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Logical Reasoning: Flaws in the Reasoning

Every named way an argument goes wrong, from circular reasoning to percentage-versus-number, each drawn as the exact spot where the structure fails.

19 topics · 70 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Flaw in the Reasoning as an Abstract Description

  1. How it worksHow do you translate 'the chef is overweight, so his food is bad' into the abstract wording a flaw answer uses?
  2. How it worksWalk me through prephrasing a flaw in plain words before reading a single answer choice.
  3. Common mistakeWhy isn't an answer that merely restates one of the premises ever a correct flaw description?
  4. Going furtherWhat changes when a stem says 'vulnerable to criticism on the grounds that' instead of 'flawed because'?
Your turnmedium1 of 3
Gallery owner: Among the 137 painters whose work came to auction in this city last season, those who trained at the Brennan Academy sold for 41 percent more on average than those who trained elsewhere. Delacroix-Hu trained at Brennan; Okonjo did not. So a Delacroix-Hu canvas will fetch more than an Okonjo canvas. The reasoning above is most vulnerable to criticism on the grounds that it

Ad Hominem and Source Attack

  1. How it worksHow does an argument slide from 'the speaker is biased' to 'the speaker is wrong' without earning it?
  2. Worked exampleShow me the flaw in 'The senator who proposed the tax cheats at golf, so the tax is a bad idea.'
  3. Common mistakeWhy isn't pointing out who funded a scientist's study always a logical fallacy?
  4. Going furtherWhat changes when the argument is about whether to trust a person's testimony rather than whether a claim is true?
Your turneasy1 of 3
Council member: Dr. Halloran's report recommends that the town spend 30 million dollars replacing its water mains. But Dr. Halloran was retained by the engineering firm that would bid on the work, and she stands to be paid for 5 further years of consulting if the project goes ahead. Her recommendation should be rejected. The reasoning above is flawed because it

Circular Reasoning

  1. How it worksHow does 'Lying is wrong because it is immoral' close into a loop with no support from outside?
  2. Worked exampleShow me the circle in 'It is the best seller because more copies of it sold than of any other book.'
  3. Common mistakeWhy isn't restating a premise in fresh words the same thing as reasoning in a circle?
Your turnmedium1 of 3
Critic: The 648-year-old manuscript in the abbey library is authentic. The abbey's catalogue, compiled by monks who handled it daily, lists it as authentic, and that catalogue is reliable about the 43 manuscripts it covers, as is shown by its correct listing of this manuscript as authentic. The reasoning above is flawed because it

Equivocation

  1. How it worksHow does 'natural' shift from 'occurring in nature' to 'good for you' between a premise and a conclusion?
  2. Worked exampleShow me the word that shifts meaning in 'Only man is rational, and no woman is a man, so no woman is rational.'
  3. Going furtherWhat happens when the shifting term is a quantity word like 'few' rather than a noun?
  4. Common mistakeWhy isn't every repeated word inside an argument a candidate for equivocation?
Your turnmedium1 of 3
Advertisement: Every ingredient in our 11 herbal blends occurs in nature and none is synthesized in a laboratory. What occurs in nature is natural, and natural products are the ones a shopper concerned with health should choose. So anyone comparing our blends with the 18 synthetic teas on the shelf should choose ours. The argument is flawed because it

Straw Man

  1. How it worksHow does a responder swap 'we should trim the budget' for 'we should abolish the program' and attack that instead?
  2. Worked exampleShow me the distortion in 'You want a speed limit, so you think nobody should ever drive anywhere.'
  3. Common mistakeWhy isn't every misreading of an opponent's view a straw man?
  4. Going furtherWhat changes when the distortion makes an opponent's position stronger rather than weaker?
Your turneasy1 of 3
Alvarez: The district should cut the athletics budget by 31 percent and move the savings to the library. Brody: Alvarez would have our children grow up without physical education. Studies of 65 districts show that students who get no exercise at school do worse on every measure of health. Alvarez's proposal should be rejected. Brody's reply is most vulnerable to criticism on the grounds that it

False Dilemma

  1. How it worksHow do you find the doors an arguer painted out of the hallway when they offered only two?
  2. Worked exampleShow me the missing options in 'Since we cannot ban cars entirely, we should do nothing about emissions.'
  3. Common mistakeWhy isn't every either-or statement a false dilemma?
Your turneasy1 of 3
Transit official: We cannot close the 19 downtown streets to private cars; deliveries alone would make that unworkable. So there is nothing the city can do about the 29 percent of its emissions that come from downtown traffic, and the proposed congestion charge should be dropped. The reasoning above is flawed because it

Appeal to Authority

  1. How it worksHow does citing an expert from outside their own field turn evidence into pure decoration?
  2. Worked exampleShow me the flaw in 'A Nobel-winning physicist endorses this diet, so the diet must work.'
  3. Going furtherWhat changes when the authority cited is a large majority of experts rather than one person?
  4. Common mistakeWhy isn't relying on a qualified expert speaking inside their own field a fallacy?
Your turneasy1 of 3
Host: Dr. Ivers won the Kessler Prize, awarded for 75 years now, for her work on planetary atmospheres, and she has said in 9 separate interviews that the new sleep supplement works. Anyone who still doubts the supplement is setting aside the judgment of one of our finest scientists. The host's reasoning is flawed because it

Appeal to Popularity

  1. How it worksHow does 'most physicians once bled their patients' snap the link between popularity and correctness?
  2. Worked exampleShow me the flaw in 'Nine out of ten shoppers pick this brand, so it is the highest quality brand.'
  3. Common mistakeWhy isn't popularity irrelevant when the conclusion is about what will sell rather than what is true?
Your turneasy1 of 3
Advertisement: Of the 151 thousand shoppers who bought a paint sprayer last year, 71 percent chose the Verity model, and no rival came close. The Verity is therefore the best-built sprayer a shopper can buy. The advertisement's reasoning is flawed because it

Appeal to Ignorance

  1. How it worksHow does an argument convert the absence of evidence into evidence of absence without permission?
  2. Worked exampleShow me the flaw in 'No study has found harm from the additive, so the additive is safe.'
  3. Common mistakeWhy isn't absence of evidence always worthless as evidence?
  4. Going furtherWhat changes when a thorough search really was carried out and still turned up nothing?
Your turneasy1 of 3
Manufacturer: In the 19 years since our additive was approved, not one of the 28 published studies of it has reported harm to human health. The additive is therefore harmless. The manufacturer's reasoning is flawed because it

Composition and Division

  1. How it worksHow does part-to-whole reasoning break when a property refuses to add up across the parts?
  2. Worked exampleShow me the flaw in 'Every player on the team is a star, so the team is unbeatable.'
  3. Worked exampleShow me the whole-to-part flaw in 'That orchestra is the finest in the country, so its oboist is the finest oboist.'
  4. Common mistakeWhy isn't every part-to-whole inference broken, given that every red brick does make a red wall?
Your turneasy1 of 3
Sports columnist: Each of the 6 players the club signed this winter was the leading scorer on his previous team, and the club's payroll now ranks 5 in the league. The club will therefore field the league's most effective attacking side. The columnist's reasoning is flawed because it

Unrepresentative Sample

  1. How it worksHow does a sample drawn from one corner of a population tilt the conclusion drawn from it?
  2. Worked exampleShow me the flaw in polling gym members to conclude that most adults exercise daily.
  3. Going furtherWhat happens to a conclusion when you can name the direction the sample is skewed in?
  4. Common mistakeWhy isn't an enormous sample automatically a representative one?
Your turneasy1 of 3
Researcher: We interviewed 687 adults as they left the county's public libraries, and 84 percent of them had read a book in the past week. Reading is therefore in far better health among adults in this county than the national figures suggest. The researcher's reasoning is flawed because it

Small Sample

  1. How it worksHow does a tiny sample let ordinary randomness masquerade as a real pattern?
  2. Worked exampleShow me the flaw in 'Three of my five neighbors drive trucks, so most people statewide drive trucks.'
  3. Common mistakeWhy isn't a small sample a problem when the population being studied is itself tiny?
Your turneasy1 of 3
Columnist: I asked the 9 people in my carpool which candidate they support, and 4 of them named the challenger, more than named anyone else. The challenger will therefore win the city's election, in which about 189 thousand ballots will be cast. The columnist's reasoning is flawed because it

Self-Selection and Survey Bias

  1. How it worksHow does a call-in poll collect opinions from exactly the people most likely to hold extreme ones?
  2. Worked exampleShow me the bias in 'Of customers who mailed back the card, 95 percent were satisfied, so most customers are.'
  3. Common mistakeWhy isn't an anonymous survey automatically free of bias?
  4. Going furtherWhat changes when the people refusing to answer differ systematically from the people who answer?
Your turneasy1 of 3
Manager: We enclosed a comment card with each of the 69 thousand orders we shipped last quarter. Of the cards mailed back, 94 percent reported satisfaction with the product. Most of our customers are therefore satisfied with it. The manager's reasoning is flawed because it

Percentage Versus Number

  1. How it worksHow does a changing denominator let a percentage and a raw count move in opposite directions?
  2. Worked exampleShow me how 'accidents fell from 10 percent to 5 percent' can still mean more accidents than before.
  3. Going furtherWhat extra fact do you need before a percentage claim can support a claim about totals?
  4. Common mistakeWhy isn't a larger percentage always a larger number?
Your turneasy1 of 3
Administrator: Deaths in our surgical ward accounted for 20 percent of all deaths in the hospital last year, up from 10 percent the year before. Surgery at this hospital has therefore become more dangerous. The administrator's reasoning is flawed because it

Confusing What Is Possible With What Is Certain

  1. How it worksHow do you track a claim's strength word by word as it climbs from 'may' to 'probably' to 'must'?
  2. Worked exampleShow me the overreach in 'Smoking can cause cancer, so this patient's cancer was caused by smoking.'
  3. Common mistakeWhy isn't a conclusion safe just because the premises make it fairly likely?
Your turneasy1 of 3
Physician: Exposure to the solvent can cause a rare liver condition. Petrov was exposed to the solvent throughout the 20 years he worked at the plant, where 63 percent of workers were exposed, and Petrov now has the condition. The solvent therefore caused Petrov's illness. The physician's reasoning is flawed because it

Post Hoc and Correlation Mistaken for Cause

  1. How it worksHow do reverse causation, a hidden third cause, and pure coincidence each explain the same correlation?
  2. Worked exampleShow me the three rival explanations for 'ice cream sales and drownings rise together, so ice cream causes drowning.'
  3. Common mistakeWhy isn't a correlation useless as evidence about what causes what?
  4. Going furtherWhat kind of new fact turns a bare correlation into a defensible causal claim?
Your turneasy1 of 3
Mayor: We installed 151 new streetlights in the eastern district in March. In the 14 months since, reported burglaries there have fallen by 38 percent. The lights are what brought the burglaries down. The mayor's reasoning is flawed because it

Overgeneralization from One Case

  1. How it worksHow does an argument stretch a single case into a rule that covers every case?
  2. Worked exampleShow me the flaw in 'My grandfather smoked until he was 95, so smoking does not shorten life.'
  3. Common mistakeWhy isn't one counterexample equally weak when it is used to knock down a universal claim?
Your turneasy1 of 3
Letter writer: My aunt worked in the mill for 40 years and lived to 98. The studies claiming that mill work shortens life by about 9 years are therefore mistaken. The letter writer's reasoning is flawed because it

Internal Contradiction

  1. How it worksHow do you spot a stimulus whose own premise rules out the conclusion it is offered for?
  2. Worked exampleShow me the self-contradiction in 'Nothing can be known for certain, and I know that for certain.'
  3. Going furtherWhat changes when the contradiction sits between two speakers rather than inside one argument?
Your turnmedium1 of 3
Critic: No statement about a work of art can be established as true or false, since taste settles every such question. That is exactly why the claim that the Corbeau frescoes are the finest of the 19 surviving cycles of that century is established beyond dispute. The critic's reasoning is flawed because it

Confusing a Necessary Condition With a Sufficient One

  1. How it worksHow does an arrow drawn from A to B flatly refuse to be traversed backwards?
  2. Worked exampleWhy does 'every student who passed studied, so anyone who studied passed' reverse a conditional instead of contraposing it?
  3. Common mistakeWhy isn't 'only if' the same as 'if' once you draw the arrow?
  4. Going furtherWhat happens to an arrow when you negate both ends and reverse its direction?
  5. Ties togetherHow does this same confusion reappear dressed up as a wrong assumption answer?
Your turneasy1 of 3
Coach: No swimmer has ever qualified for the national meet without training at least 25 hours a week. Delgado trains 25 hours a week and has for 6 seasons. Delgado will therefore qualify for the national meet this year. The coach's reasoning is flawed because it

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