The fallacy fallacy applies to both informal and formal logic and represents a fundamental misunderstanding of what logic is, although it is seductive and even people well versed in logic occasionally make this mistake, especially in a debate.
A person commits the fallacy when he or she assumes that because they have established that an argument is invalid, they have proven that the conclusion is false.
But that is not what validity tells us. Validity is concerned with truth preservation. The rules of inference seek to ensure that if you start with true statements as your premises, and you properly apply the rules of inference, then you will not end up with a false conclusion. So the rules of validity ensure that we never go from true premises to a false conclusion. And that is all.
But this leads to two special cases of validity:
Every argument where the conclusion is a tautology is valid, because
it is impossible for a tautology to be false and therefore there is
no truth-value assignment where both:
(All the premises are true AND the conclusion is false).
Basically you can't move from true statements to a false statement when the conclusion is guaranteed to be true.
A second special case of validity is that every argument with
inconsistent or contradictory premises is logically valid, because
there is no truth value assignment where all the premises will be
true, and therefore there is no truth-value assignment where
both (All the Premises are true AND the conclusion false).
Basically you cannot move from true premises to a false conclusion if
you are guaranteed to start with at least one false premise to begin with.
cf. Bergmann, Merrie, and James Moor, and Jack Nelson. *The Logic Book*,
3rd edition. pp. 21-23
When we detect a fallacy in an argument, what we have established is that the argument fails to establish a warrant for the conclusion; or to put it more plainly: the argument has not credibly established the truth of the conclusion. But this is not the same as establishing that the conclusion is false.