Fallacy Fallacy


Taxonomy: Logical Fallacy > Formal Fallacy > Bad Reasons Fallacy > Fallacy Fallacy


Argument A for the conclusion C is fallacious.
Therefore, C is false.


Like anything else, the concept of logical fallacy can be misunderstood and misused, and can even become a source of fallacious reasoning. To say that an argument is fallacious is, among other things, to claim that there is not a sufficiently strong logical connection between the premisses and the conclusion. This says nothing about the truth or falsity of the conclusion, so it is unwarranted to conclude that it's false simply because some argument for it is fallacious.

It's easy to come up with fallacious arguments for a proposition, whether true or false. What can be hard is to find a cogent argument for it, even when it's true. For example, it's now believed by mathematicians that the proposition known as "Fermat's last theorem" is true, yet it took over three centuries for anyone to prove it. In the meantime, many invalid arguments were presented for it2.

As can be seen in the Taxonomy, above, the Fallacy Fallacy is a subfallacy of the more general Bad Reasons fallacy; specifically, it is the case when the "bad reasons" are that the argument commits a fallacy.



Aoyagi Aichou wrote to ask about the following situation: suppose someone argues that a particular argument must not be fallacious because its conclusion is true. Aoyagi correctly noticed a similarity to the fallacy fallacy, but that it does not fit the Form of the fallacy given above. In the Form of the fallacy fallacy, one argues that because a certain argument for a conclusion is fallacious that, therefore, the conclusion must be false. In Aoyagi's case, in contrast, one argues from the conclusion's truth to the non-fallaciousness of the argument.

Both forms of argument are invalid: just as it's possible to give a valid argument for a false conclusion, it's possible to give an invalid argument for a true conclusion. If we express the idea underlying the fallacy fallacy as a rule, it would be: If an argument is fallacious then it's conclusion is false. Its contrapositive would be: If the conclusion of an argument is true―that is, not false―then the argument is not fallacious." Both rules are not generally true, but the latter would support the kind of invalid inference that Aoyagi asks about. For this reason, I would consider it a logical variant of the fallacy fallacy.


  1. David Hackett Fischer, Historians' Fallacies: Toward a Logic of Historical Thought (Harper & Row, 1970), pp. 305-306. Fischer's conception of "the fallacist's fallacy" is much broader than the mistake discussed here, but that mistake is a subfallacy of it.
  2. See: Simon Singh, "The Whole Story", Simon Singh, accessed: 10/24/2017. In fact, Andrew Wiles' first "proof" of the theorem was invalid.

Acknowledgment: Thanks to Adrian Larson.