Fallacy-fallacy

Core claim: A refuted or invalid argument is mistakenly taken as evidence that the conclusion it supported is false.

• An argument for proposition P is shown to be logically invalid, and this is used to conclude “therefore not-P”.
• The validity of the reasoning process is conflated with the truth value of the conclusion (i.e., assuming a bad proof means the claim is wrong).
• A counter-argument is dismissed solely because it contains a logical error, without addressing whether the underlying claim might still be true via other valid arguments.

• This fallacy often acts as a red herring: by focusing on the opponent's poor logic, one distracts from having to provide strong evidence for their own position or refute the actual facts.
• It is distinct from simply pointing out that an argument is weak; it specifically asserts that the negation of the conclusion follows from the invalidity of the argument.

• The conclusion is indeed false, and the refutation of the specific argument is part of a broader, valid case against the proposition (e.g., “Your proof is flawed, AND here are three independent reasons why the claim is factually wrong”).
• The fallacious argument was essential to proving the point, and its failure logically implies the conclusion is impossible (deductive logic) or becomes exceedingly unlikely (abductive logic).

• Argument from ignorance (MD) – claims something is false because it hasn’t been proven true. Ask: Is the error “no proof = false” (→ argument from ignorance) or “bad proof = false” (→ fallacy-fallacy)?
• Straw man (MD) – misrepresenting an opponent's position to make it easier to attack. Ask: Is the opponent's logic being attacked as if it were their position (→ fallacy-fallacy), or is their position itself distorted (→ straw man)?
• Argumentum ad minutiam (MD) – distorting an argument to a minor, easily refutable point and pretending this defeats the entire position. Ask: Is the attacker focusing on one minor logical flaw in the reasoning (→ fallacy-fallacy), or reducing the whole complex argument to a single trivial detail that is easy to dismiss (→ ad minutiam)?
• Motte-and-bailey fallacy (MD) – attacking the weak, easily refutable version of a position (“bailey”) and claiming victory over the strong, defensible core (“motte”). Ask: Is the error assuming that because one specific argument is bad, the conclusion is false (→ fallacy-fallacy), or is it conflating two different strengths of a claim and attacking only the weak one while claiming to have defeated the strong one (→ motte-and-bailey)?

Input: “You claimed that all swans are white based on seeing only 100 white swans. That's a hasty generalization, so your logic is flawed. Therefore, there must be //no// black swans.”
Output: The inductive argument was indeed weak, but this does not prove the negative (that black swans don't exist). It only means that specific evidence wasn't sufficient to prove the universal claim.

Input: “Your mathematical proof for this theorem has a division-by-zero error on line 5. Since your proof is invalid, the theorem must be false.”
Output: An invalid proof does not disprove a theorem; it only means that particular derivation failed. The theorem might still be true and provable via other methods.

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