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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 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.
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.
https://effectiviology.com/fallacy-fallacy/
https://en.wikipedia.org/wiki/Argument_from_fallacy
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.
The "fallacy fallacy" exemplifies one of the weaknesses with a rationalist/analytical approach to philosophy. Here is a syllogism to make this point
In general, we are almost never able to "prove" a conclusion in philosophy
Instead, we accumulate "reasons" or "justifications" that suggest one should accept a conclusion.
For most such justifications, REFUTATIONS of that justification fall afoul of Quine's noting that all facts can be explained multiple different ways. Most justifications can be recast as more complex arguments, avoiding thru complexification any refutations or identification of fallacies. Untweaked, the justification is falsified, but weakening thru tweaking is very often possible.
Intermediate conclusion -- the standard of asking for proof of the falsity of eitehr an argument or a conclusion (a claim is wrong) is an impossible standard fallacy
There are, extrapolating from Quine, nearly innumerable mutually contradictory conclusions one may draw about our world.
Interim conclusion 2. IF the support for a conclusion about our world relies upon fallacies or falsehoods -- even if they may at some point be correctable by caveats/weakening the argument -- showing the argument is flawed, by inference to the multiple mutually contradictory claims about everything, IS support for the falsity of the ultimate claim.
So, yes, the "fallacy fallacy" does not "prove" that the conclusion is false.
But as such a proof is generally unachievable,
And the standard for supporting a conclusion is "support" not "proof"
Final conclusion: The lack of such a "proof" is no fault, and the "fallacy fallacy" is not actually a fallacy.
