[Math Lair] Relevance Fallacies

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A relevance fallacy is a type of informal fallacy that relies on irrelevant emotional appeal, instead of logical argument, to reach conclusions. Arguments that commit such fallacies play to our emotions, such as fear, guilt, pity, loyalty, and biases, instead of drawing conclusions rationally.

Ignoratio Elenchi (Red Herring) is the only relevance fallacy considered by Aristotle. Most of the rest of the fallacies below are relatively recently named (even the ones with Latin names), mostly in the nineteenth and twentieth centuries.

Here is a sample of relevance fallacies:

Ignoratio Elenchi (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. All relevance fallacies are types of this fallacy.
Argumentum ad Verecundiam (Appeal to Authority)
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; we quite simply don't have the time or other resources to investigate and argue everything from first principles. 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:
Argumentum ad Populum (Appeal to Popularity)
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".
Argumentum ad Baculum (Appeal to Force)
This fallacy is committed when the arguer resorts to force the acceptance of a conclusion by threating someone with harm, either directly or indirectly. For example:
Argumentum ad Misericordiam (Appeal to Pity)
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.
Argumentum ad Ignorantiam (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."
Argumentum ad Antiquam
This is the fallacy of arguing in favour of something simply because it is old. For example, "That's the way we've always done it."
Argumentum ad Novitam
The opposite of Argumentum ad Antiquam, this fallacy is the fallacy of arguing in favour of something simply because it is new or newer than something else.
Argumentum ad Crumenam
This fallacy occurs when it is argued that someone is correct because that person has more money.
Argumentum ad Lazarum
This fallacy occurs when it is argued that someone is correct because they are poor. This fallacy is the opposite of Argumentum ad Crumenam.
Argumentum ad Nauseam
This fallacy involves arguing that an assertion is true because it is heard frequently.
Argumentum ad Personam (Appeal to Personal Interest).
This fallacy involves appealing to another person's preferences, biases, predispositions, and the like in order to have them accept the argument.
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 (which isn't really an argument at all), 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.
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.
Tu Quoque
Tu Quoque is Latin for "you too". 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.