Argument from ignorance

“Can you prove it doesn’t?”

Jordan: Playing classical music to my tomato plants makes them grow bigger.

Casey: Has anyone actually tested that?

Jordan: Has anyone proven it doesn’t work? Until someone does, I’m going with yes.

Jordan’s only support is that the claim hasn’t been disproven. But most untested claims haven’t been disproven, true or not, simply because nobody has run the test. Casey asked for a reason to believe it; Jordan answered by demanding a reason to disbelieve it, which moves the burden of proof onto the person who didn’t make the claim. Music might affect tomatoes. Without a test, though, the honest answer is “we don’t know”, not “yes”.

“No complaints, so it works”

A small online shop redesigns its checkout page. A month later the owner says: “Not one customer has complained about the new checkout on phones, so it’s working fine.” The shop’s contact form is linked only from the desktop version of the site.

This is the other direction: no evidence of a problem, so no problem. But a customer on a phone who gets stuck has no easy way to complain, and will most likely just leave. The silence would look the same whether the checkout works or not, so it can’t tell the owner which is true. Checking how many phone shoppers who start checking out actually finish would be evidence; the lack of complaints isn’t.

A study that found nothing

“A study gave blue-light-blocking glasses to twelve people for one week and found no difference in how well they slept. So those glasses don’t do anything.”

This sounds scientific, and a real search did take place. But a study that small and that short could easily miss a modest effect even if one existed. “The study found no evidence of an effect” is being read as “the study found evidence of no effect”, and those are different results. A study that finds nothing counts against an effect only to the degree that it was likely to detect one. (The glasses may or may not work; this study can’t settle it either way.)

Stated bare, both directions leave out any reason to think the evidence would have been found:

Add a premise about the search, and the second direction becomes legitimate reasoning from negative evidence, with the same shape as modus tollens:

The added premise is where the argument is won or lost, and it’s a factual claim about the situation, not a matter of logic. The first direction can be repaired the same way: “if P were false, we would have heard by now” (see the dentist example below). Douglas Walton points out that the match with modus tollens is loose: the “if” holds in normal circumstances rather than without exception, so the conclusion is a presumption that new evidence can overturn.

Filling the gap with the wrong premise produces a formal fallacy instead. “If there’s evidence for P, P is true. There’s no evidence for P. So P is false” is Denying the antecedent: evidence is one way to know P is true, but P can be true with no evidence yet found.

• Not disproven, so true (“you can’t prove it isn’t so”). Most tempting with claims that are hard or impossible to test, where a lack of disproof is guaranteed whether the claim is true or not. Bertrand Russell’s standard illustration is a china teapot orbiting the sun, too small for any telescope to see: nobody can disprove it, and that is no reason to believe it.
• Not proven, so false (“there’s no evidence for that”). Sound when the evidence would be expected; fallacious when nobody has looked, or nobody could have.
• “No evidence of” read as “evidence of no”: a search too weak to find the thing is reported as if it had shown the thing isn’t there, as in the study example.
• Shifting the burden of proof (“prove me wrong”): making a claim, then treating the other person’s failure to refute it as a win. This is close to the name’s original sense. John Locke, who named the argumentum ad ignorantiam in 1690, described it as pressing an opponent to accept what you offer as proof “or to assign a better”.

Walton sorts arguments from ignorance into three kinds: ones based on a record assumed to be complete, ones based on negative evidence from a search, and ones about who must prove what in a discussion.

Not the same error: the argument from personal incredulity. “I can’t imagine how that could work, so it doesn’t” rests on the limits of one person’s imagination or understanding, not on an absence of evidence, and involves no search at all. The two often appear together, but they fail for different reasons.

Absence of evidence often is evidence of absence. Walton’s book-length study treats this as a common, legitimate kind of reasoning, which he also calls lack-of-knowledge inference or negative evidence. It holds up when:

• The evidence would exist if the claim were true. A working smoke alarm that stays silent is good evidence there’s no fire in the room, because a fire would set it off.
• The search could have found it. A thorough search of a small room that turns up no keys is good evidence they aren’t there. A glance around a cluttered garage isn’t.
• The record is complete. If a train’s official timetable lists every stop and your town isn’t on it, the train doesn’t stop there. The assumption that a record contains everything relevant is called epistemic closure; databases that treat anything not stored as false rely on a version of it called the closed-world assumption.
• The confidence matches the search. Negative evidence usually supports “probably not”, and more or better searching earns more confidence. In probability terms, a missing piece of evidence counts against a claim only to the extent that it’s more likely to be missing if the claim is false than if it’s true. If it would be missing either way, its absence tells you nothing.
• You’re declining to believe, not concluding false. Not accepting a claim that hasn’t been supported is reasonable, and leaves the question open. The burden of proof normally falls on whoever makes the claim. The error is the step from “not shown” to “shown false”.
• It’s a rule for acting, not a claim about what’s true. Courts, safety procedures and similar systems set defaults for what to do when the evidence runs out, such as treating a wire as live until it has been tested. These are decisions about how to act under uncertainty.

The test: would you expect to have found evidence by now, if the claim were true?

“I’d have heard by now”

“My dentist’s office always texts or calls when they have to cancel. I haven’t heard anything, so my appointment tomorrow is still on.”

This is the “not disproven, so true” direction, and it’s reasonable. The speaker knows how cancellations are announced, so if the appointment had been canceled, they would expect to have a message. That’s the first condition above: the evidence would exist if the claim were true (here, the claim that it was canceled). A text can still go astray, so this is a good reason rather than a proof.

A “not guilty” verdict

The evidence against a defendant doesn’t prove guilt beyond a reasonable doubt, and the jury returns a verdict of “not guilty”.

It can look like “not proven guilty, so innocent”, but the verdict doesn’t say that. The presumption of innocence is a procedural rule, set in advance, about who has to prove what and what happens if they can’t. It reflects a judgment that the two possible mistakes aren’t equally bad: convicting an innocent person is treated as worse than acquitting a guilty one. “Not guilty” means the prosecution didn’t meet its burden, not that the court found the defendant innocent. This is the rule for acting condition. It would become an argument from ignorance only if someone treated the verdict as proof that the defendant didn’t do it.

Evidence you haven’t seen is easy to overlook. People judge from the information in front of them, Daniel Kahneman’s “what you see is all there is”, and rarely stop to ask what’s missing or whether they would have seen it. A lack of evidence then feels like a finding, even when no search could have produced one.

The legitimate version is also part of everyday life. People reason from a silent smoke alarm or an empty inbox all the time, and usually get it right, so the habit gets applied without checking whether anyone looked. In disagreements, negatives are often hard to prove, which lets “you can’t disprove it” make an unsupported claim look stronger than it is.

• Ask what you’d expect to see if the claim were true, and whether anyone has actually looked for it. Martin Hinton reduces the question to two checks: is the evidence really not available, and is it reasonable to expect that it would be?
• Ask whether the absence would look the same either way. No complaints from users who have no way to complain, or no sighting of something nobody could see, carries no information.
• When the search was weak, say “we don’t know” rather than picking a side. If the question matters, the remedy is usually a better search.
• When asked to disprove a claim, it’s fair to ask first what the reason for believing it is.

The argument from ignorance is a matter of reasoning rather than an empirical effect, but psychologists have studied how people judge these arguments and why some are stronger than others.

• Oaksford and Hahn (2004) gave a Bayesian (probability-based) account. They argued that some arguments from ignorance have the same structure as inductive reasoning that is widely accepted, and that the textbook examples are “not unsound but simply weak”. In a single experiment with two topics, people rated how convincing arguments were in short dialogues. Ratings were affected by whether the argument was positive (“the drug is toxic, because a toxic effect was observed”) or negative (“the drug is not toxic, because no toxic effects were observed”), by the amount of evidence (one study versus fifty), and by how strongly a character already believed the conclusion. Negative arguments were rated less convincing than positive ones, as the account predicts under conditions common for real tests.
• Hahn, Oaksford and Bayindir (2005) reproduced those three findings with different topics and a different evidence manipulation: the reliability of the source instead of the number of studies.
• Hahn and Oaksford (2007) extended the approach to other classic fallacies (circular arguments and slippery slopes), arguing that these are argument forms whose strength depends on their content, and reported experiments testing whether people’s judgments follow the factors the Bayesian account predicts.

The account is not universally accepted. Hinton (2018), for example, disputes Oaksford and Hahn’s claim that complete records are rarely available in real life, pointing to everyday cases like an attendance list or a team lineup where they plainly are.