Formal fallacy

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In logic and philosophy, a formal fallacy^[a] is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic.^[2] It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion.^[3] Thus, a formal fallacy is a fallacy in which deduction goes wrong, and is no longer a logical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic.

While a logical argument is a non sequitur if, and only if, it is invalid, the term "non sequitur" typically refers to those types of invalid arguments which do not constitute formal fallacies covered by particular terms (e.g., affirming the consequent). In other words, in practice, "non sequitur" refers to an unnamed formal fallacy.

A special case is a mathematical fallacy, an intentionally invalid mathematical proof, often with the error subtle and somehow concealed. Mathematical fallacies are typically crafted and exhibited for educational purposes, usually taking the form of spurious proofs of obvious contradictions.

A formal fallacy is contrasted with an informal fallacy which may have a valid logical form and yet be unsound because one or more premises are false. A formal fallacy, however, may have a true premise, but a false conclusion.

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