Proof by intimidation (or argumentum verbosum) is a jocular phrase used mainly in mathematics to refer to a specific form of hand-waving, whereby one attempts to advance an argument by marking it as obvious or trivial, or by giving an argument loaded with jargon and obscure results. It attempts to intimidate the audience into simply accepting the result without evidence, by appealing to their ignorance and lack of understanding.
The phrase is often used when the author is an authority in their field, presenting their proof to people who respect a priori the author's insistence of the validity of the proof, while in other cases, the author might simply claim that their statement is true because it is trivial or because they say so. Usage of this phrase is for the most part in good humour, though it can also appear in serious criticism. A proof by intimidation is often associated with phrases such as:
- "It is self-evident that..."
- "It can be easily shown that..."
- "... does not warrant a proof."
- "The proof is left as an exercise for the reader."
Outside mathematics, "proof by intimidation" is also cited by critics of junk science, to describe cases in which scientific evidence is thrown aside in favour of dubious arguments—such as those presented to the public by articulate advocates who pose as experts in their field.
Proof by intimidation may also back valid assertions. Ronald A. Fisher claimed in the book credited with the new evolutionary synthesis, "...by the analogy of compound interest the present value of the future offspring of persons aged x is easily seen to be...", thence presenting a novel integral-laden definition of reproductive value. At this, Hal Caswell remarked, "With all due respect to Fisher, I have yet to meet anyone who finds this equation 'easily seen.'" Valid proofs were provided by subsequent researchers such as Leo A. Goodman (1968).
He took umbrage when someone interrupted his lecturing by pointing out some glaring mistake. He became red in the face and raised his voice, often to full shouting range. It was reported that on occasion he had asked the objector to leave the classroom. The expression "proof by intimidation" was coined after Feller's lectures (by Mark Kac). During a Feller lecture, the hearer was made to feel privy to some wondrous secret, one that often vanished by magic as he walked out of the classroom at the end of the period. Like many great teachers, Feller was a bit of a con man.
- Argument from authority – An argument that justifies the conclusion via an appeal to authority
- Chewbacca defense – Nonsensical diversionary legal defense strategy
- Gish gallop – Rhetorical technique
- Hand-waving – Term for attempting to be seen as effective
- Obscurantism – Practice of obscuring information
- Proof by example – Erroneous method of proof
- Sophist – Teacher in ancient Greece (5th century BC)
- Bennett, Bo. "Proof by Intimidation". logicallyfallacious.com. Retrieved 2019-12-01.
- Michael H. F. Wilkinson. "Cogno-Intellectualism, Rhetorical Logic, and the Craske-Trump Theorem" (PDF). Annals of Improbable Research. 6 (5): 15–16. Retrieved 2008-02-22.
- Tony Hey (1999). "Richard Feynman and computation" (PDF). Contemporary Physics. 40 (4): 257–265. Bibcode:1999ConPh..40..257H. doi:10.1080/001075199181459. Retrieved 2008-02-22.
- Marjorie K. Jeffcoat (July 2003). "Junk science: Appearances can be deceiving". Journal of the American Dental Association. 134 (7): 802–803. doi:10.14219/jada.archive.2003.0268. PMID 12892436.
- Fisher, Ronald Aylmer (1930). The genetical theory of natural selection. Oxford: The Clarendon Press. p. 27. OCLC 18500548.
- Caswell, Hal (2001). Matrix Population Models. Sinauer Associates, Incorporated. p. 92. ISBN 0-87893-096-5.
- Goodman, Leo A. (1968-03-01). "An elementary approach to the population projection-matrix, to the population reproductive value, and to related topics in the mathematical theory of population growth". Demography. Duke University Press. 5 (1): 382–409. doi:10.1007/bf03208583. ISSN 0070-3370. S2CID 46970216.