Proof by example

Proof by example (also known as "inappropriate generalisation") is a logical fallacy whereby one or more examples are claimed as "proof" for a more general statement.

This fallacy has the following argument form::I know that x $in$ 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.: Therefore, all people are murderers.

This argument is obviously flawed, but arguments of the same form can sometimes seem superficially convincing, as in the following example:

:I've seen John's brother steal something. John's family must be thieves.

When valid

However, argument by example is valid when it leads from a singular premise to an "existential" conclusion. For example

:Socrates is wise. :Therefore, someone is wise.

This is an informal version of the logical rule known as Existential Introduction (also known as "Particularisation" or "Existential Generalization").

Formally

;Existential Introduction:: $underline{varphi(eta / alpha)},!$ : $exists alpha, varphi,!$

ee also

*Modus ponens
*Affirming the consequent
*Inductive reasoning
*Bayesian probability

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Proof by example

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