Formal fallacy

In <a href="/facts/Logic/8JnpJLtt">logic</a> and <a href="/facts/Philosophical_logic/Ld8lnKDA">philosophy</a>, a formal fallacy is a pattern of <a href="/facts/Reason/tcBImN8J">reasoning</a> rendered <a href="/facts/Validity_(logic)/oMGkywGC">invalid</a> by a flaw in its logical structure. <a href="/facts/Propositional_calculus/MNt5v31V">Propositional logic</a>, for example, is concerned with the meanings of sentences and the relationships between them. It focuses on the role of logical operators, called propositional connectives, in determining whether a sentence is true. An error in the sequence will result in a <a href="/facts/Deductive/HadA1zWS">deductive</a> <a href="/facts/Argument/1K1e3Xg4">argument</a> that is invalid. The argument itself could have true <a href="/facts/Premise/HluL8lcd">premises</a>, but still have a false <a href="/facts/Logical_consequence/AyDXp4dn">conclusion</a>. Thus, a formal fallacy is a <a href="/facts/Fallacy/IRVuLSef">fallacy</a> in which deduction goes wrong, and is no longer a <a href="/facts/Logic/8JnpJLtt">logical</a> 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., <a href="/facts/Affirming_the_consequent/dK0zDWFB">affirming the consequent</a>). In other words, in practice, "non sequitur" refers to an unnamed formal fallacy.
A special case is a <a href="/facts/Mathematical_fallacy/tUIV7DQV">mathematical fallacy</a>, an intentionally invalid <a href="/facts/Mathematical_proof/7ECDrU80">mathematical proof</a>, 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 <a href="/facts/Contradiction/PQHH5a2J">contradictions</a>.
A formal fallacy is contrasted with an <a href="/facts/Informal_fallacy/MfICjFRF">informal fallacy</a> which may have a valid <a href="/facts/Logical_form/foVBtMX4">logical form</a> and yet be <a href="/facts/Soundness/ndpamd2A">unsound</a> because one or more <a href="/facts/Premise/HluL8lcd">premises</a> are false. A formal fallacy, however, may have a true premise, but a false conclusion. The term 'logical fallacy' is sometimes used in everyday conversation, and refers to a formal fallacy.

Formal fallacy open-in-new

Formal fallacy