[Math Lair] Informal Fallacies

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An informal fallacy is a type of fallacy that is not an error in the form (or structure) of the argument. Fallacies that involve errors in an argument's form are called formal fallacies. Aristotle was the first to identify fallacies. In On Sophistical Refutations he identified thirteen, divided into two groups: Linguistic fallacies and non-linguistic fallacies. Since then, over 100 fallacies have been identified. The study of informal fallacies is important to the field of informal logic.

Informal fallacies may be classified in various ways. One classification scheme involves three general categories:

Here is a list of some common informal fallacies:

Appeals to Authority, Popularity, Force, and Pity
The Appeal to Authority uses the opinion of an authority or famous person to support an assertion. This line of argument is not always incorrect; for most things in our lives, we have to rely on the word of an authority. The fallacy lies in using an authority in place of arguing based on the subject matter, or taking as authoritative a statement that might not be authoritative. Some examples:

The Appeal to Popularity is a fallacy that asserts that an assertion is correct based on its support by a large group of people. For example: "The movie Harry Potter And The Philosopher's Stone grossed a record amount of money in its first week. Therefore, it is a very high-quality movie".

The Appeal to Force is committed when the arguer resorts to force the acceptance of a conclusion by threating someone with harm, either directly or indirectly. For example:

The Appeal to Pity is in a way the opposite of the Appeal to Force. It suggests that harm will come to the arguer unless a certain conclusion is accepted.

Fallacy of Collective Inference
This fallacy is related to appeal to authority. It occurs when several different authorities are used to support premises in an argument, but where no one authority would agree with all of the premises or the conclusion.
Argument from Ignorance
This fallacy occurs whenever someone argues that something must be true because it has not been proven false, or false because it has not been proven true. For example, "Psychic phenomena don't exist, since no-one has proved that they are real," or "Psychic phenomena exist, since no-one has proven them to be false."
Ad Hominem
Literally, an argument directed "at the man". There are two forms of ad hominem: the abusive variety occurs when an arguer attacks those making an assertion, and the circumstantial variety occurs when one argues that one's opponent ought to accept the truth of an assertion because of the opponent's particular circumstances.
Fallacies of Accident and Reverse Accident (Dicto Simpliciter)
The Fallacy of Accident (Secundum Quid) is committed when a general rule is applied to a particular case whose circumstances make the rule inapplicable. It is the fallacy made when one goes from the general to the specific. For example: "Over 50% of students in America don't finish high school. You are a student in America. Therefore you probably won't finish high school". Whether this statement is true or not depends on the situation that the person being spoken to is in. The fallacy of Reverse Accident (a.k.a. "Hasty Generalisation") occurs when one goes from the specific to the general. For example: "Jane said she didn't like me. Therefore no-one likes me."
Begging the Question
Begging the Question occurs when one "proves" a statement by assuming that it's true to begin with. This can be done subtly. In symbolic logic, begging the question can be denoted by the logical statement X -> X, which doesn't really prove anything logically. Because English is such a rich language, it's easy to do this quite subtly. Consider a sentence that I was going to write in an earlier draft of this page: "Begging the question is not a valid method of drawing conclusions, because you can't make deductions by assuming what you want to prove." If you read the previous sentence carefully, you'll note that both the premise and the conclusion are the same, so nothing is accomplished.
Loaded Question
A loaded question (also known as a complex question) is a question that is comprised of two statements and so may contain hidden assumptions. An example of such a question is "Have you stopped using drugs yet?". Whether you answer either "yes" or "no" to this question, you imply that you have used drugs.
In English as well as other languages, many words have multiple meanings. Changing the meaning of a word in mid-argument is committing the fallacy of Equivocation. Here are some examples:
Post Hoc Ergo Propter Hoc
This fallacy occurs when something is assumed to be the cause of an event merely because it happened before an event. For example, "99 percent of hard drug users started with cannabis. Therefore, marijuana is a 'gateway drug'".
Fallacies of Composition and Division
The fallacy of composition is to conclude that a property shared by all members of a set must apply to that set, or that a property shared by all parts of something must apply to the whole. For example: "Sodium is highly reactive, and Chlorine is highly poisonous. Table salt is sodium chloride, a compound containing sodium and chlorine. Therefore salt is highly reactive and poisonous." The fallacy of division is the converse of the fallacy of composition, that is to conclude that a property of something must apply to all its parts, or that a property of a set must apply to all members of that set.
Slippery Slope
This argument states that, if one event occurs, other harmful events will also, without giving any proof of a causal relationship. For example, "If we legalize marijuana, then we would have to legalize heroin and crack and we'll have a nation full of drug addicts on welfare. Therefore we cannot afford to legalize marijuana".
Bifurcation occurs when one assumes that only two alternatives are available in a situation, when in truth there are others.
Fallacy of the continuum
The assumption that small differences are always unimportant. For example, "I know the budget is tight, but what difference will $1 a day make?"
Illicit contrast
This fallacy involves leading the listener to draw an inappropriate inference by placing unusual emphasis on certain words or phrases.
Argument by innuendo
This fallacy involves directing the listener to a certain conclusion by a careful selection of words or phrases. For example: "Is Joe a good person? Well, we've never caught him doing anything illegal."
Red Herring
To commit this fallacy is to introduce irrelevant material to the issue being discussed, so that everyone's attention is diverted away from the points being made, towards a different conclusion.
Straw Man
The straw man fallacy is to misrepresent a position so that it is easier to "knock down", proceed to do so, and then claim that the original position has been destroyed.
Extended Analogy
This fallacy is to assume that two different situations are analogous to one another. Typically found when arguing about a general rule that involves the two situations.
Tu Quoque
"Tu Quoque" means "you too" in Latin. This fallacy occurs when an action is said to be acceptable because the opposing party has done it. For example:
Person 1
You were driving way too fast there!
Person 2
So? You drive too quickly too.