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Proof by verbosity |
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Proof by verbosity is a term used to describe an excessively verbose mathematical proof that may or may not actually prove the result. Such proofs are most often presented by students who don't fully grasp the concepts they are writing about. Students presenting such proofs often either hope to hide their lack of understanding or are uncertain how extensive their proof is expected to be.
The term is commonly used jokingly amongst colleagues reviewing their work when one proof discussed is much longer than others presented for the same problem.
Proof by verbosity should not be confused with proof by exhaustion, the latter being a valid form of proof. The difference lies in that a proof by exhaustion is used when a number of dissimilar cases must be independently proven, whereas a proof by verbosity tends to be repetitive, with many overlapping proofs for specific cases of a more general problem. Nor should this be confused with argument from repetition in which the same (unproven) argument is repeated many times, possibly in different ways or by different people, as a mechanism of reinforcement of the (still unproven) point in the listener's or reader's mind.
Proof by verbosity is also used colloquially in forensic debate to describe a logical fallacy (sometimes called "argumentum verbosium") that tries to persuade by overwhelming those considering an argument with such a volume of material that the argument sounds plausible, superficially appears to be well-researched, and that is so laborious to untangle and check supporting facts that the argument is allowed to slide by unchallenged. It is the fallacy epitomized by the familiar quote: "If you can't dazzle them with your brilliance, then baffle them with your bullshit."
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