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.
[edit] 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
[edit] See also
- Modus ponens
- Affirming the consequent
- Inductive reasoning
- Bayesian probability
- Proof by construction
