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Proof by example
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Proof by example : ウィキペディア英語版
Proof by example

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.〔http://www.auburn.edu/~marchjl/fallacies.htm〕
This fallacy has the following structure, and argument form:
Structure:
:I know that X is such.
:Therefore, anything related to X is also such.
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.
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. 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:
: \underline\,\!
: \exists \alpha\, \varphi\,\!

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