Association fallacy

The association fallacy is a formal fallacy that asserts that properties of one thing must also be properties of another thing if both things belong to the same group. For example, a fallacious arguer may claim that "bears are animals, and bears are dangerous; therefore your dog, which is also an animal, must be dangerous."

When it is an attempt to win favor by exploiting the audience's preexisting spite or disdain for something else, it is called guilt by association or an appeal to spite (Latin: argumentum ad odium). Guilt by association can be a component of ad hominem arguments which attack the speaker rather than addressing the claims, but they are a distinct class of fallacious argument, and both are able to exist independently of the other.

Using the language of set theory, the formal fallacy can be written as follows:

In the notation of first-order logic, this type of fallacy can be expressed as (∃x ∈ S : φ(x)) ⇒ (∀x ∈ S : φ(x)).

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 S1 and S2, but representing this as an Euler diagram makes it clear that B could be in S2 but not S1.

This form of the argument is as follows:

An example of this fallacy would be "My opponent for office just received an endorsement from the Puppy Haters Association. Is that the sort of person you would want to vote for?"

Some syllogistic examples of guilt by association: