Guilt by association

An association fallacy is an informal inductive fallacy of the hasty-generalization or red-herring type and which asserts, by irrelevant association and often by appeal to emotion, that qualities of one thing are inherently qualities of another. Two types of association fallacies are sometimes referred to as guilt by association and honor by association.

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."

The fallacy in the argument can be illustrated through the use of an Euler diagram: "A" satisfies the requirement that it is part of both sets "B" and "C", but if one represents this as an Euler diagram, it can clearly be seen that it is possible that a part of set "B" is not part of set "C", refuting the conclusion that "all Bs are Cs".

Some syllogistic examples of guilt by association:

A real-world example of guilt by association is that, in response to mass shooting incidents in the U.S. and public speculation that the perpetrators had Asperger syndrome, many people throughout society wrongfully stigmatized and stereotyped people with the disorder as being potentially violent and having the potential to become shooters. Especially after the Sandy Hook Elementary School shooting, the media (after the early reporting) and autism-advocacy organizations proffered expert opinions debunking this myth and attempting to better educate the public about autism to dissuade the stigmatization.

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