Logical Fallacy # 4: The Fallacy Fallacy

From Wikipedia:

Argument from fallacy is the formal fallacy of analyzing an argument and inferring that, since it contains a fallacy, its conclusion must be false.[1] It is also called argument to logic (argumentum ad logicam), fallacy fallacy,[2] fallacist's fallacy,[3] and bad reasons fallacy.[4]
Fallacious arguments can arrive at true conclusions, so this is an informal fallacy of relevance.[5]

Form[edit]:

It has the general argument form:

If P, then Q.

P is a fallacious argument.

Therefore, Q is false.[6]

Thus, it is a special case of denying the antecedent where the antecedent, rather than being a proposition that is false, is an entire argument that is fallacious. A fallacious argument, just as with a false antecedent, can still have a consequent that happens to be true. The fallacy is in concluding the consequent of a fallacious argument has to be false.

That the argument is fallacious only means that the argument cannot succeed in proving its consequent.[7] But showing how one argument in a complex thesis is fallaciously reasoned does not necessarily invalidate the proof; the complete proof could still logically imply its conclusion if that conclusion is not dependent on the fallacy:

All great historical and philosophical arguments have probably been fallacious in some respect... If the argument is a single chain, and one link fails, the chain itself fails with it. But most historians' arguments are not single chains. They are rather like a kind of chain mail which can fail in some part and still retain its shape and function.  --David Hackett Fischer, Historians' fallacies[3]