Proof by example
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| - | '''Cherry picking''', '''suppressing evidence''', or the '''fallacy of incomplete evidence''' is the act of pointing to individual cases or data that seem to confirm a particular position, while ignoring a significant portion of related cases or data that may contradict that position. It is a kind of fallacy of selective attention, the most common example of which is the [[confirmation bias]]. | + | '''Proof by example''' (also known as '''inappropriate generalization''') is a [[Informal fallacy|logical fallacy]] whereby one or more examples are claimed as "proof" for a more general statement. |
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| + | This fallacy has the following structure, and [[argument form]]: | ||
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| + | Structure: | ||
| + | :I know that X is such. | ||
| + | :Therefore, anything related to X is also such. | ||
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| + | [[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. | ||
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| + | The following example demonstrates why this is a logical fallacy: | ||
| + | : I've seen a person shoot someone dead. | ||
| + | : Therefore, all people are murderers. | ||
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| + | The flaw in this argument is very evident, but arguments of the same form can sometimes seem somewhat convincing, as in the following example: | ||
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| + | :I've seen Gypsies steal. So, Gypsies must be thieves. | ||
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| + | ==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 [[List of rules of inference#Rules of classical predicate calculus|existential introduction]] (also known as ''particularisation'' or ''existential generalization''). | ||
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| + | Formally | ||
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| + | ;Existential Introduction: | ||
| + | : <math>\underline{\varphi(\beta / \alpha)}\,\!</math> | ||
| + | : <math>\exists \alpha\, \varphi\,\!</math> | ||
| ==See also== | ==See also== | ||
| - | *''[[Ad hoc]]'' | + | *[[Affirming the consequent]] |
| - | *[[Biased sample]] | + | *[[Anecdotal evidence]] |
| - | *[[Confirmation bias]] | + | *[[Bayesian probability]] |
| - | *[[Data dredging]] | + | *[[Counterexample]] |
| - | *[[Fallacy of quoting out of context]] | + | *[[Inductive reasoning]] |
| - | *[[False balance]] | + | **[[Problem of induction]] |
| - | *[[Hasty generalization]] | + | *[[Modus ponens]] |
| - | *[[Hawthorne effect]] | + | *[[Proof by construction]] |
| - | *[[Jumping to conclusions]] | + | |
| - | *[[Othello error]] | + | |
| - | *[[Pars destruens/pars construens]] | + | |
| - | *[[Proof by example]] | + | |
| - | *[[Quasi-experiment]] | + | |
| - | *[[Selection bias]] | + | |
| - | *[[Special pleading]] | + | |
| {{GFDL}} | {{GFDL}} | ||
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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.
[edit]
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>
[edit]
See also
- Affirming the consequent
- Anecdotal evidence
- Bayesian probability
- Counterexample
- Inductive reasoning
- Modus ponens
- Proof by construction
Unless indicated otherwise, the text in this article is either based on Wikipedia article "Proof by example" or another language Wikipedia page thereof used under the terms of the GNU Free Documentation License; or on research by Jahsonic and friends. See Art and Popular Culture's copyright notice.
