An association fallacy is a faulty generalisation which asserts that the qualities of one thing are inherently qualities of another, merely via an irrelevant association. Association fallacies come in various shapes and sizes; but most of them are a type of red herring fallacy that introduces irrelevant premises into an argument and draws an invalid conclusion.
The formal structure of the association fallacy is:
Premise 1: A is a B
Premise 2: A is also a C
Conclusion: Therefore, all Bs are Cs.
The fallacy in the argument can be illustrated through the use of the following 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’.
An example of the association fallacy is the argument ‘All dogs have four legs; my cat has four legs. Therefore, my cat is a dog.’ Another example is where some atheists oppose the idea of free will because Christians believe in it. (This is despite the fact that prominent atheists such as Professor Daniel Dennett also believe in free will).
Special cases of this fallacy include guilt by association, or conversely honour by association. Guilt by association can sometimes 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 same argument. An example 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? In this way, appeals to emotion can also be included for added rhetorical effect.
A form of the association fallacy often used by those denying a well-established scientific or historical proposition is the so-called ‘Galileo Gambit.’ The argument goes that since Galileo was ridiculed in his time but later acknowledged to be right, that since their non-mainstream views are provoking ridicule and rejection from other scientists, they too will later be recognized as correct.