Proof by example
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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.
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 Gypsies steal. So, Gypsies must be thieves.
When valid
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
- <math>\underline{\varphi(\beta / \alpha)}\,\!</math>
- <math>\exists \alpha\, \varphi\,\!</math>
See also
- Affirming the consequent
- Anecdotal evidence
- Bayesian probability
- Counterexample
- Inductive reasoning
- Modus ponens
- Proof by construction