Whither Proofs?

Why must we bother with proofs at all? Most people don’t put much thought into religion, and are content to know the gods exist through feelings of connection and occasional revelation.

One problem: those are proofs!

We’ve picked up a warped idea of what a proof is via math class. Our teachers tried to wow us with long, subtle chains of reasoning that are impressive mental achievements, but on the elaborate side of proof’s definition. In reality, all proofs consist of two things: an assertion, and one or more bits of evidence that the assertion are true. Length and subtlety are optional:

Assertion: At least one number is even and prime.[10]

Evidence: 2.

There’s nothing in the definition that says proofs must be convincing beyond all doubt, either. Take this example:

Assertion: the length of the longest side of a right-angle triangle multiplied by itself is equal to the sum of the lengths of the two remaining sides multiplied by themselves.

Evidence: Draw such a triangle on a sheet of paper, with plenty of margin. Draw three cubes around it, with one side of each shared with the triangle. Cut out both of the two smaller squares, and place one of them over the untouched larger square. Fill in the remaining visible portion of the largest by cutting up the remaining square. Once done, no part of it will be visible, and no part of the last square will be left.

This is a pretty lousy proof. For one thing, it never really explains why the math works out. Since it operates in the physical world, it’s easy to make a measurement error and falsely conclude you’ve shown it to be wrong. Worst of all, it only proves a single triangle at a time. Repeating the procedure for a thousand triangles only shows that there are a thousand triangles that live up to the assertion; any or all of the infinite remainder might not.

A mathematician would reject that proof outright, and for good reason. In the universe of math, we know every law and every way those laws combine. We have no excuse for considering something “reasonably” true, because we have all the tools we need to verify that it’s absolutely true.

In the real world, we don’t know all the rules. We don’t even know if the rules are constant, or change on very long time-scales, and so we’ll never reach absolute certainty. Instead, every proposed proof is given a court trial of sorts; we gather up all the contrary proofs and evidence we know of, and ask if the sum total gives us a reason to reject the proof. If so, we toss it out and either look for something better or put a different proof on trial. If not, we stamp it as “reasonably likely to be true, until further evidence comes in.”

That lack of certainty doesn’t make the above proof useless. It’s unlikely that a misfit triangle would lurk between two tested ones. Even if this assertion is only approximately true, it would be less complicated and easier than the real answer, and gives valuable hints towards a better proof. Absolute certainty isn’t needed, at least in real life.

We can easily rearrange those earlier statements about the gods into proof form:

Assertion: God exists.

Evidence: Sometimes, I can feel his presence.

Assertion: God exists.

Evidence: The world fits together too nicely to be the product of chance, and must instead have been designed.

You won’t see either of those argued about directly in a philosophical journal, yet both make assertions based on evidence just like their more formal cousins. Both, in fact, are just informal versions of the Proof from Transcendence and the Proof from Design, which have been seriously debated in those same journals for longer than journals have existed. By examining the evidence for both, we can evaluate their assertions in the same way. As I hope to demonstrate in later chapters, perhaps that feeling you get from your god has very natural causes, or there are other explanations for design out there that don’t require the supernatural.

Every informal assertion about god can be formalized and turned into a proof. By looking at the simpler and cleaner logic of the second, we can examine both at the same time and see how effective they are at proving the existence of a god.

It’s no wonder believers are uneasy with formal proofs.

Gotta Catch Them All

I’m left with one final objection to overcome. Given the unending multitude of proofs for a god, how could I possibly cover them all?

Let’s turn back to Comfort and Behe’s proofs. While both seem very different on the surface, they share one common trait: they point to some order within the universe, and declare that the only possible source for that order comes from a god. Instead of spending a few paragraphs going into specific details on each, I could have instead demonstrated a way to produce order that does not require a god as a counter-example. I then throw the question back, and ask how either person knows this mechanism, or another like it, wasn’t responsible instead.

That is exactly what I do in the chapter on Proof by Design. By exploiting these common traits, I can cover a multitude of proofs with a single argument. Coming up with counter-examples is much easier than coming up with proofs, and by raising a number of them I can at least call into question the certainty behind such proofs. This saves me a lot of effort, and serves as partial insulation against proofs that are not in this book or that have yet to be invented. It helps that proofs only seem to come in a few categories:

• Something exists, and only a god could have created that something. Examples include the universe (Proof from First Cause), consciousness (Proof from Intelligence), and holy texts (you can guess this one).
• There is an order to things that could only be created by a god. Examples include life (Proof from Fine Tuning), and morality.
• We are required to have a god, in some way. Examples include logical arguments (Proof from Logical Necessity), the universality of belief (Proof from Popularity), and the benefits of belief (The Pragmatic Argument).

As you read through this book, you might notice that even within these categories there’s a lot of overlap. I could have easily placed the Proof from Fine Tuning in any of them, to name but one. In answering the last objection, I’ve dredged up an intriguing question: is it possible to construct a universal counter-proof to any god?

I’ll leave that to the last chapter. In the meantime, I have a lot of intellectual ground to cover…

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[10]  Take a pile of X pennies, candies, or elephants. If you can divide them into two equal piles, X is an even number. Now take the above pile and try to rearrange it into a rectangle with no leftovers. If the only one you can manage is one item high and X long, or vice-versa, X is a prime number.