14 Logical Fallacies That Keep Showing Up In Bad Arguments

There are a lot of ways that people make terrible and invalid arguments.

Making a good argument is about using logic to prove a conclusion based on some given facts. In a valid argument, the conclusion actually does follow from the facts.

Unfortunately, this can go wrong in many ways. Facts don't always support conclusions in the way an argument's author thinks they do.

Sometimes, conditional statements get improperly reversed, or causes and effects get mixed up.

Fallacies show up in online arguments, political debates, and justifications for unjust things like racial profiling. Here are some of the most common fallacies and why they don't work logically.

Conditional probability fallacies

This is a fallacy based on a misunderstanding of how conditional probabilities work, especially when applied to small subgroups of a population, or very unlikely events. The probability that A happens given B does not actually equal the probability that B happens given A.

This is a big practical problem with racial profiling. On 9/11, all of the terrorists that attacked New York and Washington were Muslims. This led some people to conflate Islam and terrorism..

The issue is that the population of Muslim terrorists is very small, and the population of Muslims is very large. As a thought experiment, suppose that there are 1,000 terrorists in the world, and suppose that 90% of that group consists of Muslim extremists. The fallacious idea then is that this means that 90% of Muslims are terrorists. But there are over a billion Muslims in the world, and only 900 of them are terrorists. So, the probability that a randomly chosen Muslim is a terrorist is incredibly small - on the order of 0.00009%.

Argument from fallacy

This one involves two people. One person gives a bad argument for a particular conclusion, and then the second person commits an argument from fallacy when they wrongly conclude that because the argument is wrong, the conclusion must be false.

As an example, suppose a college freshman writes on Tumblr that the fact that the male-centric comedy "Neighbors" succeeded at the box office proves that Hollywood is sexist and doesn't respect female comedians. Then a poster at reddit/mensrights posts this argument and says "See, this is a dumb argument. Therefore, Hollywood isn't misogynist".

Just because our Tumblr blogger's argument is terrible doesn't mean that Hollywood isn't, in fact, sexist, and our Redditor is making a fallacious counter-argument.

Appeal to probability

Concluding that because something can happen, or is likely to happen, it will happen. This is implicit in a ton of punditry and political strategy. The Republicans built most of their action plans throughout 2013 and early 2014 around the assumption that Obamacare would fail to meet its enrollment goals, based on the fact that this was something that could happen. Obamacare did, at the very least, hit its initial individual marketplace enrollment goals.

Fallacy of the converse

This fallacy and the next one involve mistakes in conditional "if-then" statements.

"If A, then B" in a logical context just means that whenever A is true, B is also true. Similarly, "All A's are B's" means that anything that is an A is also a B. There's no notion that A is causing B, just this relationship between properties.

One consequence of this relationship is that if B is true, we can't conclude anything about whether or not A is true, and if A happens to be false, we don't know anything about whether or not B is true. Making these mistakes leads to these two fallacies.

The fallacy of the converse involves the first mistake above - assuming that if the second "then" clause is true, then the first "if" clause is also true. Here's an example:

Everyone at Business Insider is smart and good looking, and Rachel Maddow is smart and good looking. Therefore, Rachel Maddow works at BI.

While my premises are true, unfortunately Ms. Maddow is not among my coworkers.

Fallacy of the inverse

This is the second mistake above - assuming that if we don't have the first "If" clause then we also don't have the second "then" clause:

If it's raining outside, I will be wearing a jacket. It's not raining outside, therefore I am not wearing a jacket.

This doesn't work, since there are plenty of other reasons I might wear a jacket. It was cold out this morning, so I was wearing a jacket, even though it was sunny.

Post hoc, ergo propter hoc

Latin for "After this, therefore because of this." This is a common fallacy involving cause and effect. Someone making this fallacy believes that because one thing happened before another thing, the first thing caused the second thing. This is at the root of many superstitions - I put on mismatched socks one morning, and that afternoon I was offered a job, so clearly these are my lucky mismatched socks and they are the reason I got the job.

In general, cause and effect have a bunch of tricky nuances, and validly establishing causation in an argument is very hard.

REUTERS/Jean-Paul Pelissier

Quitting smoking may reduce his chances of cancer, but won't eliminate them.

Fallacy of the single cause

This is a belief that an effect has just one cause, rather than a number of possible partial causes that influence that effect, or the the idea that because something is a cause of another thing means that it is the only cause:

Smoking causes cancer, so if I quit smoking, I will never get cancer.

There are many other things that cause cancer, so while my chances of getting cancer will probably drop if I were to quit smoking, I can't conclude that I will never get cancer.

This fallacy is a problem because when a major event happens, we try to find what the single cause of that event was, when in reality, things often have many complex, interconnected causes.

Correlation implies causation

This is one of the more famous of the causal fallacies. This is the assumption that because two quantities increase or decrease in the same way as each other, or two properties show up together, that one of those variables is causing the other. For example:

Cities with more hospitals also tend to have more people with cancer. Therefore, hospitals cause cancer.

This is fallacious because it's probably the case that these are both effects of city size. If more people live in a city, then that city needs more hospitals, and there are more people overall, which means that there will be more people with cancer.

We recently reported on a wonderful website that shows why this doesn't work - lots of quantities may move with each other by sheer coincidence, or because they are both being influenced by some other underlying cause. One of the best examples from that site is the very strong correlation between the divorce rate in Maine and per capita consumption of margarine in the U.S. It would be pretty surprising if these rates had a causal relationship with each other.

Argument to moderation

Assuming that the middle ground between two options is the best option. This is another fallacy that shows up in politics.

Suppose one political party in a local legislature wants to build a new subway line from downtown to the state university campus in the suburbs. The other party is entirely opposed to the subway line. The inappropriate middle ground would be to build the subway line halfway from downtown to the university, leading to a mostly useless subway system.

AP

Possibly our theoretical casino developer.

False dilemma

This is the flipside to the argument to moderation. There, we assumed that there was some middle ground alternative when none exists. In a false dilemma, a person is saying that you only have two alternatives when there might be more.

A developer might argue that either a city gives him funds to build his casino, or the city will continue to have persistent high unemployment. This argument doesn't work, since there are probably other ways the city could improve their economic situation: tax breaks for small businesses, investments in better infrastructure, or improving their schools.

Argument ad hominem

Attacking the person making an argument, rather than the argument itself. This is a fallacy because when you are trying to tear down an argument, you need to actually find a reason why the argument is wrong.

As an example, here's a pithy one-star Amazon review, taken verbatim, of Thomas Piketty's "Capital in the 21st Century":

This Marxist French fool doesn't have a grasp on reality ( like most socialist) this waste of paper is good for only one thing, a bon fire! What a bunch of garbage!

The critic does not directly address Piketty's arguments on the nature of wealth inequality, but instead his or her conclusion (Piketty's book is garbage and is only good for being burned) hinges on saying that Piketty is a Marxist, French, a fool, and a socialist.

Fallacy of composition

Concluding something is true of a whole because it's true of the parts of that whole. For example:

My startup will be efficient and successful, because I and everyone I have hired are efficient and successful.

Saying that the component people of the startup are successful is not enough to say that the startup will work. There may be organizational deficiencies, or interpersonal arguments. It's also possible the startup has a terrible product idea with no viable market.

Fallacy of division

This is the flipside of the fallacy of composition: concluding that the parts of something have a property because the whole entity has that property. For example,

A car can propel itself at 65 miles per hour. Therefore, the front left tire of that car can also propel itself at 65 miles per hour.

Both the fallacies of composition and division revolve around the fact that in many cases, the whole is not the sum of its parts.

Faulty generalizations

There are many ways in which the relationship between generalizations and specific instances can be abused. One of the more common ones is to over-generalize from an unrepresentative group. For example:

The overwhelming majority of my friends are liberals who support higher taxes on the wealthy. So, any politician who is a liberal and supports this issue is very likely to get elected.

I live in New York City and associate mostly with people who have political views similar to my own. It's wrong for me to generalize from the highly unrepresentative sample of my friends to voters everywhere in the country.