The Wizard Did It Fallacy

How Theists Roll Three Fallacies Into One

On Tuesday, Bentham’s Bulldog published a post on the argument for knowledge.

I, like many on the skeptical side of the aisle, was unimpressed. Knowing full well that BB probably just wrote this post in an afternoon and thus didn’t put forward his best argument for such a post, I only responded to one aspect of it that you can find here:

(Also this post isn’t a dunk or polemic against BB. He’s not the only one who reasons in this way, but the mistake he makes is common enough that it’s worth pointing out. BB is just a readily available example.)

The Philosophy Doctoral student Mountain Owl had a similar criticism:

Owl and I had a brief conversation that culminated in us labeling this kind of fallacious probabilistic thinking the “Wizard Did It” Fallacy. As Owl puts it:

Let’s explain!

Intentionality Complicates Hypothesis Testing

The Wizard Did It Fallacy (TWDIF) is a fallacy people use in the philosophy of religion, specifically when using the language of hypothesis testing to advocate for God’s existence. There are three components of TWDIF:

1. Exploiting intentional hypotheses (What I call the Loaded Dice Fallacy)

2. Over-reliance on analogous reasoning over evidential data (Disanalogy)

3. Lack of explanatory content relative to alternative hypotheses (Double Standards)

Typically, those committing TWDIF will say something like this:

“A (particular) dataset is much less expected on a nontheist hypotheses relative to a theistic hypotheses.”

In the case of BB’s latest post, he specifically said “If theism is true, then it is a lot likelier that you’d know many things than if atheism is true.”

The Bed-Making Gremlins

The first problem with TWDIF reasoning is that a theistic hypothesis, as defined by one that postulates a being that has sufficient power and intention to create certain outcomes or datasets will always be more likely than a hypothesis that doesn’t.

Let’s use an example: You’re a messy kid who never makes his bed. You come home from school one day to find a made bed. Your parents have been away all day, so they didn’t do it. What’s the best explanation of your bed being made?

To start off, I’ll concede that it’s most likely that some sort of intentional agent made the bed. That’s uncontroversial. The problem is that, with no additional information or considerations, we can say any intentional agent making the bed is more likely than the bed being made randomly. And so, per this reasoning, it’s more reasonable to believe that the bed-making gremlins made your bed, than it is that it randomly became made on its own.

The problem is that the bed-making gremlins are completely made up, and don’t have any evidence supporting them outside of the mystery of the made bed. So, it can’t be correct that it’s more reasonable to believe in the bed-making gremlins relative to a spontaneous or random explanation just because the data supports the bed-making gremlins hypothesis over spontaneity or randomness.

It’s obviously much more reasonable to assume a third, undefined hypothesis, not yet considered. In this way, it’s not enough to say that the data better fit the hypothesis, but that there also needs to be additional evidence that helps us shape or formulate that theory. Absent such data, we should suspend judgment on which explanations are most likely.

At this point, theists will object to this example due to points of disanalogy, and I would agree with them. For one, God is different from the bed-making gremlins as, to theists, we have other points of evidence pointing toward God. Fair enough. What’s more, the fallaciousness of this reasoning is unclear because we are very familiar with the circumstances of bed-making, and so it’s unclear why it would be correct to infer non-intentionality.

Also, I mentioned a wizard, why are we talking about gremlins? Let’s pivot to another metaphor to make the fallacy more concrete.

Loaded Dice

Let’s say we are playing a game of dice, where we have 2 dice. I roll 12 (that is, two-sixes) 4-times in a row. According to google, there’s a one in 5 billion chance (or so) of that happening fairly. Did I cheat?

Proponents that say yes will look at these odds and say that it’s very unlikely that this roll happens fairly. They would also say that, if I was cheating, the probability of this dice roll would be far closer to one by virtue of the dice being loaded or I otherwise have the ability to create that dice roll at will. That is, I have the ability (through the dice being loaded or some other hidden, unfair skill) and intention (the desire to cheat) to create the desired outcome (rolling 12 four consecutive times).

The Bayes factor (which is the ratio of the marginal likelihoods of the data under the two competing hypotheses) radically favors the cheating hypothesis. So obviously I cheated, right?

Well, not exactly. For one, any combination of dice rolling over four rolls is going to be vanishingly improbable. Heck, any specific outcome on a single roll of two dice is relatively improbable. Specifically: the probability of two die landing in any specific ordered pair is 1 in 36 (less than 3 percent), and the probability of rolling at least one specific number is 11 in 36 (less than 33 percent).

Put another way, if I roll a 2 and a 2 equalling a 4, that’s less than a one-third chance of happening, with that specific combination being less than 3 percent. The hypothesis that I was using two loaded dice that would give me those (or any) specific numbers is much higher than those odds.

Yet we still don’t immediately assume that every dice roll is loaded just because of the relative odds or Bayes factor. Why?

Well, the “chance” hypothesis is going to be improbable relative to the “rigged” hypothesis, no matter the permutation and no matter if the dice are loaded or not. And so, we need more information other than the mere odds of certain outcomes. Vanishingly improbable things happen all the time, after all.

Theists, of course, know this, which is why they appeal to intentionality in the first place, as intentionality is something we intuitively understand. But the problem with this explanation is that intentionality is too conclusive of an explanation. It’s so good of an explanation that it crowds out any other explanation, because no other explanation by its nature approaches a probability so close to one.

And so, a rigged game of chance is a great illustration of how postulating an intentional agent ruins our assessment of hypotheses because a priori nearly every not-certain or improbable hypothesis is going to appear more improbable relative to one that postulates intentionality, even if the intentional hypothesis is determined false under further examination.

Just as we shouldn’t conclude a game of chance is rigged just because something relatively improbable happened, we shouldn’t conclude that an intentional agent is responsible for a set of inexplicable events just because it’s more probable than a non-intentional hypothesis. The content of the surrounding circumstances matter.

Cheating Logic

Assuming intentionality as a default solution is thus analogous to believing the reason you’ve lost any game of chance is because your opponent is cheating, and that the reason you’ve won any game of chance is because your opponent is still cheating, but doesn’t want you to think they’re cheating.

All to say, the data by itself is not enough evidence to say the game is rigged. What is rigged, however, is your response: You’re assuming no randomness or non-intentionality in either scenario. It can’t be proven wrong, and that itself is its own form of cheating. Think about it:

• Why is the sky blue? God did that, it’s much more likely and expected on the hypothesis that God intentionally did that than alternative hypotheses.

• Why does my chinchilla not let me handle her? God did that, it’s much more likely and expected on the hypothesis that God intentionally did that than alternative hypotheses.

• Why does gravity operate in the way it does? God did that, it’s much more likely and expected on the hypothesis that God intentionally did that than alternative hypotheses.

And so on.

Affinity For Analogy, Not Confidence

And this leads us to the second problem with TWDIF: it conflates the human affinity for analogy with well-evidenced confidence. David Hume talked about this at length: Humans naturally have a strong predisposition to reason about novel circumstances with analogy, even when the analogy proves disanalogous.

To name one example, humans are predisposed to think of the human body as the product of intentional design rather than shaped by natural forces, not because we have evidence that human bodies can be designed, but because the analogy is familiar, as we are familiar with people designing things.

We thus mistakenly compare our affinity for analogous explanations (for which we have abundant data of people designing machines) with the confidence we have in an explanation based on empirical reasoning (for which we have little data of human bodies being designed, outside of Mary Shelley novels).

Most humans have a better understanding of the workings of intentional (human) agents than they do of complicated science and probability, and thus they will gravitate to intentional explanations over non-intentional ones because of that familiarity. As the experience of science teaches us, this isn’t good reasoning. Intuitive analogous reasoning is not a reliable guide for how the universe works beyond circumstances that we are familiar.

Where Is The Precision? Where Is The Explanation?

The third problem with TWDIF reasoning is its lack of precision and explanation. At this point, I feel like I’m a broken record, as I’ve written before: we need precision in our hypotheses to assess them.

Though specific philosophical and scientific theories/hypotheses may seem improbable because they lack key evidence that prevents them from being maximally or obviously probable, TWDIF hypotheses provide neither measurable evidence nor precise explanations!

In this way, we typically quantify our confidence in various scientific or naturalistic theories based on the measured strength of specific or precise hypotheses. That is to say, the very tools we use to assess the improbability of naturalistic or scientific hypotheses derive from the quantifiable components of these theories.

And that raises the question: Where do we get the quantified confidence and precision for Intentional Theistic Hypotheses? How can I assess what God could or would do? From what data sample are we deriving this probability and forecasting confidence?

It would seem that TWDIF reasoning is merely asserting the hypothesis, with the familiarity observers have with (human) intentional agents doing much of the cognitive heavy lifting. The standard rigor of scientific (or otherwise philosophical) explanation is just…not there.

Think about it: The sentence “God created humans” contains far less explanatory content than the sentence “Natural selection shaped human biology,” while raising far more questions. That’s because “created” in the God sentence is under-defined relative to “shaped” in the natural selection sentence.

People are satisfied with the God explanation because it’s an intentional (and thus probable) hypothesis, it uses familiar and intuitive analogous reasoning, but when we examine it for causal content on par with other hypotheses, it’s empty in comparison.

Enter The Wizard

As I said before, TWDIF is more than just one fallacy, but three fallacies rolled into one:

• We can call the first fallacy involving intentional vs. unintentional hypotheses the loaded dice fallacy.

• The second fallacy is a fallacy of disanalogy while using analogous reasoning.

• The third fallacy is a double standard, holding the measurable flaws of naturalistic or non-intentional hypotheses against such hypotheses, while not proposing measurability in theistic hypotheses in the first place.

The reason I want to roll these fallacies into one big fallacy is because it’s committed at sufficient frequency that it needs its own name. The purpose of illustrating this fallacy is to demonstrate to non-skeptics how bad and unsatisfactory their explanations are by reasonable standards of explanation.

That is, if you replace “God did it” as a hypothesis with “A wizard did it” hypothesis in philosophy of religion debates, it should become abundantly clear why these hypotheses are bad.

Let’s compare a magic wizard as an explanation to God:

• Much like God, a wizard is an intentional agent, and thus an analogous hypothesis. A wizard will always seem more probable than a non-intentional hypothesis when assessing mysteries.

• Much as God as a familiar analogous explanation confuses argument-assessors with well-evidenced, confident explanations, so too does a wizard work as an explanation. We have just as much evidence of wizards performing magic as God does miracles, and we also intuitively understand magic just as we understand miracles, and so the reasoning is equally compelling.

• Much as God works miracles, wizards work magic or sorcery that escapes scientific explanation. We don’t need to explain the mechanics of the wizard’s magic just as we don’t need to explain the mechanics of God’s miracles.

You can then “answer” all sorts of questions in philosophy of religion (some of these problems I don’t see as problems, but I’m just illustrating the point) using this reasoning. It’s functionally the same as “God did it” examples:

• Why does the universe appear fine tuned? A wizard did it.

• Why do we have knowledge? A wizard did it.

• Why are there psychophysical laws? A wizard did it.

And so on. I’m well aware that a theist can appeal to a priori beliefs to demonstrate that God is more likely than a wizard, and that’s fine. But my point here is that, absent these prior beliefs (which nontheists will not find compelling):

• Appealing to intentional agents whose existence is doubtful,

• That relies heavily on analogous familiarity over evidenced confidence,

• With minimal explanatory content,

…are bad explanations to nontheists (as it should be for everyone).

This dismissive judgment isn’t from an a priori dismissal of theistic explanations, but because these explanations fail to meet explanatory standards used in other domains.

A decade ago, it was pretty common for edgy Reddit atheists to say they didn’t see any evidence for the existence of God, and I believe this line of reasoning is what they meant. The evidence and explanations were so bad that they didn’t amount to explanations at all.

I won’t go that far. After all, not every argument for God uses TWDIF reasoning.

But to the extent that this reasoning has become ubiquitous in online philosophy of religion circles, I suggest theists and Christian apologists try a different tactic.