### Pray for Me by Mark Stone

July 2018. I consider myself a deeply spiritual person, but I subscribe to no organized religion. When certain acquiantances or family members realize this about me, their inclination is to pray for me. And I'm okay with that. Let me explain.

An organized religion consists of a set of foundational principles enabling practitioners to make evaluations of right and wrong on the basis of those principles. Think of these evaluations as moral truths. In this sense, religion bears a strong resemblance to mathematics -- any formal system of mathematics has a set of axioms as its starting point, and a set of mathematical truths that can be derived from those axioms. Just as human nature has a desire for one true religion from which all moral truths can be derived, mathematicians for centuries hoped for one set of axioms from which all the truths of mathematics could be derived.

As it turns out mathematics is messier than that. Trouble begins because math must deal with the infinite. Infinity alone is not the problem. We have lots of formulae that are perfect descriptors and predictors of infinite sets of numbers. For example, I can tell you what the sum of all numbers is from 1 to N for any value of N quite easily. The answer is encapsulated in the formula N*(N+1)/2.

In math, systems that behave this way are called linear systems. They have three characteristics:

- They are knowable;
- They are predictable;
- The computational complexity of the predicting formula is less than the computational complexity of the system as a whole.

That last one is a bit subtle, but essentially it means that using the formula is more efficient than working out the answer by direct calculation. In the example above, directly calculating 1 + 2 + 3 may be easier than using the formula, but the whole system includes an infinity of numbers, and for even moderate numbers (10, or 29, for example) the formula is obviously easier than adding it all up directly.

In math we also have nonlinear systems. These are systems for which the computational complexity of the predicting formula is greater than the computational complexity of the system as a whole. We are all highly dependent on nonlinear systems in our everyday lives, because these systems are the basis for modern encryption in digital communication. Encryption works because the computational work needed to predict an encrypting key is at least as great as the computational work needed to enumerate the next key in a sequence. The digits of Pi, the digits of the square root of 2, the set of prime numbers -- these are all examples of nonlinear systems.

Nonlinear systems are knowable. They are predictable. But predictability exceeds the complexity of the systems themselves. This means they possess a fourth characteristic -- they lack countability. In other words, they cannot be mapped to, say, the set of all positive integers. Thus they are both infite and uncountable (or, as mathematicians often say, denumerable).

And that's the problem with math -- there are different kinds of infinity. Countably infinite systems can be apprehended by the language of math -- their truths can be efficiently derived from first principles. Even some uncountably infinite systems can be apprehended by the language of math. For example, the inverse square law states that the surface area of a sphere is proportional to the square of the radius of the sphere. But nonlinear infinite systems can only be apprehended by a language so complex that it would be unusable as a language. The truth is out there; we just can't grasp it.

All of this was proved by mathematicians in the first half of the 20th century, culminating in the work of Kurt Goedel. The theorem which bears his name essentially says that any set of axioms rich enough to express truths about nonlinear systems cannot be both consistent and complete. Either the language itself leads us into contradictions, or the language lacks the capacity to express some truths.

So what does this have to do with prayer? Bear with me; we're halfway there.

I assume that any useful system of ethics is at least as complex as the system of mathematics. I also assume that God, should one exist, apprehends all moral truths. I infer from this that God is a nonlinear system -- capable of apprehending all of an uncountably infinite number of truths, but incapable of being fully expressed in any language we humans can apprehend. If you pause for a moment and think about it, most relgious texts in all the major religions essentially acknowledge this.

We have to conclude then that while God may have an absolute and unerring knowledge of right and wrong, the language of God does not. This isn't a limitation on God; far from it. It's a limitation on language, a limitation proved by the same 20th century mathematicians.

I said at the outset that I was a deeply spiritual person. So how do I take all of this into my own sense of spirituality? I have the deepest respect for the world's religions. Generations of scholars and thinkers far smarter than me have labored to bring as much of moral truth as they can within the lens of their religion's first principles. The fact that their results are imperfect and incomplete is not a reflection on the quality or piety of their work. It is simply a limitation on language, a limitation that ethics, like mathematics, cannot overcome.

So I take the hopeful view that each religion captures an aspect of ultimate moral truth, and is therefore worthy of study. The one mistake that a religious practitioner can make is to claim that their religion has unique access to the entireity of moral truths. Provably, this cannot be the case.

Diversity, it turns out, is built into the very fabric of existence.

But diversity has profound consequences. Here's a seemingly mundane claim: one cannot meaningfully assert a contradiction. I cannot, for example, say "2 + 2 = 4" and "2 + 2 = 5" and expect anyone to make sense of what I am saying. Taking it a step further, one cannot meaningfully assert something which is based on a contradiction. If the logic that holds my assertions together depends on saying something like "2 + 2 = 4" and "2 + 2 = 5" then the whole bundle of assertions lacks meaning. That's essentially what Goedel's lesson is: in systems as complex as mathematics or ethics, you can express a subset of all the truths, or you can express a contradiction, in which case your expression lacks meaning. So in ethics, the set of all meaningful expressions is necessarily a subset of the set of all moral truths.

But how does language get its meaning? As humans, how do we manage to understand each other?

According to Wittgenstein, language is fundamentally social. Communication, on this view, is a transaction between two or more speakers who, by virtue of the fact that they understand one another, implicitly share a set of rules about how language works and what language means. In Wittgenstein's terms, they are playing a common "language game."

Wittgenstein argues that language must work this way because the alternative -- a private language -- is impossible. Such a purported private language would lack a fundamental characteristic of language, namely corrigibility. In other words, in a private language there would be no feedback loop to confirm that our expressions had been understood, nor any feedback loop to confirm that we understood what was being expressed to us. In order for meaning to adhere to language, that language must be grounded in actions and changes in the world around us that enable us, even if only implicitly, to confirm that the meaning of expressions aligns with the actions and changes in the world.

Think, for example, of the closest thing we experience to a private language -- the language of dreams. Because no one else can share our dreams, dreams lack this characteristic of corrigibility. Think of a recent dream you've had. Did you have it last night? Have you had it on other nights? Do you have that dream every night? Can you be sure you don't? What happened in that dream? Do you remember the details? Do they make sense and hold together consistently? We have no independent evidence to which we can refer about our dreams, and thus they slip away from us like sand through our fingers. Any meaning we try to ascribe to them adheres just as loosely. The full structure of a language game simply isn't present in this context because there is no other player in the game.

If we accept what seems like a small point on Wittgenstein's part -- that language is fundamentally social -- some powerful conclusions follow immediately. In this social lens meaning derives from the transaction of the one expressing language and those receiving and interpreting the expression. That means that the speaker does not own the entire meaning of their words, and instead meaning is contributed by each participant in the language game.

So when someone says "I will pray for you" the meaning of their expression is a function both of what they are capable of intending and of what I am capable of understanding. Further neither of us can get this linguistic transaction off the ground without the whole context of the history of relgions in which we have each participated -- the players of this language game that have preceded us.

And note what the speaker cannot mean: they cannot mean that they understand the one true religion and are asking their one true God to intercede and show mercy to me because of my lack of understanding. Such an assertion would fall prey to Goedel's theorem and thus lack meaning. Whatever meaning their words have must stop short of this inconsistency.

Further, I have the humility to recognize that their religion undoubtedly has a window into some of the multitude of moral truths. Thus it would be short sighted of me to shut their perspective out altogether. And indeed I probably can't even if I wanted to -- their words do resonate with me; they do have meaning.

I recognize the good intention in their words. Even if I do not fully understand it, I can appreciate and honor it. So I would say "By all means, pray for me. And in turn, I shall hold you in my thoughts and well wishes."