Argument from fallacy

Naming the fallacy as a verdict

Sam: We should take the Ridge Trail. It must be an easy hike, because thousands of people do it every summer.

Alex: That’s an appeal to popularity. So it’s probably a hard hike.

Alex is right about the argument: lots of people doing a hike doesn’t show it’s easy. But Alex then treats the fallacy as evidence for the opposite, and it isn’t. The trail may be easy or hard, and the bad argument tells you nothing either way. The trail guide’s elevation profile would. This is the clear-cut case: a correct diagnosis, followed by a conclusion the diagnosis can’t support.

The debate that settles nothing

Two coworkers argue in a meeting about moving the daily check-in to 9:30. The one in favor gets flustered, misremembers the survey numbers and contradicts herself. The one against picks every point apart. The manager says: “Well, that settles it. We’ll keep it at 9:00.”

Nobody named a fallacy, but the move is the same. The manager has learned that one person argued badly for 9:30, not that 9:30 is a bad idea. A better-prepared advocate, or the survey itself, might make a strong case. Treating a question as settled by who argued better confuses the performance with the question. It’s also a kind of weak man: defeating the worst version of a position and treating the position as defeated (see Straw man).

A bad headline for a real finding

A news story announces “Science proves coffee makes you live longer!” based on a single study. A reader points out that one observational study can’t prove anything of the kind, and concludes: “So coffee has nothing to do with how long people live.”

The reader has caught a real overstatement. But the bad argument belonged to the headline writer, and the claim may have other support: the study’s actual, more cautious finding, and whatever other research exists. Rejecting a headline’s reasoning is fair; concluding that the opposite of the headline is true skips over all the evidence the headline didn’t mention.

The fallacious version has the same shape as the “not proven, so false” direction of the argument from ignorance: a failure of support is treated as proof of the opposite.

Even a formal fallacy can have a true conclusion. “If it rained, the grass is wet. The grass is wet. So it rained” is affirming the consequent, and it’s invalid. It rained anyway. Invalid means the premises don’t guarantee the conclusion, not that the conclusion is false.

The historian David Hackett Fischer described a broader fallacist’s fallacy in Historians’ Fallacies (1970), a book-length catalog of reasoning errors in historical writing, and presented it as a “fallacy of distraction” to which a fallacist “himself is especially susceptible”. It “consists in any of” several “false propositions”. The first two are:

• “An argument which is structurally fallacious in some respect is therefore structurally false in all respects”: treating one flaw as sinking the whole argument.
• “An argument which is structurally false in some respect, or even in every respect, is therefore substantively false in its conclusion”: the argument from fallacy in the sense of this page.

Later reference works use several names for it. Milos Jenicek’s Fallacy-Free Reasoning in Medicine (2009) lists it as the fallacy fallacy, with argumentum ad logicam and the fallacist’s fallacy as synonyms, and Kenneth Pope and Melba Vasquez’s ethics guide for therapists calls it the argument to logic: “assuming that a proposition must be false because an argument offered in support of that proposition was fallacious.” The Latin name looks classical, but no early source for it turned up in checking this entry; it appears mainly in modern fallacy lists. Scholarly treatment of the error is thin in general: the Stanford Encyclopedia of Philosophy‘s article on fallacies doesn’t discuss it, and most of what exists is short entries in reference works like these.

A bad argument is still a reason to change what you think, just not to reverse it.

• Declining to accept the conclusion. “That doesn’t show it” is the right response to a flawed argument. Not believing a claim that hasn’t been supported leaves the question open.
• Lowering confidence that rested on that argument. If the fallacious argument was your only reason for believing something, your belief should drop back to wherever it would be without it. That’s usually “don’t know”, not “false”.
• The claim was about the argument itself. If someone claims “this proof is correct” or “this study shows X”, finding the flaw refutes that claim directly.
• There’s independent evidence against the conclusion. Pointing out the fallacy and then giving separate reasons to think the conclusion is false is two moves, and both can be sound.
• The best available case has been looked for and is still bad. If people with every reason and opportunity to find good support for a claim can only produce fallacies, that can count as weak evidence against it, for the same reasons that negative evidence can under Argument from ignorance. The strength depends on how thorough the search was, not on the fallacy itself.

The test: do you have a reason to think the claim is false, or only a reason to think this argument doesn’t show it’s true?

Withdrawing a belief

“I was sure the website redesign caused our drop in sales, because the drop started the week it launched. But that’s just ‘it came after, so it was caused by it.’ I’m going to stop blaming the redesign until we’ve looked at other causes.”

This rejects a conclusion right after spotting a fallacy (post hoc ergo propter hoc), which looks like the error. But the speaker’s belief rested entirely on that argument, and they don’t conclude that the redesign didn’t cause the drop; they suspend judgment and plan to check. That’s the lowering confidence condition above.

The broken proof

A student announces they’ve proved that every even number greater than 2 is the sum of two primes. Their teacher finds a step that quietly assumes the result. “Your proof doesn’t work, so no, you haven’t proved it.”

The teacher rejects a claim because the argument for it is flawed, but the claim being rejected is “I’ve proved it”, which is a claim about the argument. The teacher says nothing about whether the statement itself (a famous open problem known as Goldbach’s conjecture) is true. That’s the claim was about the argument condition above.

Arguments and conclusions arrive packaged together, so defeating one feels like defeating the other. In a disagreement, it’s natural to keep score: if one side’s argument falls apart, the other side seems to have won, and “winning” gets read as being right.

Naming a fallacy can make this worse. A label like “appeal to popularity” sounds like a verdict, and it’s easy to stop there. That’s why every error page on this site carries the same reminder: a flawed argument can still reach a true conclusion.

The Genetic fallacy has a close parallel. A belief held for a poor reason isn’t false for that reason, just unsupported, in the same way that a claim defended by a poor argument isn’t refuted by it.

• Say “that doesn’t show it”, not “so it’s false”. It’s the accurate claim, and it’s usually all you need.
• Ask what other evidence bears on the question. If the conclusion matters, look for the best case for it, not only the one in front of you.
• When your own argument is shown to be fallacious, don’t defend it; ask whether there’s a better reason for the conclusion, and drop the conclusion if there isn’t.