Lesson plan
Proof by example
In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof. The structure, argument form and formal form of a proof by example generally proceeds as follows: Structure: :I know that X is such. :Therefore, anything related to X is also such. Argument form: :I know that x, which is a member of group X, has the property P. :Therefore, all other elements of X must have the property P. Formal form: : \exists x:P(x)\;\;\vdash\;\;\forall x:P(x) The following example demonstrates why this line of reasoning is a logical fallacy: : I've seen a person shoot someone dead. : Therefore, all people are murderers. In the common discourse, a proof by example can also be used to describe an attempt to establish a claim using statistically insignificant examples. In which case, the merit of each argument might have to be assessed on an individual basis.
Article summary
In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof. The structure, argument form and formal form of a proof by example generally proceeds as follows: Structure: :I know that X is such. :Therefore, anything related to X is also such. Argument form: :I know that x, which is a member of group X, has the property P. :Therefore, all other elements of X must have the property P. Formal form: : \exists x:P(x)\;\;\vdash\;\;\forall x:P(x) The following example demonstrates why this line of reasoning is a logical fallacy: : I've seen a person shoot someone dead. : Therefore, all people are murderers. In the common discourse, a proof by example can also be used to describe an attempt to establish a claim using statistically insignificant examples. In which case, the merit of each argument might have to be assessed on an individual basis.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.