Gödel and the Proof of God

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Gödel and the Proof of GodIn 1931, Kurt Gödel introduced his Incompleteness Theorem to the world, and established that any system cannot be proven to be true using only its own content as premises — that is to say, it must rely on at least one external component for its validity. Likewise, that external component also cannot be proven to be true, intrinsically. The theorem is, essentially, a mathematical expression of the famous liar’s paradox:

This sentence is false.

Regardless of the point of origin, the riddle cannot be solved.

Gödel’s Incompleteness Theorem was, in and of itself, one of the most profound mathematical precepts to appear in the 20th century — or perhaps, ever. But its implications go far beyond mere mathematics; the uncertainty that arises from the theorem resonates deeply throughout all scientific and philosophical communities. Indeed, the entire philosophical notion of falsification — as proposed by Karl Popper — is indubitably supported and perpetuated heavily by the influence of Gödel’s theorem; we cannot know anything with absolute certainty, because no theory can rely upon itself for verification. Testing must be external and perpetual, and certainty can only be approached — not achieved. Ultimately, our perception of reality is limited to observation and evidence. The purest notion of “proof” is too absolute and fixed, and all but the term’s most casual and general usage must be abandoned.

For hundreds of years, organized theology has been declining, and we can thank science, almost exclusively, for this evanescence. Even the passionate fervor of Islam — still demonstrably inequitable, barbaric, and dogmatic beyond reconciliation — fails to hold the sway on the world that religions once did. It’s true that suicide bombers shock the world every day. But despite the attention incidents like these receive, they hardly hold the long-term influence of erstwhile organized movements like the Spanish Inquisition. The story continues to unfold, but I believe it is safe to say that reason and science are winning — and Gödel’s Incompleteness Theorem plays no small role in this game.

Indeed, in the world of scientific philosophy, Gödel’s theorem is a gift, nearly beyond compare. And yet, almost from the minute of its publication, it gave theologians a desperately needed justification for the existence of God. Religious people latched onto the theorem as a justification for the existence of an omnipotent creator.

To illustrate, draw a circle, and think of it as a complete system. The Incompleteness Theorem holds that any such system must rely on other components outside of itself in order to be established and validated — or “proven,” if you will (at least contextually). Further, that external component, or at least some other external component must be “unprovable.” There is no way to get around it.

Now draw another circle around the system and the component outside it. We can call that a more complex system, but the same rules apply: some other component or components necessarily must exist outside that system — and are equally “unprovable.” And you can keep drawing these circles ad infinitum. It changes nothing about the core fundamental veracity of the Incompleteness Theorem.

The reason this appeals so much to theologians is that no matter how many circles you draw, each new system must rely on one or more “unprovable” components. And this, they say, clearly must mean only one thing: God does exist. And at this point in our discussion, I must respectfully insert my most ardent disagreement; I posit that it is a most blatant form of non sequitur to claim that some “unprovable” component, external to a closed and “provable” system, must necessarily culminate in the existence of God. In fact, such a conclusion seems downright arrogant.

I am not a positivist, and as such, I don’t believe scientific discovery is the culmination of all knowledge. I am comfortable with the notion that — while theories may not currently be falsifiable, there is at least some likelihood that they may one day be falsifiable in scientific terms. Does this mean that I’m holding out for the ultimate and (nearly) irrefutable proof of the existence of Santa Claus?

The question is (and should be) rhetorical.

As critical thinkers, we have an obligation to pursue knowledge and truth with care. But there the boundaries of scientific exploration do exist — although they may be fuzzy at times. But there exists a point at which the critical mind can — with a great degree of confidence — proclaim a theory to be absurd, and such theories may be reasonably excluded from scientific approach.

Has Santa Claus been properly falsified? Probably. Don’t tell my children. Yet.

But what about things String Theory and other quantum proposals? Have they been vetted? Or more importantly, is it even possible to vet them? The answer is, no. We take these precepts on faith — just like everything else in the scientific world. And this is the point at which we must decide — even reluctantly — that we can proceed with research even though the the theories are not yet properly scientifically falsifiable. I can’t do that with Santa Claus, but I can with quantum mechanics; the latter somewhat elegantly explains enough of our universe that I can believe its theories will one day hold up to rigorous falsification — even if they cannot now.

But I cannot do this with God. Indeed, God as an explanation for the universe has been a historical litany of flaws, inconsistencies, and errors. One has only to look at the shameful (if overdue) apologies made by the Catholic Church — on every subject from heliocentrism to homosexuality — to understand how much religion spuriously and conveniently relies on absurdities to explain reality.

I subscribe deeply  to Gödel’s Incompleteness Theorem, and as such, I recognize the deep faith that must be applied to “unprovable” external components to any system. But that doesn’t mean I find comfort from a hasty ascription of this uncertainty to “God.” Equally, I don’t ascribe it to Santa Clause, Thoden, or Pan. But I do leave the door cracked…

What is it about the human condition that demands instant explanatory gratification? Why do so many of us feel compelled to dive into the arms of an untenable myth-story in order to justify the mysteries of the universe? For me, it’s enough to say I just don’t know.


 

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