What exactly is a formal fallacy?
ELI5: Formal and Informal Fallacies
Formal or Informal Fallacy?
It doesn't matter. You shouldn't waste your time trying to categorize fallacies or give them names or anything like this. Your life will be better if you just ignore all of this stuff. Don't get sucked down the fallacy rabbit hole. There's nothing good down there.
More on reddit.comAre informal fallacies pointed out too broadly?
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According to textbooks and Wikipedia, a formal fallacy is a argument that is rendered invalid by a flaw in its logical form, aka an argument where you can tell it is invalid just by looking at its form (hence the word formal) and not content. However, how can these so called logical fallacies like "denying the antecedent" be invalid just by looking at the form, when there are obviously cases like that that are deductively valid? Here are some examples I came up with:
(R->R), ~R, ∴~R (P=Q)
((R v S)->S), ~(R v S), ∴~S (~P entails ~Q alone)
(R->(S & ~S)), ~R, ∴~(S & ~S) (Q is a contradiction)
All these forms are cases of "denying the antecedent" but are obviously deductively valid, in the sense that if the premises are true, the conclusion must be true. Then, only SOME arguments like "denying the antecedent" that are "formally invalid" are actually invalid, not ALL. And so, knowing an argument is formally invalid does not really tell us whether it is valid or not, which does not help at all. Therefore, I think there actually cannot be such thing as a formal fallacy.
(well, I guess there IS one form of argument that can be said to be formally invalid, and that would be an argument where all premises are logical tautologies and the conclusion is a logical contradiction...but no one who discusses formal fallacies ever talks about this, so)