This article is part three of a four part series on bad arguments to avoid
In this article:
- Fallacy of division
- Fallacy of composition
- Hasty generalization
- Apex fallacy
- Motte and Bailey
- Inflation of conflict
- Science was wrong before
- Appeal to the stone
- Slothful induction
- Affirming the consequent
- Denying the antecedent
Fallacy of division (opposite of fallacy of composition)
“What is true of the whole, is not necessarily true of the parts.”
The fallacy of division occurs when it is reasoned that if something is true of the whole, it must be true of all or some of its parts.
Fallacy of division example #1
America is the richest country in the world, therefore “Americans” must be the richest citizens in the world (actually it’s the Swiss)
America is the richest country in the world, therefore Joe Dirt from Silvertown must be rich.
Fallacy of division example #2
Singapore has the highest average IQ in the world, therefore Singaporean shopkeeper Lee Tan must be smarter than British student Alex O’Connor.
Fallacy of division example #3
The Toronto Raptors are the best NBA basketball team, therefore Raptors small forward Ogugua “OG” Anunoby must be the best small forward in the NBA (I think LeBron James might have something to say about that)
Fallacy of composition (opposite of fallacy of division)
“What is true of the parts, is not necessarily true of the whole.”
The fallacy of composition occurs when it is reasoned that if something is true of the parts of the whole, it must be true of the whole.
Fallacy of composition example #1
The Expendables has the greatest action star line up of all time, therefore it must be the best action movie of all time.
Note: Terminator 2 is the best action movie of all time!
Fallacy of composition example #2
We are the World has the greatest ensemble of superstar musicians ever assembled for a song, therefore it must be the best song of all time.
Fallacy of composition example #3
If someone stands up out of their seat at a concert or sporting match, they’ll be able to see better. Therefore, if everyone stands up, everyone will be able to see better.
Hasty generalizations occur when one is too quick to draw a conclusion or make a large-scale generalization about all or most members of a group, based on only one or a few instances, or a small sample size, which maybe atypical or unrepresentative of the larger group as a whole.
Hasty generalization example #1
The last three people I’ve spoken to in this city were rude. Everyone in this city is rude.
It’s unwise to draw conclusions or make generalizations about “everyone” in an entire group or city based on only one or just a few interactions, or too small a sample size, which maybe atypical or unrepresentative of the larger group or population as a whole.
Just because a few people in the city are rude, that doesn’t mean that “everyone” or “most people” in the city are rude.
Hasty generalization example #2
The last three women I’ve spoken to in this club were stuck up bitches. All women are stuck up bitches.
You may have had a few bad interactions with men/women but that doesn’t mean that “all” men/women are bad.
Hasty generalization example #3
The guy behind the counter was rude to me, he must be a dick.
You may have had a bad interaction with the guy, but he may just be having a bad day. It’s unwise to draw conclusions or make generalizations about who someone is, or how they “always” are, based on only one interaction with them.
- A small sample size doesn’t necessarily mean that it’s atypical of the larger group
- A large sample size doesn’t guarantee that it is typical of the larger group
Sample sizes can be small without being atypical
The last three people that ate the soup got food poisoning and died. This suggests a causal connection between the soup and death.
Sample sizes being large does not guarantee that it is typical
If a large sample isn’t random, it may not be typical of the larger group.
Ten thousand voters from New York were surveyed over the phone and 85% said they wouldn’t vote for Donald Trump in the 2020 U.S. Presidential election. Clearly Joe Biden will be elected U.S. President in 2020.
However, New Yorkers tend to overwhelmingly vote Democrat, so this is not necessarily an indication of how the rest of America will vote. The survey needs to include other states and be more random.
A concise introduction to Logic – Patrick Hurley
Introduction to Logic – Irving Copi & Carl Cohen
The apex fallacy is a variation of the fallacy of composition, and is also a selective attention fallacy, where a group is evaluated as a whole, based on the performance of its top performing members.
The apex fallacy makes the mistake of making a judgement about an entire group, by only looking at the people at the top, whilst ignoring the average of the group, and those at the bottom.
Apex fallacy example #1
“There are more male than female billionaires, CEO’s, executives, politicians, doctors, attorneys etc. therefore men enjoy a more privileged existence in society than women.”
Not so fast. Yes, men enjoy more positions of power at the top, but they also occupy more positions at the bottom. The majority of billionaires and CEO’s are men, but so are the majority of bankrupt, unemployed, homeless and incarcerated men too.
Apex fallacy example #2
“The best long distance runners come from Africa, therefore, all Africans are good long distance runners.”
Not necessarily. You can’t judge an entire group by only focussing on the top performers.
Motte and Bailey
Motte and Bailey is an intellectually dishonest style of argumentation that works like this:
Motte and Bailey argument structure
- Person 1: Advocates for a controversial position that is difficult to defend or justify (Bailey)
- Person 2: Attacks the argument/debunks the claim, provides counterarguments
- Person 1: Claims they’re not advocating for the controversial position (when they really are) accuses the other person of being uncharitable, strawmanning, avoiding the “real issues” etc. as they retreat back into arguing for an easily defended uncontroversial position (Motte) even though that wasn’t the point being contested
- Person 2: Backs off, or tries unsuccessfully to argue the easily defended uncontroversial Motte position
- Person 1: Once the argument is over, they return to advocating for the controversial Bailey position
Motte and Bailey
Bailey = Weaker, less defensible, controversial position that is being advocated
Motte = Stronger, easily defended, uncontroversial position that the arguer retreats to when the Bailey is attacked
This may sound complicated, so let’s look at some examples:
Motte and Bailey example #1
Feminist groups calling all men rapists, demanding people support affirmative action, affirmative consent laws etc. and then when protested, fall back on (even though that wasn’t the point being contested):
“Women deserve equality”
“Feminism is all about equality”
“You do believe in equality don’t you?”
Motte and Bailey example #2
A Christian church might claim that in order to be a “true” Christian one must:
- Pray to God to forgive their sins
- Accept Jesus as their savior
- Get baptised at their church
- Read the Bible every day (preferably the King James Bible)
- Go to Church every week (in particular their church)
- Speak in tongues
- Tithe 10%
…but then when pressed by critics claim that all anyone needs to do to become a “true” Christian is:
- Believe Jesus died for their sins
- Accept Jesus into their heart
Motte and Bailey example #3
An alternative medicine advocate might claim that their quack medicine can cure a wide range of diseases including cancer, but then when pressed or countered by scientific evidence, claim that it’s just a placebo that works if people believe in it.
How to deal with Motte and Bailey
If it seems like someone is trying to Motte and Bailey you (advance a controversial position and then when challenged fall back on an easily defended uncontroversial position) ask them to state clearly what their position is.
If they claim they’ve only advocating for the Motte (uncontroversial position) try to provide evidence of when they’ve clearly advocated for the Bailey (controversial position) in the past.
Motte and Bailey was originally formulated by British Philosopher Nicholas Shackel. You can read the original paper here
Inflation of conflict
Inflation of conflict is a fallacy that occurs when it is argued that if experts in a field of knowledge disagree on a particular issue, the experts must know nothing, and the legitimacy of their entire field is put to question.
This is of course blowing things way out of proportion, just because the experts disagree in a particular area, that doesn’t mean the experts know nothing, or that we should question the legitimacy of their entire field.
Inflation of conflict is a form of black and white thinking, either we know the exact truth, or we know nothing at all.
Questions to ask yourself before dismissing the findings of experts due to disagreement:
- How much disagreement between experts really exists? Is it being blown out of proportion?
- Are those that disagree contrarians? Outliers? How credible are they?
- Is the disagreement in some niche area? Is it relevant to what’s being dismissed?
Note: Just because experts aren’t in 100% unanimous agreement about something, that doesn’t mean there isn’t a consensus, or that there is significant debate on the topic.
Inflation of conflict example
A creationist might point to disagreement among scientists as to whether the Universe is 13 billion or 14 billion years old as evidence that they don’t know what they’re talking about.
“Even the experts can’t agree!”
That doesn’t mean that the biblical date of 6, 000 years is just as accurate.
Science was wrong before
Sometimes people will try to dismiss scientific consensus (especially if it goes against a sacred cow) by using one of the following rebuttals:
“Science doesn’t know everything”
“Science has been wrong before”
“Scientists don’t even agree on X”
Yes, it’s true that scientists have been wrong before, and they’ll continue to be wrong in the future.
However, the fact that science is constantly revising and updating it’s knowledge as new evidence comes to hand is a feature of science, not a bug.
“Yes, science has been wrong, but the scientific method is self-correcting. And it is always scientists who have unearthed new evidence who do the correcting, never people who ignore the scientific method.” – Skeptico
Just because “science has been wrong before”, that’s not an excuse a good reason to dismiss scientific consensus or evidence as if it were “just a theory”.
“Creationists make it sound as though a ‘theory’ is something you dreamt up after being drunk all night.” – Isaac Asimov
Often the people that give the “science doesn’t know everything” or “science was wrong before” or “evolution is just a theory” type arguments are anti-intellectual and anti-science, and have a bad habit of equivocating the common usage of the term “theory” (meaning “idea” or “guess”) with the scientific meaning of theory (“a detailed explanation that can be repeatedly tested and verified in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results”).
Appeal to the stone
Appeal to the stone is the opposite of argument by assertion.
- Argument by assertion asserts that something is true or false without evidence
- Appeal to the stone dismisses an argument or statement as absurd, without giving reasons or evidence for its absurdity
Appeal to the stone example #1
Person A: “Did you know that the NSA is spying on the whole world?”
Person B: “What a load of shit”
Person A: “It’s true! I’ve got evidence!”
Person B: “Sure you do”
Person A: “Wanna see it?”
Person B: “No. I haven’t got time to listen to this crap.”
Appeal to the stone example #2
Person A: “I think Donald Trump will become the next US President”
Person B: “Are you serious? What a stupid thing to say.”
Person A: “I know he’s not a politician, and never been in office, but he’s just announced his intention to run, and he’s talked about on doing it for years, and I think his money and celebrity status from the Apprentice will help him get votes.”
Person B: “Yeah right. You clearly don’t know what the hell you’re talking about. You sound like an idiot. Bye.”
Appeal to the stone example #3
Person A: “I think the Jussie Smollett hate crime was staged.”
Person B: “What? You think he made it up? What about the noose around his neck? What about the guys that said “This is MAGA country!” WTF are you talking about?”
Person A: “The Chicago Police think he staged the attack and hired people to beat him up to boost his career, because he was dissatisfied with his salary”.
Person B: “That’s just fucking retarded. Fucking conspiracy theorists…” (Walks off)
As a general rule, if someone dismisses an argument as:
Without giving reasons or evidence for the absurdity, they’re committing the appeal to the stone fallacy.
If someone does this to you in a conversation or an argument, you can try to ask them why they disagree, what’s wrong with your argument etc. however they might just double down:
“You know why”
“It just is”
“You seriously expect me to respond to that?”
However, if you’re in a debate, you can let the audience know that your opponent calling your argument dumb, stupid, ridiculous etc. doesn’t make it so. It’s just a cop out to avoid having to address it.
See also: Pooh-pooh
Pooh-pooh is when you dismiss an argument or statement as being unworthy of serious consideration.
Slothful induction (aka “appeal to coincidence”)
“It is foolish to be convinced without evidence, but it is equally foolish to refuse to be convinced by real evidence.” – Upton Sinclair
Slothful induction isn’t a bad argument, but rather a stubborn refusal to acknowledge the facts, to follow the evidence where it leads, to change your mind about something despite overwhelming evidence for it. It’s the opposite of a hasty generalization where you jump to conclusions off insufficient evidence.
It’s good to be skeptical, to have high standards for evidence, but there is no need to dig your heels in and stubbornly refuse to change your mind when that evidence is presented.
Slothful inductions usually occur when someone is emotionally attached to a belief or outcome, or they have a vested interest in their position, or they simply don’t care about the truth.
Slothful induction example #1
“I know he lies a lot, but he’s not a liar, he just doesn’t always tell the truth.”
Slothful induction example #2
“I know she’s cheated on all her previous boyfriends, slept around a bit, done some porn etc. but she’s not a slut, she’s just looking for love.”
Slothful induction example #3
“Even though 97% of climate scientists agree that the earth is warming up, I still need to see more evidence.”
How quickly will you acknowledge the facts?
How quickly will you follow the evidence where it leads, and change your mind when that evidence is presented?
Don’t be that guy that refuses to change his mind no matter what. When you’re presented with overwhelming evidence for or against something, follow the evidence where it leads without dragging your feet or being difficult about it.
“There are two ways to be fooled. One is to believe what isn’t true; the other is to refuse to believe what is true.” – Søren Kierkegaard
Affirming the consequent
The last two fallacies in this article are related to each other:
- Affirming the consequent
- Denying the antecedent
First, a quick explanation of what the “antecedent” and “consequent” are:
Antecedent vs Consequent
- Antecedent: What comes after the “if” in an “if/then” statement. The antecedent comes before the consequent. Sounds like “Ancestor”.
- Consequent: What comes after the “then” in an “if/then” statement. The consequent comes after the antecedent. Sounds like “Consequence”.
Don’t worry, this will become clearer with examples.
Affirming the consequent (aka inverse modus ponens)
Affirming the consequent logical form:
P1: If P, then Q
C: Therefore, P
Affirming the consequent is fallacious because the conclusion doesn’t necessarily follow from the premises. P leads to Q, but the argument doesn’t state that it exclusively or necessarily leads to Q, or that Q is always preceded by P.
Affirming the consequent is easiest to explain/understand via examples:
Affirming the consequent example #1
P1: All NBA players play basketball
P2: My friend plays basketball
C: My friend is an NBA player
Just because all NBA players play basketball, that doesn’t mean that anyone that plays basketball is in the NBA.
Affirming the consequent example #2
P1: If I’m in Hollywood, I’m in America
P2: I’m in America
C: Therefore, I’m in Hollywood
If I’m in Hollywood, then I’m in America. But it doesn’t necessarily follow that because I’m in America, then I must be in Hollywood.
Affirming the consequent example #3
P1: If you drink poison, you will die
P2: An old man died
C: He must have drunk poison
Not necessarily. The conclusion doesn’t follow from the premises.
Denying the antecedent (aka inverse modus tollens)
Denying the antecedent is a fallacy that occurs in a standard if/then premise, when it is invalidly concluded that the denial of the antecedent (what comes after the “if”), necessarily leads to the denial of the consequent (what comes after the “then”).
Denying the antecedent logical form:
P1: If P, then Q
P2: Not P
C: Therefore, not Q
Denying the antecedent is fallacious because the conclusion doesn’t necessarily follow from the premises. P leads to Q, but the argument doesn’t state that it exclusively or necessarily leads to Q, or that P is the only way to Q. Therefore, not P, doesn’t necessarily mean not Q.
If the argument was:
P1: P, if and only if P, then Q
P2: Not Q
C: Therefore, not P
Then it would be valid due to the “if and only if”. However, the argument doesn’t specify this exclusivity. P might not be the only condition of Q.
Denying the antecedent is easiest to explain/understand via examples:
Denying the antecedent example #1
P1: If you’re a fighter pilot, you have a job
P2: You’re not a fighter pilot
C: Therefore, you don’t have a job
Denying the antecedent example #2
P1: If you’re an NBA player, you’re a professional athlete
P2: Roger Federer is not an NBA player
C: Therefore, Roger Federer is not a professional athlete
Denying the antecedent example #3
P1: If you you’re in Toronto, you’re in Canada
P2: You’re not in Toronto
C: Therefore, you’re not in Canada
This concludes part three of a four part series on bad arguments to avoid.