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I'm confused on how the 'fallacy fallacy' is applied in an argument. Let's say a person, let's call them X, proposes an argument to another person, let's call them Y.

X proposes an argument to Y which contains a logical fallacy (e.g, begging the question). Y notices this and calls X out, to which X refines the argument but this time X has now comitted an ad hominem fallacy.

So does fallacy fallacy only apply to informal fallacies, or does it apply to formal fallacies as well?

  • The fallacy fallacy declares the conclusion false when the argument for it is invalid. What difference does it make if the argument is formal or informal? – Conifold Nov 8 at 0:00
  • So let's say an argument is valid, but it uses an informal fallacy like argumentum ad populum. Doesn't that make it so fallacy fallacy can't be used because the conclusion follows from the premises? Point I'm trying to make is, if formal fallacies don't make an argument invalid. Wouldn't it be only formal fallacies that fallacy fallacy applies to? – Metanore Nov 8 at 0:05
  • Informal fallacies occur in informal arguments, and those are then (informally) invalid. Either an argument declares that something is true because most people believe it, and is invalid, or it doesn't, and there is no fallacy (at least, not ad populum). – Conifold Nov 8 at 0:48
  • @Metanore an argument is valid, or not. If it "uses a fallacy" it is invalid. That is the whole thing about fallacies: they are "obvious" points that make an argument invalid. "Traps to avoid" if you will. – paul23 Nov 8 at 0:48
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SHORT ANSWER

The fallacy fallacy applies to any argument, formal or informal, that argues a conclusion is wrong because it was arrived at by faulty reasoning. Sometimes, even though we reason incorrectly, we might still have the correct answer.

LONG ANSWER

Let's start with an example: if I argue that the answer to a question on a geometry test in high school is the shortest path between two points is a straight line between them, and you ask why, and I say because my music teacher told me so, I have given the right answer, but for the wrong reason. I insist that it's the right answer, but you point out that I have appealed to authority and conclude I'm wrong. You have now followed up my fallacy with one of your own

Can this apply to formal arguments too? Sure. Let's say that you are doing math, and you are asked to determine x, and through a series of steps, you arrive at x being 4, which happens to be correct, but in your work, you have the right answer because you've made two errors which cancel each other out (I've seen a lot of sign errors with integers lead to this). A fellow student might point out the errors and say, "look, you've made errors, so your answer is wrong", but when you correct the errors, you arrive at x being 4 anyway. Your friend has committed the fallacy fallacy.

Now, in the first case, the argumentation is informal, because the nature of what is the shortest point between two lines is a question that doesn't fit necessarily into a strict formal pattern of reasoning. In fact, sometimes the shortest path between two points is an arc as when on the surface of the sphere. But in the second case, the rules of arithmetic are quite formal with operations transforming the expression of quantities being governed by axioms. For instance, addition is commutative. Since the second case involves formalisms, the fallacy is committed in some formal way. Thus, the argument from fallacy can seen in both styles of reasoning.

REFERENCES

https://effectiviology.com/fallacy-fallacy/
https://en.wikipedia.org/wiki/Argument_from_fallacy

SEE ALSO

Does the Fallacy Fallacy make logic useless?

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    Thank you for making the distinction between informal/formal and explaining how a fallacy fallacy would work in both of these scenarios. – Metanore Nov 12 at 18:32
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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 can not move from true premises to a false conclusion if you are garunteed 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.

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