Fallacies: the names, the patterns, and why the experts warn you about the names

In January 2007 the UK's Advertising Standards Authority ruled on a poster you may have seen a version of. It said "More than 80% of dentists recommend Colgate". Two members of the public complained, the ASA opened its own inquiry, and the ruling went against the advertiser. The survey behind the poster had let each dentist recommend several brands at once, and enough of them did that another competitor's brand was recommended almost as much as Colgate was. Nobody had asked the dentists to pick one.¹

Notice what the ruling did not say. It did not say that dentists are not experts on toothpaste, or that you shouldn't listen to them. It said that the poster claimed the dentists asserted something they hadn't. The argument was "experts say X, so X", and the trouble was with what the experts actually said.

That is the whole of this lesson in one case. You are about to learn the standard names for bad arguments, and one of those names, appeal to authority, fits the Colgate poster. But "appeal to authority" also fits every time you take a doctor's word about a dose or a mechanic's word about a brake pad, and those arguments are good. The name tells you the shape. It doesn't tell you the verdict. The people who study fallacies for a living have been saying this for fifty years, and most of the fallacy lists you'll meet online haven't caught up. This lesson teaches you to use the names the way an expert does: as a hypothesis about what might be wrong, to be tested with the six-step check you already own.

Where the list comes from

Aristotle wrote the first one. In On Sophistical Refutations he set out thirteen ways of "producing the false appearance of an argument". Six "depend on language": ambiguity, amphiboly, combination, division of words, accent, form of expression. Seven don't: accident, the use of an expression "absolutely or not absolutely but with some qualification", "ignorance of what refutation is", the consequent, "assuming the original conclusion", "stating as cause what is not the cause", and "the making of more than one question into one".²³ You'll recognise several. Assuming the original conclusion is begging the question. Stating as cause what is not the cause is false cause. The consequent is affirming the consequent from lesson 3.

Two things about that list matter for how you use its descendants. First, it's nearly 2,400 years old, and most of what you'll meet online is a lightly edited version of it. Second, it was built for a game: the formal debating contests of Aristotle's Athens, in which one speaker tried to force another into a contradiction. A "sophistical refutation" was a move that looked like a winning move in that game and wasn't. The list was never designed to catalogue everything that goes wrong when a newspaper columnist or a planning committee reasons badly, which is part of why it fits real life awkwardly.

The list grew piecemeal. John Locke, in 1690, named three kinds of "ad" argument that have stuck: ad verecundiam (to modesty, now called appeal to authority), ad ignorantiam (to ignorance), and ad hominem (to the person). Richard Whately and John Stuart Mill in the nineteenth century added their own sortings.³ Textbooks have sorted the modern list ever since, each a little differently. Knachel's free Fundamental Methods of Logic, for one, sorts its fallacies chapter into four families: distraction, weak induction, illicit presumption, and linguistic emphasis.⁴ I'll use a five-way map in the same spirit, sorted by what goes wrong: relevance, weak induction, presumption, ambiguity, and part-and-whole transference. Don't memorise anyone's grouping; the groups exist to make the cogent twins easier to see.

The Stanford Encyclopedia's working definition is the one to hold on to: a fallacy is "an argument that seems to be better than it really is".³ Keep the word seems. A fallacy isn't a bad argument. It's a bad argument with a good disguise, and the disguise is usually that it looks like a good argument you've seen before.

The five groups, with the schema and the twin

Here is the list, compressed. For each fallacy I give a two-line schema, in the style of the appendix to a Lander University logic course that I found more useful than any textbook page,⁵ and then the cogent twin: the good argument that has the same surface shape. The twin is the important half. If you learn only the names, you'll spend the rest of your life convicting good arguments.

Fallacies of relevance. The premises are true and beside the point.

• Appeal to force. Accept p, or something bad happens to you. Twin: a genuine warning ("if you sign this, you'll be liable"), which is a premise about consequences, not a threat about belief.
• Appeal to pity. Someone suffers; therefore p. Twin: an argument in which suffering is the relevant fact, as in a claim for damages.
• Appeal to the people. Everyone believes p; therefore p. Twin: a claim about what many independent, informed observers report, which is evidence (a thousand sailors who saw the same rock).
• Argument against the person (ad hominem), in three forms: abusive (he's a bad person, so p is false), circumstantial (she'd benefit from p, so p is false), and tu quoque (you do it too, so your argument fails). Twin: a credibility challenge when the claim rests on the person's word. We'll spend a whole section on this one.
• Accident. A general rule, applied to a case it was never meant for. Twin: the rule, applied to a case it does cover.
• Straw man. Refute a distorted version of p; conclude that p is refuted. Twin: refuting the strongest version. This is lesson 7's charity, failing.
• Missing the point and red herring. The premises support some conclusion, just not this one. Twin: a genuine change of subject, announced as such.

Fallacies of weak induction. The premises are relevant but too weak.

• Appeal to unqualified authority. E says p; therefore p, where E isn't in a position to know. Twin: E says p, where E is a qualified, unbiased expert in the field, and the experts agree.
• Appeal to ignorance. p is unproved; therefore not-p. (That is the Lander schema word for word.⁵) Twin: p is unproved after a search that would have found it, so probably not-p.
• Hasty generalisation. A few cases have property F; therefore all do. Twin: a large, representative sample has F. Lesson 5's rules apply.
• False cause. A came before B, or with B; therefore A caused B. Twin: a method-of-difference comparison, or a mechanism plus a dose-response pattern.
• Slippery slope. If we take step one, then two, then three, then disaster; therefore not step one. Twin: the same chain with a mechanism and evidence for each link.
• Weak analogy. A is like B in some respects; B has F; therefore A has F, where the shared respects aren't the ones that matter. Twin: an analogy on the relevant features.

Fallacies of presumption. The premises quietly assume what's at issue.

• Begging the question. p, because q, where q is p in other words. Twin: none, though a valid argument whose premise is obviously true and whose conclusion is obviously true can look circular without being so.
• Complex question. "Have you stopped doing X?" bundles two questions into one so that any answer concedes the first.
• False dichotomy. Either A or B; not A; therefore B, where C was available. Twin: a real either/or, where the options really are exhaustive.
• Suppressed evidence. The premises are true, and the fact that would have changed the verdict is left out.

Fallacies of ambiguity. A word or a sentence changes meaning in transit.

• Equivocation. A term used in one sense in a premise and another in the conclusion.
• Amphiboly. A sentence whose grammar allows two readings, with the argument using both.

Fallacies of illicit transference. A property moves between part and whole.

• Composition. Each part has F; therefore the whole has F.
• Division. The whole has F; therefore each part has F.

That's the list. It is a decent index of the ways arguments go wrong, and you should know it. Now the part textbooks put in small print.

The mechanism: every fallacy is a good move in the wrong place

The idea that makes the list usable is this. Nearly every pattern on it is also the shape of a legitimate argument. Appealing to experts is how nearly all of your knowledge arrived; you did not personally verify the boiling point of water or the existence of Australia. The Internet Encyclopedia of Philosophy says it plainly: "Most reasoning of this kind is not fallacious, and much of our knowledge properly comes from listening to authorities."⁶ Attacking the person is what every cross-examination does, and the courts think it is so important that they have made it a constitutional right, as you'll see. Slippery slope and appeal to ignorance are inductive arguments about consequences and about searches, and lesson 6 gave you the tool that measures them.

So the name can't be the verdict. What decides is whether this instance is the good version or the bad one, and that is a question about content and context, which is exactly what the six-step check tests. Douglas Walton, who did more than anyone to make this precise, called each pattern an argumentation scheme and attached to each a short list of critical questions. Ask the questions; if the argument survives them, it's cogent; if it fails one, you've found the flaw and you can say exactly which it is.⁷ That's a far better thing to be able to say than a Latin name.

For appeal to expert opinion the scheme is: E is an expert in a field S; A is a claim in S; E asserts A; therefore A. Walton's six critical questions:

1. Expertise. How credible is E as an expert?
2. Field. Is E an expert in the field that A is in?
3. Opinion. What did E actually assert?
4. Trustworthiness. Is E personally reliable, or is there a reason to doubt it (a payment, a stake)?
5. Consistency. Is A consistent with what other experts say?
6. Backup evidence. Is E's assertion based on evidence?⁷

Run the Colgate poster through them. Expertise: dentists, fine. Field: toothpaste, fine. Opinion: here it falls over. The dentists asserted "I'd recommend Colgate, among others"; the poster asserted "dentists recommend Colgate over other brands". Trustworthiness: the survey was commissioned by Colgate, and the ruling found that the survey's own scripts hadn't made clear to the dentists that the research was for Colgate and could be used in advertising, which is a reason to look closely rather than a conviction. Consistency: another brand scored almost as high, so the experts were not lined up behind one answer. Backup evidence: not really at issue. Verdict: weak here, and it fails on question 3.¹ Notice how much more you now know than "it's an appeal to authority". You know which question it fails, which means you know what a fixed version of the poster would have to say.

Worked example 1: the expert who was in the wrong field

Lesson 6 gave you the Sally Clark case for the prosecutor's fallacy. It also contains the cleanest failed appeal to authority I know of, and this time you'll run the questions before I do.

Recall the facts from the Royal Statistical Society's statement of 23 October 2001. In R v. Sally Clark, "a medical expert witness drew on published studies to obtain a figure for the frequency of sudden infant death syndrome (SIDS, or 'cot death') in families having some of the characteristics of the defendant's family. He went on to square this figure to obtain a value of 1 in 73 million for the frequency of two cases of SIDS in such a family." The Society's judgement: "This approach is, in general, statistically invalid. It would only be valid if SIDS cases arose independently within families, an assumption that would need to be justified empirically."⁸

The jury heard that figure from an expert. Take the six questions and run them yourself before reading on. Expertise, field, opinion, trustworthiness, consistency, backup evidence. Which one fails?

That last quotation is worth a second look, because it is itself an appeal to authority, and a cogent one. The RSS is arguing: statistical claims should come from statisticians. Run the questions on the RSS. Expertise, yes. Field, yes: it's a statistical society talking about statistics. Opinion: quoted in full. Trustworthiness: a learned society with no stake in the verdict. Consistency: I know of no statistician who disagreed. Backup evidence: the statement gives its reasons. So the same shape, "an authority says so", is fallacious in the witness box and cogent in the press release, and the difference is visible only when you ask the questions.

The law, incidentally, has its own version of the six questions. In Daubert v. Merrell Dow Pharmaceuticals (1993) the US Supreme Court told trial judges that when deciding whether scientific expert testimony is admissible they may consider "whether it can be (and has been) tested", whether it has been through peer review and publication, "the known or potential rate of error", and whether it has "general acceptance" in the relevant community. And it said something a logic teacher would underline: "The focus, of course, must be solely on principles and methodology, not on the conclusions that they generate."⁹ Test the link, not the conclusion. That is step 4 of the check, written into US federal law.

Worked example 2: attacking the person, twice

Here are two arguments with the same shape: don't accept what this person says, because of something about the person. One of them is a fallacy. Decide which before you read the verdicts.

Case A. Richard Green was the main prosecution witness in an Alaska burglary trial. He identified the defendant, Davis, near a stolen safe. At the time, Green was himself on juvenile probation for burgling two cabins. The defence wanted to tell the jury that, to argue that Green had a motive to point at someone else quickly, or to say what the police wanted to hear, because a revoked probation would have been his own problem. The trial judge barred any mention of it.¹⁰

Case B. This one is hypothetical, because I could not find a documented instance I could present fairly, and this course doesn't invent one and pass it off as real. A plumber tells you your boiler's heat exchanger is cracked and needs replacing. You later learn she was rude to a neighbour and once had a parking fine. You conclude the boiler is fine.

The US Supreme Court agreed with case A, seven votes to two, in Davis v. Alaska (1974). Chief Justice Burger wrote: "We have recognized that the exposure of a witness' motivation in testifying is a proper and important function of the constitutionally protected right of cross-examination." The jurors, he said, "were entitled to have the benefit of the defense theory before them so that they could make an informed judgment". And he drew the line that this lesson turns on. A general attack on a witness's character is one thing; "a more particular attack on the witness' credibility is effected by means of cross-examination directed toward revealing possible biases, prejudices, or ulterior motives".¹⁰ That is the good ad hominem, and a court thought it important enough to overturn a conviction for.

Walton's thesis, after a book-length study, is that no ad hominem argument is inherently fallacious.¹¹ The IEP gives the everyday test in a sentence: "attacks on a person for their immoral sexual conduct are irrelevant to the quality of the person's reasoning about Kepler's astronomy, but they are relevant to arguments promoting the person for a leadership position in a church or mosque or city council."⁶ Ask what the claim rests on. If it rests on the person, the person is fair game.

The wrinkle: a conflict of interest

Now the harder version, the circumstantial form: don't trust this because of who paid for it. In 2016 three researchers at the University of California published an analysis of internal documents of the Sugar Research Foundation, a trade body. They found that in 1965 the Foundation had commissioned a review of the dietary causes of heart disease from Harvard researchers, paying them $6,500 (about $48,900 in 2016 dollars). The review, published in the New England Journal of Medicine in 1967, "singled out fat and cholesterol as the dietary causes of CHD and downplayed evidence that sucrose consumption was also a risk factor." The Foundation "set the review's objective, contributed articles for inclusion, and received drafts. The SRF's funding and role was not disclosed."¹²

Worked example 3: the same words, weak and then strong

Lesson 6 gave you "there is no evidence the drug is harmful". Here it gets its name, appeal to ignorance, and here is why the name settles nothing.

Version one: the drug was licensed last month and nobody has run a safety study. "No evidence of harm" is then almost exactly as likely if the drug is harmful as if it isn't, because nobody looked. Likelihood ratio near 1; the argument is weak; the schema "p is unproved, therefore not-p" fits and convicts.

Version two: the same words after fifteen years and several large studies that would have found harm if harm existed. Now "no evidence of harm" is far more likely under "safe" than under "harmful". Same schema, strong argument.

The documented case of the weak version is one of the most carefully written documents in the history of engineering. After the loss of the space shuttle Challenger in 1986, the physicist Richard Feynman sat on the presidential commission and wrote his own appendix to its report. On the solid rocket booster seals, which had shown erosion on earlier flights:

"The phenomenon of accepting for flight, seals that had shown erosion and blow-by in previous flights, is very clear. The Challenger flight is an excellent example. There are several references to flights that had gone before. The acceptance and success of these flights is taken as evidence of safety. But erosion and blow-by are not what the design expected. They are warnings that something is wrong ... The fact that this danger did not lead to a catastrophe before is no guarantee that it will not the next time, unless it is completely understood. When playing Russian roulette the fact that the first shot got off safely is little comfort for the next."¹³

Look at what makes the argument from past flights weak, in lesson 6's terms. If the joint fails, say, one flight in a hundred, then a run of twenty successes has probability about 0.82; if it's as safe as management believed, the probability is about 1. The ratio is about 1.2. Twenty safe flights should barely have moved anyone, and Feynman's point is sharper still: the flights were not even a test of the thing that worried the engineers, because the erosion had already shown the joint was operating outside its design. The management estimate of the risk, by the way, was "1 in 100,000", against the working engineers' "1 in 100", and Feynman noted that the former "would imply that one could put a Shuttle up each day for 300 years expecting to lose only one".¹³

And the strong version, documented. In 2019 a Danish team followed 657,461 children born between 1999 and 2010, comparing those who had received the MMR vaccine with those who hadn't. The adjusted hazard ratio for autism was 0.93 (95% confidence interval 0.85 to 1.02), and no increased risk appeared in any subgroup or any period after vaccination. The authors' conclusion: the study "strongly supports that MMR vaccination does not increase the risk for autism".¹⁴ That is "no evidence of harm" after a search that would have found it. Same words as the drug licensed last month; a strong argument this time, and the difference is entirely in what the search could have found.

Slippery slope, with and without a mechanism

The same Feynman appendix contains a slippery slope that was strong, which is rarer than you'd think. He wrote that "certification criteria used in Flight Readiness Reviews often develop a gradually decreasing strictness. The argument that the same risk was flown before without failure is often accepted as an argument for the safety of accepting it again."¹³ That is a chain: accept a little erosion, and the accepted erosion becomes the new baseline, and the next review measures against the baseline rather than the design. Each link has a mechanism (the comparison point moves) and evidence (the review records). The slope is real. Feynman's own example: when deciding whether flight 51-L was safe in the face of ring erosion on flight 51-C, "it was noted that the erosion depth was only one-third of the radius", and this was described as "a safety factor of three".¹³

Now a hypothetical slope with no mechanism at all: "if we let one student hand in an essay late, soon nobody in the school will meet a deadline." What moves the school from one extension to universal lateness? Nothing is offered. Ask for the mechanism, and if none comes, the argument is weak. That question, not the name, is the test.

Worked example 4: the straw man, in a courtroom

Lesson 7 taught you charity: reconstruct the version the other person would sign. The straw man is what happens when you don't, and courts see it often enough that judges have a phrase for it.

In 2015 the Wisconsin Court of Appeals decided Wolf v. American Family Mutual Insurance, a dispute about whether a change in the state's car-insurance law reached into a policy written before the law took effect. The policy contained an "elasticity clause", which adjusts a policy's terms to match changes in the law. Ms Wolf's brief cited an earlier case to establish that elasticity clauses are enforceable. The court's reply:

"Wolf ostensibly cites Roehl for the proposition that elasticity clauses are enforceable. Of course they are. However, her contention attacks a straw man. American Family does not contend the elasticity clause is unenforceable; rather, it argues that the elasticity clause does not implement changes which are not 'in conflict with' the terms of the policy because these legislative changes have not become effective until a policy is renewed or issued."¹⁵

See the move. The insurer's actual argument was narrow: this clause doesn't apply to this change, for this reason. The brief answered a broad claim the insurer never made, that such clauses never apply. The answer was correct and irrelevant. Rapoport's first rule from lesson 7, restate the opponent's position so well they'd thank you, would have caught it in a sentence: "American Family says the clause is enforceable but doesn't reach this change." Once you've written that down, you can't argue against something else without noticing.

The rest of the list, in documented cases

Hasty generalisation and false cause. In 1998 the Lancet published a paper by Andrew Wakefield and colleagues describing "12 children (mean age 6 years [range 3-10], 11 boys)" referred to a gastroenterology unit. Its findings section reported: "Onset of behavioural symptoms was associated, by the parents, with measles, mumps, and rubella vaccination in eight of the 12 children." Its interpretation was that the condition "was generally associated in time with possible environmental triggers".¹⁶ Twelve children, selected because they had already been referred with these problems, is the schema of hasty generalisation. And "associated, by the parents", in time, is the schema of post hoc: A came before B, therefore A caused B. The paper itself was cautious in its wording; the public argument built on it was not.

In February 2010 the Lancet retracted the paper. The retraction says that, following the General Medical Council's findings, "it has become clear that several elements of the 1998 paper by Wakefield et al are incorrect ... In particular, the claims in the original paper that children were 'consecutively referred' and that investigations were 'approved' by the local ethics committee have been proven to be false. Therefore we fully retract this paper from the published record."¹⁷ Hold that thought for the fallacy fallacy below.

Division. In 1950 the sociologist W. S. Robinson took the 1930 US census and computed, for the nine census divisions, the correlation between the percentage of residents who were foreign-born and the percentage who were illiterate. He chose that pair, he said, because "we know what the sign ought to be": schooling standards were lower for the foreign-born, so more immigrants should mean more illiteracy. Across individuals the data agreed: the correlation between being foreign-born and being illiterate was 0.118, positive. But across the nine divisions it was minus 0.619, and on a state basis minus 0.526. The regions with more immigrants had less illiteracy.¹⁸ The group-level figure wasn't just exaggerated; it pointed the wrong way, because the foreign-born mostly lived in states where schools were good and nearly everyone, native or immigrant, could read. The group correlation described where immigrants lived, not immigrants. Concluding from "regions with F have G" to "people with F have G" is division, and epidemiologists still call it the ecological fallacy, after this paper.

Composition is the same error the other way, and I'll give it hypothetically: every player on the team is the best in her position, so the team is the best. Whether that follows depends on whether the property adds up, and "best" often doesn't.

Equivocation. Two documented cases. In March 2016 the ASA ruled against a broadband provider's advertisement for a "TOTALLY UNLIMITED" service. The provider ran traffic prioritisation that, when a line was busy, could reduce some traffic to 5% of the line's capacity. The ASA's reasoning, as reported: a "'totally unlimited' claim was stronger, and ... consumers would understand it to mean that the service was free from any provider-imposed limitations."¹⁹ The advertiser meant "unlimited" in one sense (no data cap); the reader took it in another (no limits); the argument "it's unlimited, so buy it" ran on the gap. The textbook form has the shift inside one argument; the advertising form has it between writer and reader; the ASA's job is to police that gap, and the ruling names the two senses.

The second is Feynman's again. That "safety factor of three" claim: in engineering, a safety factor is the designed margin above the loads a structure is meant to carry, "to allow for uncertain excesses of load, or unknown extra loads, or weaknesses in the material". Erosion of a seal that was designed to have no erosion is not a margin of that kind; it's a failure that hasn't finished. Feynman: "This is a strange use of the engineer's term, 'safety factor.'"¹³ One phrase, two meanings, and the argument for flying rode across from one to the other.

Begging the question. Circular reasoning: the conclusion is smuggled into a premise. A hypothetical: "this policy is the fairest option, because no other option treats people as fairly." The second half is the first half rearranged. Two notes. In ordinary English "that begs the question" now usually means "that raises the question", and you should know both usages and keep them apart; in logic the phrase means the circle. And a circle can be hard to see when the premise is a long way from the conclusion in the text; lesson 7's reconstruction, which puts the premises next to the conclusion, is what exposes it.

False dichotomy and complex question I'll leave hypothetical and short. "Either we cut the budget or we go bankrupt" is a false dichotomy if there's a third option (raise revenue), and a true one if there isn't; you check by looking for the third option, not by spotting the "either". "Have you stopped skipping the safety checks?" is a complex question; the answer is to separate the two questions and answer each.

Now the honest part: why the experts warn you about the names

You have the list. Before I tell you what the people who study fallacies think of it, make a guess.

In 1970 Charles Hamblin published Fallacies, and it is the reason a lesson like this one exists. He looked at what he called the standard treatment, "the typical or average account as it appears in the typical short chapter or appendix of the average modern textbook", and wrote: "what we find in most cases, I think it should be admitted, is as debased, worn-out and dogmatic a treatment as could be imagined: incredibly tradition bound, yet lacking in logic and in historical sense alike, and almost without connection to anything else in modern Logic at all."³ His complaint was that textbooks defined a fallacy as "an argument that seems to be valid but is not so", then listed items the definition doesn't fit. Begging the question is valid: p, therefore p, has no counterexample. The complex question isn't an argument at all; it's a question. The definition and the list had never been reconciled, and the textbooks kept copying both from each other anyway.

Three objections followed that you should be able to state.

Finocchiaro (1981): textbook fallacies are rare in real discourse. Real arguments go wrong in ways that don't fit the categories, and the categories, when you look for instances, are hard to find. He preferred to talk of "fallacious arguments" and to analyse each on its own terms.³

Massey (1981): there is an asymmetry between proving validity and proving invalidity. To show an argument valid, you show it has a valid form. But showing it has an invalid form proves nothing, because every argument has many forms and one of the others might be valid. Massey's conclusion: "no argument can be convicted of being a fallacy on logical grounds."³ Read that again, because it's the deepest point in the lesson. You cannot convict an argument by matching it to a pattern. You have to go into the content. Which is what the critical questions do.

Boudry, Paglieri and Pigliucci (2015): the Fallacy Fork. In their words: "if fallacies are construed as demonstrably invalid form of reasoning, then they have very limited applicability in real life (few actual instances). On the other hand, if our definitions of fallacies are sophisticated enough to capture real-life complexities, they can no longer be held up as an effective tool for discriminating good and bad forms of reasoning." And: "almost every known type of fallacy is a close neighbor to sound inferences or acceptable moves in a debate."²⁰ Every twin in the list above is an instance of that sentence.

The diagram is the fork. Whichever prong you take, the name on its own cannot do the job people want it to do. Boudry and colleagues conclude that fallacy theory should give way to case-by-case evaluation. That is one live position in the field.

The defenders and reformers don't dispute the fork so much as build around it. Walton keeps the names and redefines a fallacy as a misuse of an argumentation scheme in a particular kind of dialogue, judged by the critical questions; a move that's fine in a negotiation may be a fallacy in an inquiry.⁷³ The pragma-dialectical school in Amsterdam, van Eemeren and Grootendorst, rebuilt the whole subject as ten rules for a critical discussion, starting with a freedom rule: one may not prevent the other party from expressing their view. A fallacy, on this account, is any violation of a rule. That covers the traditional list and adds moves it missed.³ Johnson and Blair, who founded the informal-logic movement in Canada, sort fallacies as failures of one of three conditions on a cogent argument: acceptability, relevance, sufficiency,³ which you met in lesson 7 as the ARG conditions. On that view the list is a set of common ways to fail one of three tests, and the tests are what you actually run.

What would settle it. Corpus studies: take a large body of real argument, count how often each pattern occurs, and count how often the instances are actually defective. Instruction studies: teach one group the names and another the critical questions and see who evaluates real arguments better at a delay. We have the second kind only in outline. A 2015 meta-analysis of 341 effect sizes found that critical-thinking instruction works overall (a weighted mean effect of g = 0.30), with dialogue and authentic problems mattering most, but it did not isolate fallacy labels as an ingredient.²¹ So the honest position is that the disagreement is open.

This course's line, said plainly. Teach the names, because you will meet them and because they are a good index of the ways arguments fail. Teach every name with its critical questions and its cogent twin, never alone. And treat a name as a hypothesis: "this might be an appeal to ignorance" means "go and check whether anyone looked", not "case closed". Walton would sign that, and so, I think, would Boudry, whose practical advice is to evaluate the argument in front of you. The IEP, which lists 231 fallacy names, puts the warning on the tin: "Simply applying the fallacy name to a passage cannot substitute for a detailed examination of the passage and its context or circumstances."⁶

The fallacy fallacy

One more pattern, and it's the one that the names create. Suppose you show that someone's argument for p is fallacious. What do you now know about p?

The Lancet retraction is the clean case. The retraction established that the 1998 paper's argument stood on false premises: the children were not "consecutively referred" and the investigations were not "approved" by an ethics committee.¹⁷ That destroys the argument. It says nothing, by itself, about whether MMR causes autism; a paper with honest premises could in principle have found the same thing. What settles the claim is the evidence gathered when people looked properly, which is where the Danish cohort of 657,461 children comes in, with its hazard ratio of 0.93.¹⁴ The claim is false because the search that would have found it found nothing, not because one argument for it collapsed. Keep those two verdicts separate and you'll never commit the fallacy fallacy. It's the same discipline as lesson 2's: test the link, then test the premises, and only then say something about the conclusion.

What people get wrong

"Any appeal to authority is a fallacy." Most of what you know came from authorities and you were right to accept it. The fallacy is the appeal to an authority who is out of field, or against the consensus, or misquoted, or compromised. Run the six questions.⁶⁷

"Ad hominem is always a fallacy." Davis v. Alaska is the answer. When a claim rests on someone's word, their motives are the evidence.¹⁰¹¹

"Slippery slope and appeal to ignorance are always fallacies." They are inductive arguments. Feynman's Flight Readiness Reviews were a real slope with a mechanism; the Danish cohort is a real absence of evidence that is strong evidence of absence. The likelihood ratio decides, not the name.¹³¹⁴

"Begs the question means raises the question." In everyday English it now does. In logic it means the circle. Know which one you're using.

"Spotting the name settles it." Massey: you cannot convict an argument on logical grounds by matching it to a form. Boudry: nearly every named fallacy has a cogent twin. IEP: the name "cannot substitute for a detailed examination".³²⁰⁶

"A fallacious argument has a false conclusion." The fallacy fallacy. The retraction destroyed an argument; the cohort study settled the claim.

"The list is complete, coherent, and ancient in its current form." It began as thirteen items for a debating game, grew by accretion, has never had a definition that fits all its members, and the field disagrees about whether to keep it at all.²³

"I spot fallacies quickly, so I'm good at this." You spot them quickly on the other side. Lesson 2's belief bias predicts that an argument whose conclusion you dislike has a far better chance of striking you as fallacious, whether or not it is. If a fallacy diagnosis arrives in under ten seconds, that speed is information about you, and the right response is to run the check on your own side's argument too.

Practice

Before the quiz, close the page and write down, from memory: the five groups and one fallacy from each; Walton's six critical questions; the cogent twin of ad hominem, of appeal to ignorance, and of slippery slope; the two prongs of the Fallacy Fork; and what the fallacy fallacy forbids you to conclude. Then check. Reread only what you missed.

Connections

The names are shortcuts for the check you already own. Every critical question in this lesson is one of lesson 7's ARG conditions in a specific dress: the six expert questions test acceptability; the ad hominem test is a relevance test; the likelihood ratio from lesson 6 is how you measure grounds for the inductive patterns, and it's what decides slope and ignorance. Massey's asymmetry is lesson 2's lesson again: you show an argument invalid by finding a counterexample in its content, not by matching its shape. And belief bias, from lesson 2, is why a fallacy verdict comes so much more easily against a conclusion you dislike; the discipline is to run the questions symmetrically.

Lesson 9 takes the names and the six questions to the news, where the arguments come compressed and the source does the work of the warrant. Lesson 10 turns the check around on your own writing.

Go deeper

• Hans Hansen, "Fallacies", Stanford Encyclopedia of Philosophy (rev. 2024): the map of the whole subject, including the history and every position in the debate above, in about the length of this lesson.
• Bradley Dowden, "Fallacies", Internet Encyclopedia of Philosophy: 231 names with examples; the reference to consult when you meet a name you don't know, and it carries the same warning about names that this lesson does.
• Boudry, Paglieri and Pigliucci, "The Fake, the Flimsy, and the Fallacious", Argumentation 29 (2015): the Fallacy Fork paper, free on PhilArchive, and the strongest case for dropping the names altogether. Read it after this lesson and decide for yourself.
• Walton, Reed and Macagno, Argumentation Schemes (Cambridge, 2008): 96 schemes with their critical questions; the reference for the method this lesson uses.
• Richard Feynman, "Personal Observations on the Reliability of the Shuttle", Appendix F to the Rogers Commission report (1986): five pages, free, and the best short document I know on how good people accept bad arguments under pressure.
• Wireless Philosophy's Critical Thinking: Fallacies series on Khan Academy: short videos with practice exercises on the individual patterns.

Sources

1. Advertising Standards Authority, adjudication on Colgate-Palmolive (UK) Ltd, January 2007, as reported by Osborne Clarke, "Colgate's '80% of dentists recommend' claim under fire", 31 January 2007 (re-read at review time). The poster claim "More than 80% Of Dentists recommend Colgate"; two consumer complaints and an ASA-initiated inquiry; the survey asked dentists to recommend several toothpastes and brands, not a single choice; "another competitor's brand was recommended by dentists almost as much"; the survey scripts "did not make it sufficiently clear that the research was being conducted on behalf of Colgate or that the results could be used for advertising purposes"; complaints upheld. The 2007 adjudication itself is no longer on the ASA site, so this is cited via the law firm's contemporaneous report.
2. Aristotle, On Sophistical Refutations, trans. W. A. Pickard-Cambridge, sec. 4 to 5, MIT Classics. The six fallacies depending on language and the seven independent of it, quoted as translated.
3. Hans V. Hansen, "Fallacies", Stanford Encyclopedia of Philosophy (2015, rev. Aug 2024). Sec. 1: the working definition "an argument that seems to be better than it really is". Sec. 2: Aristotle's thirteen (2.1), Locke's three ad arguments (2.4), Whately (2.7), Mill (2.8). Sec. 3: Hamblin 1970 p. 12 on the standard treatment (the dash in Hamblin's sentence is rendered as a colon in the lesson's quotation); the standard definition "an argument that seems to be valid but is not so"; Finocchiaro on "fallacious arguments"; Massey's asymmetry and "no argument can be convicted of being a fallacy on logical grounds"; Johnson and Blair's acceptability, relevance, sufficiency; pragma-dialectics' ten rules, beginning with the rule that "one may not prevent the other party from expressing their view" (re-verified against the live entry at review time); Walton's dialogue types.
4. Matthew Knachel, Fundamental Methods of Logic, ch. on informal logical fallacies (University of Wisconsin-Milwaukee; CC BY 4.0; read on LibreTexts at review time). Sorts the fallacies into four families: Fallacies of Distraction, Fallacies of Weak Induction, Fallacies of Illicit Presumption, and Fallacies of Linguistic Emphasis; "a logical fallacy is just a bad argument", bad "in the logical sense of being incorrect". The five-way sorting used in this lesson is this course's own arrangement of the traditional list, in the same spirit.
5. Lee Archie, PHIL 103 Introduction to Logic syllabus, Lander University (v1.1, Fall 2003), appendix "Summary of Informal Fallacies". The two-line schema format; ad ignorantiam as "p is unproved. Therefore not-p is true."
6. Bradley Dowden, "Fallacies", Internet Encyclopedia of Philosophy. "Most reasoning of this kind is not fallacious, and much of our knowledge properly comes from listening to authorities"; "Simply applying the fallacy name to a passage cannot substitute for a detailed examination of the passage and its context or circumstances"; the Kepler example under ad hominem; 231 names.
7. Douglas Walton, Appeal to Expert Opinion (Penn State, 1997); Walton, Reed and Macagno, Argumentation Schemes (Cambridge UP, 2008). The scheme for expert opinion and the six critical questions: expertise, field, opinion, trustworthiness, consistency, backup evidence; a fallacy as misuse of a scheme in a dialogue type.
8. Royal Statistical Society, "Royal Statistical Society concerned by issues raised in Sally Clark case", news release, 23 October 2001. "A medical expert witness"; the squaring to 1 in 73 million; "statistically invalid"; "very strong a priori reasons for supposing that the assumption will be false"; "statistics remains a specialised area"; the call for statistical evidence to be given by "appropriately qualified statistical experts".
9. Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579 (1993). The factors for scientific testimony (testability, peer review and publication, known or potential rate of error, general acceptance); "The focus, of course, must be solely on principles and methodology, not on the conclusions that they generate"; "Vigorous cross examination, presentation of contrary evidence, and careful instruction on the burden of proof are the traditional and appropriate means of attacking shaky but admissible evidence."
10. Davis v. Alaska, 415 U.S. 308 (1974), decided 27 February 1974, Burger C.J., with Stewart J. concurring and White and Rehnquist JJ. dissenting. The witness Richard Green on juvenile probation for burglary; the protective order; "the exposure of a witness' motivation in testifying is a proper and important function of the constitutionally protected right of cross-examination"; the jurors "were entitled to have the benefit of the defense theory before them"; the "more particular attack on the witness' credibility ... directed toward revealing possible biases, prejudices, or ulterior motives".
11. Douglas Walton, Ad Hominem Arguments (University of Alabama Press, 1998). The thesis that no ad hominem argument is inherently fallacious; cross-examination of a witness's honesty as the legitimate case.
12. Cristin E. Kearns, Laura A. Schmidt and Stanton A. Glantz, "Sugar Industry and Coronary Heart Disease Research: A Historical Analysis of Internal Industry Documents", JAMA Internal Medicine 176(11), 2016, 1680 to 1685. The 1965 project; $6,500 ($48,900 in 2016 dollars) paid for the review; the review "singled out fat and cholesterol as the dietary causes of CHD and downplayed evidence that sucrose consumption was also a risk factor"; "The SRF set the review's objective, contributed articles for inclusion, and received drafts. The SRF's funding and role was not disclosed"; the recommendation to give "less weight to food industry-funded studies". The review is McGandy, Hegsted and Stare, New England Journal of Medicine, 1967.
13. R. P. Feynman, "Personal Observations on the Reliability of the Shuttle", Appendix F to the Report of the Presidential Commission on the Space Shuttle Challenger Accident, vol. 2 (1986). The estimates "from roughly 1 in 100 to 1 in 100,000", engineers high and management low, and "one could put a Shuttle up each day for 300 years expecting to lose only one"; "certification criteria used in Flight Readiness Reviews often develop a gradually decreasing strictness. The argument that the same risk was flown before without failure is often accepted as an argument for the safety of accepting it again"; the seals passage with "Russian roulette"; flight 51-L, flight 51-C, erosion "only one-third of the radius", "a safety factor of three", and "This is a strange use of the engineer's term, 'safety factor.'" The twenty-flight likelihood calculation in the text is the lesson's own arithmetic on Feynman's two figures (0.99 to the power 20 is about 0.82), not a figure from the appendix.
14. Anders Hviid, Jørgen Vinsløv Hansen, Morten Frisch and Mads Melbye, "Measles, Mumps, Rubella Vaccination and Autism: A Nationwide Cohort Study", Annals of Internal Medicine 170(8), 2019, 513 to 520. 657,461 children born in Denmark 1999 to 2010; adjusted hazard ratio 0.93 (95% CI 0.85 to 1.02); no increased risk in subgroups or time periods; "strongly supports that MMR vaccination does not increase the risk for autism".
15. Wolf v. American Family Mutual Insurance Co., 2015 WI App 36, 361 Wis. 2d 756, Wisconsin Court of Appeals, decided 4 March 2015 (Brown C.J., Neubauer P.J., Reilly J.), para. 15. The elasticity clause; "Of course they are. However, her contention attacks a straw man. American Family does not contend the elasticity clause is unenforceable ..." The dash in the original is rendered as a semicolon in the quotation above.
16. A. J. Wakefield et al., "Ileal-lymphoid-nodular hyperplasia, non-specific colitis, and pervasive developmental disorder in children", Lancet 351(9103), 1998, 637 to 641 (retracted). From the summary: "12 children (mean age 6 years [range 3-10], 11 boys)"; "Onset of behavioural symptoms was associated, by the parents, with measles, mumps, and rubella vaccination in eight of the 12 children"; "generally associated in time with possible environmental triggers".
17. The Editors of the Lancet, "Retraction: Ileal-lymphoid-nodular hyperplasia, non-specific colitis, and pervasive developmental disorder in children", Lancet 375(9713), 2010, 445. "Following the judgment of the UK General Medical Council's Fitness to Practise Panel on Jan 28, 2010, it has become clear that several elements of the 1998 paper by Wakefield et al are incorrect ... the claims in the original paper that children were 'consecutively referred' and that investigations were 'approved' by the local ethics committee have been proven to be false. Therefore we fully retract this paper from the published record."
18. W. S. Robinson, "Ecological Correlations and the Behavior of Individuals", American Sociological Review 15(3), 1950, 351 to 357; reprinted in International Journal of Epidemiology 38(2), 2009, 337 to 341, re-read at review time from the reprint PDF. 1930 census data; "we know what the sign ought to be" is Robinson's own set-up for the nativity case. Foreign birth and illiteracy: individual correlation 0.118 (positive), ecological correlation minus 0.619 across the nine census divisions and minus 0.526 across the 48 states. The reprint typesets the minus signs so faintly that naive text extraction drops them, and Robinson's contrast with the colour case ("the two correlations at least have the same sign") plus the companion commentary settle them: Subramanian, Jones, Kaddour and Krieger, "Revisiting Robinson: The perils of individualistic and ecologic fallacy", IJE 38(2), 2009, report the nativity correlation as negative, r = -0.53, at state level against 0.12 individually, and give the residential explanation (the foreign-born concentrated where educational facilities were relatively good). Colour and illiteracy: individual 0.203, ecological 0.946 (divisions) and 0.773 (states), both positive.
19. Advertising Standards Authority, ruling on Plusnet plc, 9 March 2016 (ref. A15-292223), listed on the ASA's guidance on "unlimited" claims and reported with quotations by ISPreview, "ASA Ban PlusNet Advert for Misleading 'Totally Unlimited' Broadband Claim", 9 March 2016. "A 'totally unlimited' claim was stronger, and that consumers would understand it to mean that the service was free from any provider-imposed limitations"; the traffic prioritisation leaving some traffic a minimum of 5% of line capacity; the instruction to use "totally unlimited" only where there were no provider-imposed limitations.
20. Maarten Boudry, Fabio Paglieri and Massimo Pigliucci, "The Fake, the Flimsy, and the Fallacious: Demarcating Arguments in Real Life", Argumentation 29(4), 2015, 431 to 456. The Fallacy Fork as stated in the abstract; "almost every known type of fallacy is a close neighbor to sound inferences or acceptable moves in a debate".
21. Philip C. Abrami et al., "Strategies for Teaching Students to Think Critically: A Meta-Analysis", Review of Educational Research 85(2), 2015, 275 to 314. 341 effect sizes; weighted mean g+ = 0.30; dialogue, authentic problems and mentoring associated with larger effects (from the abstract).
22. Maurice A. Finocchiaro, "Fallacies and the Evaluation of Reasoning", American Philosophical Quarterly 18(1), 1981, 13 to 22; Gerald J. Massey, "The Fallacy behind Fallacies", Midwest Studies in Philosophy 6, 1981, 489 to 500. Cited through source 3.
23. C. L. Hamblin, Fallacies (Methuen, 1970), p. 12. Cited through source 3.
24. Frans H. van Eemeren and Rob Grootendorst, Argumentation, Communication, and Fallacies (Erlbaum, 1992) and A Systematic Theory of Argumentation (Cambridge UP, 2004); Ralph H. Johnson and J. Anthony Blair, Logical Self-Defense (McGraw-Hill Ryerson, 1977). Cited through source 3.