move and interact, works only at scales similar to our own. There are other interactions at much much small scales, where quantum mechanics reigns, or much larger ones, where the immensities of time allow for the development of complexity the human mind assumes must have been designed. Science in the past few centuries has done a pretty good job of revealing scales and interactions of the universe that were and are completely invisible to ordinary human perceptions and inclinations.

Another thought about Craig’s use of this argument (and Lee dismantles his other premises for it as well) is that it calls into question his intellectual honesty. Surely he’s had critics point out the flaws in his argument before… Many people have described them, again and again … and yet he goes on promoting that argument. Why would he do that? Does he not understand his critics? Is he in his own mind so committed to a belief that, via confirmation bias, counter-evidence simply goes, so to speak, in one ear and out the other? Or is he not so much interested in pursuing the truth as promoting an agenda, or playing to credulous supporters?

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