An association fallacy is an inductive informal 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.
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
The fallacy in the argument can be illustrated through the use of a Venn diagram: "A" satisfies the requirement that it is part of both sets "B" and "C", but if one represents this as a Venn 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".
Guilt by association
Some syllogistic examples of guilt by association are:
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 a claim of P's status.
- B also makes a claim of P's status.
- Therefore, P is guilty by association.
Example: Alice believes in a theory. Bob and Carol believe in the same theory. Therefore, Alice is just like Bob and Carol.
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:
- The Fallacy Files Guilt by Association
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