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.[1][2]
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.
- 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.[2]
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.[3]
- ^ "Logical fallacies". www.auburn.edu. Archived from the original on 31 July 2002.
- ^ a b "Proof by example – Grammarist". Grammarist. Retrieved 2019-12-01.
- ^ "What is Proof By Example?". Simplicable. Retrieved 2019-12-01.