Proof by example

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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.^[1]

This fallacy has the following argument form:

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.

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

See also

• Modus ponens
• Affirming the consequent
• Inductive reasoning
• Bayesian probability
• Proof by construction

References

1. ^ http://www.auburn.edu/~marchjl/fallacies.htm