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A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves," in the construction of an argument, which may appear stronger than it really is if the fallacy is not spotted. The term was in the Western intellectual tradition introduced in the Aristotelian De Sophisticis Elenchis.
Some fallacies are committed intentionally to manipulate or persuade by deception. Others are committed unintentionally because of human limitations such as carelessness, cognitive or social biases, or plain ignorance. This includes ignorance of the right reasoning standard, but also ignorance of relevant properties of the context. For instance, the soundness of legal arguments depends on the context in which the arguments are made.
Fallacies are commonly divided into "formal" and "informal." A formal fallacy is a flaw in the structure of a deductive argument which renders the argument invalid, while an informal fallacy originates in an error in reasoning other than an improper logical form. Arguments containing informal fallacies may be formally valid, but still fallacious.
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.