Argument from personal incredulity

The card trick

“I watched his hands the whole time. There’s no way that was a trick. He really knew which card I was thinking of.”

The clear-cut case. A good magic trick is designed so that the audience can’t reconstruct the method; that’s what practice and misdirection are for. Not being able to see how it was done is exactly what you’d experience if it were a trick, so it can’t count as evidence that it wasn’t. The step from “I can’t explain it” to “so it’s real mind reading” rests entirely on the speaker’s failure to explain it.

Every shuffle is new

Sam: A well-shuffled deck is almost certainly in an order no deck has ever been in before.

Priya: That can’t be right. People have been shuffling cards for hundreds of years. Every order must have come up by now.

It sounds like common sense, and the claim does sound absurd. But a 52-card deck can be arranged in about 8 × 10⁶⁷ different orders. Even if 8 billion people had each shuffled a deck once a second since the universe began, they’d have produced only a vanishingly small fraction of them. A number this large can’t be pictured, and “hundreds of years of shuffling” feels as if it ought to be enough. Priya’s disbelief is honest, but it tracks how big the number feels, not how big it is.

Nothing could go wrong

A homeowner planning to cut down a tree in his yard says: “I’ve walked around it and thought it through. I can’t see any way it could fall toward the house, so it’s safe to do myself.”

This is the reverse direction: failing to imagine how the claim “it’s safe” could be false, and concluding that it’s true. Trees can fall in unexpected ways, and the homeowner’s inability to picture a bad outcome doesn’t mean one isn’t possible. Amos Tversky and Daniel Kahneman noted that when people judge risk by imagining what could go wrong, the risk may be grossly underestimated if some dangers are difficult to conceive of or simply don’t come to mind. The ways a plan can fail that you haven’t thought of are, by definition, the ones you can’t see.

Both can be repaired in the same way. “I can’t see how P could be true” becomes a real argument once it’s backed by something specific: a principle that rules P out, or a reason to expect that someone in the speaker’s position would understand P if it were true (see the look-alikes below).

• “It can’t be true”: can’t imagine how something works, so it doesn’t happen, as in the card deck.
• “It must be true”: can’t imagine how something could be false or could fail, so it’s true or safe, as with the tree.
• “It must be something extraordinary”: can’t explain how an ordinary cause could produce it, so the cause must be unusual, as with the card trick.
• Incredulity at scale: disbelief driven by numbers too large or too small to picture, such as the orders of a deck of cards, the odds of rare coincidences, or long spans of time.
• Philosophers’ Syndrome: Daniel Dennett’s name, in Consciousness Explained (1991), for the version found in philosophical arguments: “mistaking a failure of imagination for an insight into necessity.” Something that can’t be imagined is taken to be impossible.

The name goes back at least to the biologist Richard Dawkins’s The Blind Watchmaker (1986), which describes “what may be called the Argument from Personal Incredulity” as an extremely weak argument. The term comes from popular science writing rather than from the traditional lists of fallacies: it doesn’t appear among the fallacies in Hurley and Watson’s logic textbook or in the Stanford and Internet encyclopedias of philosophy. Dene Bebbington gave it a two-page note in Think, a journal of the Royal Institute of Philosophy, in 2011.

Is it a kind of argument from ignorance? Sources don’t agree. Some writers use the two names almost interchangeably. Dawkins observed that the argument is sometimes based on simple ignorance, while also describing more serious versions that don’t rest simply on ignorance or lack of ingenuity. This site treats them as neighbors rather than as parent and child. An Argument from ignorance reasons from a lack of evidence; an argument from personal incredulity reasons from a lack of explanation in one person’s mind, and can be made even when the evidence for the claim is plentiful. They often appear together.

Surprise and doubt are reasonable responses to a strange claim. Disbelief holds up when:

• It rests on specific knowledge that rules the claim out. “That would violate conservation of energy” isn’t a failure of imagination; it’s an appeal to a well-tested principle.
• The doubter can say what’s wrong. Someone with relevant expertise who points to a particular step that fails (“the load on this beam exceeds its rating”) is making an argument, not reporting a feeling.
• It leads to declining to believe, not to concluding false. “I don’t see how that works, so I’m not convinced yet” is fair. The burden of proof is on whoever makes the claim, and that’s different from declaring the claim false.
• It’s a prompt to check. A result that seems impossible is a good reason to look for a mistake, such as a misread gauge or a spreadsheet error, as long as the checking can end with “it was right”.

The test: can you say why it couldn’t be true, beyond not seeing how it could?

The perpetual-motion machine

An inventor demonstrates a sealed wheel that he says will keep turning forever and power a lamp, with no fuel or outside energy. An engineer watching says, “That can’t work, however clever the design.”

The engineer’s reply sounds like “I can’t imagine it, so it’s false”, and she hasn’t examined the mechanism. But her disbelief doesn’t come from failing to picture how the wheel works. It comes from the conservation of energy, one of the most thoroughly tested principles in physics: a machine that produces energy from nothing would break it, whatever is inside the box. That’s the specific knowledge that rules the claim out condition.

Show me the numbers

A bridge engineer reviewing a contractor’s design for a footbridge says: “I can’t see how this support carries the load you’ve listed. Before we sign off, send me the calculations.”

The engineer says she can’t see how it works, but she doesn’t conclude that it doesn’t. She withholds approval and asks for the calculation that would settle it, which puts the burden on the people making the claim. If the numbers check out, she’ll sign. That’s declining to believe, not concluding false. It would become the error if she rejected the design without looking at the calculations.

People often judge how likely something is by how easily they can imagine it. Tversky and Kahneman (1974) described this as a bias of imaginability, one form of the Availability heuristic: when examples or scenarios have to be constructed in the mind, the ones that are easy to construct seem more likely, though the ease of imagining them need not reflect their actual likelihood. Something that can’t be imagined at all feels close to impossible.

Not knowing is also uncomfortable. Dene Bebbington’s note begins from the observation that people prefer certainty, and would rather explain something than accept their ignorance and say “I don’t know.” Rejecting a claim that can’t be explained is one way to get that certainty back.

Finally, most people don’t know in any detail how most everyday technology works, and often don’t notice the gap, because the things work. The belief that you understand a device better than you do is the Illusion of explanatory depth. Incredulity is the moment the gap shows: a claim arrives that doesn’t fit what you thought you understood, and the claim gets rejected instead of the understanding.

• Separate “I don’t know how” from “it doesn’t”. The first is often true and nothing to be embarrassed about; only the second is a claim about the world.
• Ask whether there’s a specific reason it couldn’t be true. If there is, that reason is the argument, and it can be checked. If there isn’t, the honest position is “I don’t know”.
• Look for the explanation before rejecting the claim. How GPS finds a position, why a steel hull floats, or how a trick is done can usually be found.
• For plans and decisions, imagine failure on purpose. Asking “suppose this went wrong: what’s the most likely reason?” can bring up dangers that didn’t come to mind unprompted. It’s a practical habit, not a guarantee.