Fallacies

Try the writephilosophy Fallacies quiz to see how well you understand argumentative fallacies.

A fallacy is a mistake or error in reasoning. Fallacies can be accidental errors, or can be deliberately crafted to be misleading. Many different types of fallacy have been described across many fields.
Understanding these is useful for philosophers in two ways:

  • To identify fallacious reasoning in philosophical arguments and in potential objections and criticisms of our own views.
  • To avoid committing fallacies in our own work.

 

Affirming the Consequent
Affirming the consequent is a simple logical error of the form:

P -> Q

Q

Therefore, P.

It can confuse people because of the similar-looking valid argument form modus ponens:

P -> Q

P

Therefore, Q.

But affirming the consequent is fallacious, as you can see in the example:

If you are dead, then you are not the current president of the USA.

You are not the current president of the USA.

Therefore, you are dead.

This argument is obviously invalid, as premises 1 and 2 are true, but the conclusion is false.

Affirming the consequent is very common, however. One of the most common places for these arguments is in science:

If Einstein’s theory of relativity is true, then we would observe light bend around large masses like the sun.

We observe light bend around large masses like the sun.

Therefore, Einstein’s theory is true.

Base Rate Fallacy
The base rate fallacy or ‘prosecutor’s fallacy’ is an error made in probabilistic reasoning. It occurs when one neglects the ‘base rate’ in a probabilistic calculation. The base rate is the rate at which the outcome of interest can be expected to occur. For example:

Moira’s DNA matches the DNA found at the crime scene. The probability of matching DNA is 1 in a million. What is the probability that Moira was not at the crime scene?

Many people would answer: “1 in a million”. They reason that in order for matching DNA to be at the crime scene not left by Moira, a 1 in a million chance must have occurred, so the probability is 1 in a million.

Not so. There are many more than 1 million people out there. Let’s suppose the crime scene is in London. Restricting ourselves only to Londoners (population: 8 million), we would expect to find around 8 other DNA matches for the DNA found at the crime scene. So even if we can assume only a Londoner could have been at the scene, the probability that Moira was there based on the DNA evidence alone is 1 in 8. So the probability that it was left by someone else is 7 in 8, not 1 in a million!
Another example (originally due to Kahneman):

There are two taxi companies in the city—Yellow Cabs and Blue Cabs. The Yellow Cabs are very careful. Each night, each Yellow Cab has a probability of 1 in 100 of being in an accident. The Blue Cabs are much more gung-ho. Each night, each Blue Cab has a probability of 1 in 10 of being in an accident.

Jennifer witnesses an accident between a cab and a bicycle. The police ask her what kind of cab it was. Unfortunately, she is colour blind and doesn’t know. What is the probability that it was a Blue Cab?

Many people would answer “10 times as likely as a Yellow Cab”. But this is not correct. From this information alone, we can’t tell.

The base rate is missing. The base rate here is the number of Yellow and Blue Cabs on the streets each night. Suppose there are 1,000 Yellow Cabs, but only 10 Blue Cabs. Then on an average 1 in 10 of the Blue Cabs gets in an accident (i.e. 1 cab), while 1 in 100 of the Yellow Cabs does (i.e. 10 cabs). So it’s 10 times as likely that the cab Jennifer saw was Yellow.

Begging the Question
‘Begging the question’ is a philosophical term which has been misused outside of philosophy. In general parlance, the phrase usually means ‘leaving the question open’ or ‘suggesting the question’. In philosophy, it has a specific technical meaning. In philosophical writing, you should make sure to only use ‘begging the question’ in its technical sense.


Begging the Question
means assuming the conclusion of an argument in the premises (or sometimes in the rule used to infer the conclusion). It is related to circular reasoning. Often, the conclusion will be subtly included in the premise by rephrasing it.

Some scholars have suggested that Descartes’ famous “Cogito Ergo Sum” argument begs the question. The argument has the form:

I think, therefore, I exist

Russell argued that Descartes’ use of the first-person statement “I think” already assumes the existence of ‘I’. He claimed that Descartes was only entitled to the premise “There are thoughts”, from which ‘I exist’ does not follow.

Composition and Division
The fallacy of composition occurs when we infer that a whole thing has some property because part of the thing has that property. For instance:

Alabama is primarily Republican. Alabama is part of the USA. Therefore, the USA is primarily Republican.

Abu Hamza believes in militant jihadism. Abu Hamza was part of the Islamic community in London. Therefore, the Islamic community in London believes in militant jihadism.

The fallacy of division occurs when we infer that a part of something has a property because the whole thing does:

The British government makes all of the policy decisions which affect the UK. Nick Clegg is in the British government. Therefore, Nick Clegg makes all of the policy decisions which affect the UK.

LSE teaches over 9,000 students. The Philosophy department is part of LSE. So the philosophy department teaches over 9,000 students.

Epistemic Fallacy

 

The epistemic fallacy, also known as “the masked man fallacy” or “the intensional fallacy” is a mistake made when substituting two names of the same thing in an argument. The classic ‘masked man’ case is:

I know who Stephen is.

I don’t know who the masked man is.

Therefore, Stephen is not the masked man.

The fallacy occurs when applying a rule called ‘the indiscernibility of identicals’ (aka. Leibniz’s Law), which states that if two things are identical (e.g. Stephen and the masked man are the same person), then they must have all the same properties. This rule underpins legitimate inferences like:

Stephen has blue eyes.

The masked man does not have blue eyes.

Therefore, Stephen is not the masked man.

In the epistemic fallacy, the property which we are talking about is an epistemic property—for instance ‘knowing who Stephen is’. Epistemic properties relate to knowledge. The indiscernibility of identicals law does not apply to properties relating to knowledge about individuals, or beliefs about individuals. Using this form of argument with an epistemic property results in the epistemic fallacy.

Some more examples:

Adam knows who Jane Austen is. Adam doesn’t know who the author of Pride and Prejudice is. Therefore, Jane Austen is not the author of Pride and Prejudice.

The people of Gotham believe that Bruce Wayne is a fool. They do not believe that Batman is a fool. Therefore, Bruce Wayne is not Batman.

Mary thinks Lewis Carroll wrote Alice in Wonderland. She does not think Charles Dodgson wrote Alice in Wonderland. Therefore, Lewis Carroll is not Charles Dodgson.

Equivocation

Equivocation occurs when a term has more than one possible meaning, and we create confusion by moving between meanings within an argument.
For example, the word “bank” can mean a financial institution, or the side of a river. So we could end up with the argument:

I keep my money in a bank.

Banks are at the side of a river.

Therefore, I keep my money at the side of a river.

This argument appears valid, unless you are aware that the word ‘bank’ refers to different things in premise 1 and 2. We would say that I have ‘equivocated on the word “bank”.’

Equivocation can often be quite subtle. A common but subtle form of equivocation is confusing a thing for a name of that thing. For example:

George Orwell is Eric Blair

George Orwell is a pen-name.

Therefore, Eric Blair is a pen-name.

On the surface, this argument looks sound. But it isn’t. George Orwell is the pen-name of Eric Blair, but Eric Blair isn’t a pen-name. The problem is that while “George Orwell is Eric Blair” is a claim about the man George Orwell (he’s the same man as Eric Blair), “George Orwell is a pen-name” is a claim about the name “George Orwell”.

A good way to avoid this kind of equivocation is to put the name in quotation marks whenever you are referring to the word itself. For instance:

Charles is the heir to the throne

“Charles” is a seven-letter word.

Therefore, the heir to the throne is a seven-letter word.

It’s obvious here that the argument is invalid, as “Charles” and Charles are not the same thing. One is the man, the other a name of that man.

 

It is also possible to set up a straw man by deliberately or mistakenly reading a word with a different meaning to the one intended, or interpreting an ambiguous sentence in a different way than the author intended. For example:

“This morning, I shot an elephant in my pyjamas.”

“I don’t believe you, there’s no way an elephant could fit into your pyjamas.”

(modified from an old joke by Groucho Marx)

Existential Fallacy

 

The existential fallacy is a logical fallacy of inferring from a universal claim (e.g. “All dragons breathe fire”) to an existential claim (e.g. “A firebreathing dragon exists”). This fallacy can be compelling because such inferences often appear reasonable:

All men have the Y chromosome.

Therefore, there is a man with the Y chromosome.

However, the fallacy becomes obvious when we consider universal statements about non-existing things. These universals are trivially true. For example:

All zombies want to eat brains.

Therefore, there are zombies.

False Dichotomy

 

A false dichotomy or ‘false dilemma’ fallacy occurs when two options are presented as the only ones available, when there are in fact other possible choices. This fallacy often affects dilemma arguments, in which a critic of a position argues that the position commits us to one of two options, and then goes on to argue that both are unpalatable. If there are in fact other available options for a proponent of the position, then the critic has created a false dilemma. For example:

Playing music at 3am will annoy your neighbours. Either you have to stop playing music at 3am or annoy your neighbours.

This is a false dilemma—there are other options than stopping playing music at 3am at all or causing annoyance: you could, for instance, move to a place with no neighbours, or wear headphones to listen to music.

Either we must reduce the sentences for criminals, or risk our prisons becoming overcrowded. We don’t want to risk our prisons becoming overcrowded. So we must reduce the sentences.

This too is a false dilemma—there are many other options overlooked, including building new prisons and releasing prisoners early.

Gambler’s Fallacy

 

The gambler’s fallacy is a mistake made in probabilistic reasoning. It gets its name from a fallacious belief amongst gamblers that if you have been on a losing streak, that means it is more likely that you will soon win. The reverse (being on a winning streak meaning it is likely that you will lose) is also a fallacy (sometimes called the ‘casino owner’s fallacy’ or ‘reverse gamblers fallacy’). For example:

Suppose the chance of winning on a slot machine is 10%. You play 15 times and never win. Because you know there’s a 1 in 10 chance and you haven’t yet won, you reason that you must be really likely to win next time (or at least in the next few tries). But, of course, the probability of winning remains at 1 in 10.

Suppose I flip a fair coin and it lands heads 5 times in a row. You say that it stands to reason that it must land tails next because a run of 6 heads in a row is so unlikely. But, of course, after a run of 5 heads, a further head is just as likely as tails.

Middle Ground Fallacy

 

The middle ground fallacy or ‘compromise fallacy’ or ‘argument to moderation’ occurs when one argues that a position must be correct because it is a compromise between two more extreme views which are commonly defended. Such an argument might be bolstered by claims that the compromise view has features which would appeal to both sides in the debate. However, the argument is fallacious—the existence of an opposing position is not a good reason to suspect that moderating a view will produce something better or closer to the truth.

Naturalistic Fallacy

 

The naturalistic fallacy—sometimes called the ‘is/ought fallacy’, though the two have been used in different ways by some philosophers—is the error of inferring from the fact that something is the case to the conclusion that it should be the case. This is a common occurrence in ethical debates:

Famine causes widespread death and disease. Therefore, famine should be prevented.

In order to make such an argument valid, we need to add a premise which links the is statement to the ought statement, i.e.

Famine causes widespread death and disease. We ought to prevent anything which causes widespread death and disease. Therefore, famine should be prevented.

Without an ought statement in the premises, an ought statement conclusion cannot validly follow. Often it can be fruitful to detect naturalistic fallacies and expose the argument clearly, explicitly writing out the hidden ‘ought’ premise, as these often turn out to be controversial, and the weakest link in the argument. For example:

Homosexuality is unnatural. Therefore, homosexuality is morally wrong.

If we expose the hidden premise, the argument reads:

Homosexuality is unnatural. Anything which is unnatural is morally wrong. Therefore, homosexuality is morally wrong.

We could try to refute this argument by arguing that homosexuality isn’t unnatural—by pointing to instances of homosexuality in the animal kingdom, for instance. But it is simpler to refute the absurd hidden premise that unnatural things are immoral by offering a counterexample—for instance:

Humans flying is unnatural. Aeroplanes allow humans to fly. Anything which is unnatural is morally wrong. Therefore, aeroplanes are morally wrong.

Moralistic Fallacy

 

The moralistic fallacy resembles the naturalistic fallacy. It consists of arguing that because something should be the case, it is the case. For instance:

War and violence should be abhorrent to all. Therefore, humans abhor war and violence.

Homophobia should be prevented. Therefore, society does not tolerate homophobic attitudes.

Post Hoc Ergo Propter Hoc

 

Roughly translating as “After, therefore because of”, the post hoc ergo propter hoc fallacy involves inferring that because B followed A, A caused B. We make inferences like this all the time. For instance:

I pressed the light switch, then the light came on. Therefore, me pressing the light switch caused the light to come on.

However, these inferences are strictly invalid. Sometimes events which seem to follow causally are just co-incidental. For instance:

I drank a shot of tequila, then my cold went away. Therefore, a shot of tequila cured my cold.

It’s unlikely that the tequila actually cured my cold. More likely, the cold went away naturally, and just happened to be shortly after the tequila. When people mistakenly infer causation from correlation, or do so too hastily, without proper justification, we say that they have committed a post hoc ergo propter hoc fallacy.

For instance:

I did a rain dance, and then it rained. So my rain dance made it rain.

I went to the chiropractor and now my back feels better. So the chiropractor cured my back-pain.

Red Herring Fallacies

 

A ‘red herring’ is an argument about something not actually related to the truth/falsity of the conclusion. There are many types of red herring. Amongst the most common are:

Ad Hominem

 

Translating as “against the man”, an ad hominem argument claims that a person’s beliefs are false or arguments are unsound because they possess personal deficiencies. For instance:

Jeff failed his philosophy exam, therefore his claim that Plato wrote the Republic is false.

Tobacco companies say that e-cigarettes can be harmful. But tobacco companies are evil. So, e-cigarettes aren’t really harmful.

Note that not all arguments that relate to personal flaws are fallacious, so aren’t all cases of ad hominem. For example, if the argument is about a personal flaw, e.g.

All members of the BNP are racist. Linda is a member of the BNP. Therefore, Linda is racist.

Association Fallacy

 

Similar to an ad hominem, a guilt by association argument attempts to discredit a position by arguing that it has been held by disreputable or deficient people. For example:

Hitler was a vegetarian. Therefore, vegetarianism is immoral.

The BNP think that the UK should have stricter immigration controls. The BNP are racist. Therefore, believing in stricter immigration controls is racist.

Association fallacies can also be used to imbue a view with undue positive qualities. An example is the so-called “Galileo gambit”, also sometimes used as a “Columbus gambit”:

People don’t believe me when I say that the government are lizard people. People didn’t believe Galileo when he said the earth orbits the sun, but he turned out to be right. Therefore, I am right too.

Everyone laughs at me when I say the government can read minds. But everyone laughed at Columbus when he said the earth was round, and he was right. So I am right.

Association fallacies can also be committed more broadly—for example:

Cats are mammals. Cats are also predators. Therefore, predators are mammals.

Tu Quoque

 

Translating as ‘You also’ or ‘You too’, this form of ad hominem argument claims that a belief is false or an argument is unsound because of the hypocrisy of the person or organization defending it. For example:

Charles argues that vegetarianism is morally necessary. But I saw Charles eating a steak. So vegetarianism can’t be morally necessary.

James says the government do more to help the homeless, but he doesn’t spend his free time volunteering at a soup kitchen. So clearly it’s not important.

Appeal to Authority

 

Arguments from authority use the prestige and reputation of an individual to claim that some belief they hold must be true or argument they make must be sound. Scientific authorities are particularly used and abused in this respect. E.g.

Richard Dawkins argues that science and religion are incompatible, so they must be.

My philosophy lecturer says that the pessimistic induction is a sound argument against realism. Therefore, realism is false.

Argument from Consequences

 

An argument from consequences claims that some position will entail good (or bad) consequences, and infers that the position must be true (or false) so that those consequences can happen. When performed with good consequences, this form of argument is sometimes called wishful thinking.

If this new drug works, then we could cure cancer within a decade. Therefore, this new drug will work.

If God doesn’t exist then death is the end. So God must exist.

Argument from Ignorance

 

Arguments from ignorance play upon lack of knowledge. They often use gaps in our current understanding, either by postulating something to fill that gap, or by claiming that a view must be false because we don’t have all the details. For instance:

The theory of evolution currently cannot explain exactly how life came to be on earth. Therefore, the theory of evolution is false.

I cannot explain the strange noises in my house at night. Therefore, my house is haunted.

Fallacy Fallacy

 

The fallacy fallacy or ‘argument from fallacy’ is a mistake we see all too often in philosophy essays, in which the author argues that a position is false because an argument for it is fallacious or unsound. Just because an argument for a view fails, doesn’t entail that the view itself is wrong.
The fallacy fallacy may be characterised as a species of the ‘argument from ignorance’, where we are ignorant of arguments which would establish the position in question.To avoid the fallacy fallacy, ensure that you choose the thesis of your paper carefully. If you intend to show that Smith’s argument for X is unsound, then make sure your thesis is: “Smith fails to show that X”, not “X is false”.

The arguments for the existence of God all fail. Therefore, God doesn’t exist.

The ‘No Miracles Argument’ for scientific realism is unsound. Therefore, scientific realism is false.

Slippery Slope

 

Slippery slope arguments suggest that if A happens, it will (or may) lead to B, then C, etc. Sometimes the slippery slope ends in a particular bad consequence. Sometimes the potential consequences are left to the reader’s imagination. Other metaphors commonly used include “the foot in the door” and “the thin end of the wedge”. The argument is fallacious when the consequences are not guaranteed to happen.

“How come Andrew gets to get up? If he gets up, we’ll all get up! It’ll be anarchy!”
(Bender—The Breakfast Club)

Some slippery slope arguments use ‘guilt by association’ and ‘straw man’ techniques in order to make sensible ideas seem absurd. For instance:

If you legalise voluntary euthanasia, that will open the door to compulsory euthanizing of the elderly.

There is also a related probabilistic fallacy, where a number of highly probable independent steps have to occur to get to the unpalatable end-point, but the result is presented as if it is as probable as any single step. For example:

If we let them raise tuition fees by £1,000, then they might do it again next year, and the year after, and on and on until no one can afford to go.

At any stage, the £1,000 hike in fees might be quite likely to be implemented, but the idea that repeated increases to the point of absurd is also highly likely because each individual step is fairly probable is fallacious.

Straw Man

 

A golden rule governing philosophical work is the principle of charity—the rule that we should interpret other’s arguments and views as charitably as possible. We certainly should not represent another philosopher’s work badly, or change the argument or position to make it weaker and easier to argue against.
If you set up a weakened version of an argument in order to discredit it, you are committing the straw man fallacy. The name refers to straw dummies used as target practice—defeating a straw dummy is easy, but defeating a real person is much harder. Crucially, showing that you can defeat the straw man doesn’t show that you can defeat the real thing.The straw man fallacy can often be quite subtle—people can misrepresent arguments through accidental misunderstandings, lack of clarity in the original text, or due to secondary sources which also misrepresent the argument. But it is a crucial part of your job as a philosopher to pay close and careful attention to others’ work, and make sure you don’t create a straw man.Examples:

Descartes said “I think, therefore I am”. By this he means that you only exist when you’re thinking. But this is absurd.

Here the student fails to understand Descartes’ argument correctly—maybe he could only demonstrate that he exists while he’s thinking, but this does not entail that he doesn’t exist the rest of the time.

Agnes wants to legalise marijuana. Marijuana is a drug. Drugs are linked with violence and help to fund terrorism. Violence and terrorism are bad. Therefore, we shouldn’t legalise marijuana.

Here, the argument shifts focus from marijuana to drugs in general, misrepresenting Agnes’s original position as if she wanted to legalise all drugs. We could construct a simple counterexample to this reasoning by replacing ‘marijuana’ with ‘aspirin’.

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