Association fallacy

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An association fallacy is an inductive formal fallacy of the type hasty generalization or red herring which asserts that qualities of one thing are inherently qualities of another, merely by an irrelevant association. The two types are sometimes referred to as guilt by association and honor by association. Association fallacies are a special case of red herring, and can be based on an appeal to emotion.

Form

In notation of First-order logic, this type of fallacy can be expressed as (∃x∈S:φ(x))→ (∀x∈S:φ(x)), meaning "if there exists any x in the set S so that a property φ is true for x, then for all x in S the property φ must be true."

Premise A is a B

Premise A is also a C

Conclusion Therefore, all Bs are Cs

Fig. 1

The fallacy in the argument can best be illustrated through the use of a Venn diagram:

Fig. 2

"A" satisfies the requirement that it is part of both sets "B" and "C", but one can clearly see that it is possible that a part of set "B" is not part of set "C", refuting the conclusion that "all Bs are Cs".

Guilt by association

Examples

Some syllogistic examples of guilt by association are:

• Hitler was a vegetarian. Hitler was pure evil. Therefore, vegetarians have evil ideals.
• All dogs have four legs; my cat has four legs. Therefore, my cat is a dog. (This argument is made by the wordplay-prone Sir Humphrey Appleby in the BBC sitcom Yes, Prime Minister).

Guilt by association as an ad hominem fallacy

Guilt by association can sometimes also be a type of ad hominem fallacy, if the argument attacks a person because of the similarity between the views of someone making an argument and other proponents of the argument.

This form of the argument is as follows:

A makes claim P.

Bs also make claim P.

Therefore, A is a B.

Honor by association

The logical inverse of "guilt by association" is honor by association, where one claims that someone or something must be reputable because of the people or organizations that are related to it or otherwise support it. For example:

Examples

• Citizens of Country X have won more nobel prizes/gold medals/literary awards than citizens of Country Y. Therefore, a citizen of Country X is superior to a citizen of Country Y.

See also

• Ad hominem
• Reductio ad Hitlerum

External links

• The Fallacy Files Guilt by Association

• Propagandacritic.com "Transfer technique"
• Propagandacritic.com "Testimonial"