# Proof by example

This article needs additional citations for verification. (November 2006) (Learn how and when to remove this template message) |

**Proof by example** (also known as **inappropriate generalization**) is a logical fallacy whereby one or more examples are claimed as "proof" for a more general statement.^{[1]}

This fallacy has the following structure, and argument form:

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 have the property P.

The following example demonstrates why this is a logical fallacy:

- I've seen a person shoot someone dead.
- Therefore, all people are murderers.

The flaw in this argument is very evident, but arguments of the same form can sometimes seem somewhat convincing, as in the following example:

- I've seen nationalists harass immigrants. So, nationalists must be harassers.

## When valid[edit]

However, argument by example is valid when it leads from a singular premise to an *existential* conclusion (i.e. proving it is true for at least one case instead of for all cases). For example:

- Socrates is wise.
- Therefore, someone is wise.

(or)

- I've seen a person steal.
- Therefore, people can steal.

This is an informal version of the logical rule known as existential introduction (also known as *particularisation* or *existential generalization*).

Formally

- Existential Introduction

## See also[edit]

- Affirming the consequent
- Anecdotal evidence
- Bayesian probability
- Counterexample
- Inductive reasoning
- Modus ponens
- Proof by construction

## References[edit]

**^**"Logical fallacies". www.auburn.edu. Archived from the original on 31 July 2002.