# Fallacy Fallacy

Alias:

• Fallacist's Fallacy1

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

### Form:

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

### Exposition:

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.

### Exposure:

• Strictly speaking, the Fallacy Fallacy is committed only when a conclusion is rejected as false because an argument for it is fallacious, that is, commits a logical fallacy. Since a logical fallacy is a mistake in reasoning that is common enough to be named, not just any bad argument will do. If an argument for a conclusion does not commit a fallacy, but is invalid or uncogent for some other reason, then rejecting the conclusion as false commits the more general Bad Reasons Fallacy, rather than the Fallacy Fallacy.
• It is reasonable to, at least provisionally, reject an improbable proposition for which no adequate evidence has been presented. So, if you can show that all of the common arguments for a certain proposition are fallacious, and the burden of proof is on the proposition's proponents, then you do not commit this fallacy by rejecting that proposition. Rather, the fallacy is committed when you jump to the conclusion that just because one argument for it is fallacious, no cogent argument for it can exist. See the Bad Reasons Fallacy, for more on this point.

### Q&A:

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.

Notes:

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.