View source for Faulty generalization

{{short description|Conclusion made about all or many instances of a phenomenon, that has been reached on the basis of one or a few instances of that phenomenon}}
In [[logic]] and reasoning, a '''faulty generalization''', similar to a [[proof by example]] in [[mathematics]], is an [[informal fallacy]]. It involves drawing a conclusion about all or many instances of a phenomenon that has been reached on the basis of one or a few instances of that phenomenon.<ref name=":0">{{Cite web|url=https://mathvault.ca/math-glossary/#pbe|title=The Definitive Glossary of Higher Mathematical Jargon — Proof by Example|date=2019-08-01|website=Math Vault|language=en-US|access-date=2019-12-05}}</ref><ref name=":1">{{Cite web|url=https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/100/Hasty-Generalization|title=Hasty Generalization|website=logicallyfallacious.com|access-date=2019-12-05}}</ref> It is an example of [[jumping to conclusions]].<ref name=":2">{{Cite web|url=https://www.iep.utm.edu/fallacy/#HastyGeneralization|title=Hasty Generalization|last=Dowden|first=Bradley|website=Internet Encyclopedia of Philosophy|access-date=2019-12-05}}</ref> For example, one may generalize about all people or all members of a group, based on what one knows about just one or a few people:

* If one meets an angry person from a given country X, one may suspect that most people in country X are often angry.
* If one sees only white swans, one may suspect that all swans are white.

Expressed in more precise philosophical language, a '''fallacy of defective induction''' is a conclusion that has been made on the basis of weak premises, or one which is not justified by sufficient or unbiased evidence.<ref name=":3">{{Cite web|url=https://www.thoughtco.com/hasty-generalization-fallacy-1690919|title=Logical Fallacies: Examples of Hasty Generalizations|last=Nordquist|first=Richard|website=ThoughtCo|language=en|access-date=2019-12-05}}</ref> Unlike fallacies of relevance, in fallacies of defective induction, the premises are related to the conclusions, yet only weakly buttress the conclusions, hence a faulty generalization is produced. The essence of this '''inductive fallacy''' lies on the overestimation of an argument based on insufficiently-large samples under an implied margin or error.<ref name=":2" />

==Logic==
A faulty generalization often follows the following format:

: The proportion Q of the sample has attribute A.
: Therefore, the proportion Q of the population has attribute A.

Such a generalization proceeds from a premise about a [[Sample (statistics)|sample]] (often unrepresentative or biased), to a conclusion about the population itself.<ref name=":3" />

Faulty generalization is also a mode of thinking that takes the experiences of one person or one group, and incorrectly extends it to another.

==Inductive fallacies==
* Hasty generalization is the fallacy of examining just one or very few examples or studying a single case, and generalizing that to be representative of the whole class of objects or phenomena.
* The opposite, [[slothful induction]], is the fallacy of denying the logical conclusion of an inductive argument, dismissing an effect as "just a coincidence" when it is very likely not.
* The [[overwhelming exception]] is related to the hasty generalization, but working from the other end.  It is a generalization which is accurate, but tags on a qualification which eliminates enough cases (as exceptions); that what remains is much less impressive than what the original statement might have led one to assume.
* [[Biased sample|Fallacy of unrepresentative samples]] is a fallacy where a conclusion is drawn using samples that are unrepresentative or biased.<ref>{{Cite web|url=https://www.iep.utm.edu/fallacy#UnrepresentativeSample|title=Fallacies — Unrepresentative Sample|last=Dowden|first=Bradley|website=Internet Encyclopedia of Philosophy|access-date=2019-12-05}}</ref>
* [[Misleading vividness]] is a kind of hasty generalization that appeals to the senses.
* Statistical special pleading occurs when the interpretation of the relevant statistic is "massaged" by looking for ways to reclassify or requantify data from one portion of results, but not applying the same scrutiny to other categories.<ref name="Fischer1970">{{citation |title = Historians' Fallacies: Toward A Logic of Historical Thought |publisher= HarperCollins |isbn= 978-0-06-131545-9 |year=1970 |location= New York |oclc= 185446787 |series= Harper torchbooks |edition= first  |first= D. H. |last= Fischer |author-link= David Hackett Fischer |pages= 110–113 |url= https://archive.org/stream/HistoriansFallaciesTowardALogicOfHistoricalThought/historians_fallacies_toward_a_logic_of_historical_thought#page/n131/mode/2up}}</ref>

== Underpowered generalization ==
{{redirect|Over-extension|the error common in language-learning|Errors in early word use}}
'''Underpowered generalization''' is an [[informal fallacy]] of faulty generalization, which involves reaching an [[inductive reasoning|inductive]] [[generalization]] based on insufficient [[evidence]]<ref name=":3" />—essentially making a rushed conclusion without considering all of the variables or enough evidence. In [[statistics]], it may involve basing broad conclusions regarding the statistics of a [[Statistical survey|survey]] from a small [[Sampling (statistics)|sample group]] that fails to sufficiently represent an entire population.<ref name=":1" /><ref name="FallacyHasty">{{cite web | title=Fallacy: Hasty Generalization (Nizkor Project) | access-date=2008-10-01 | url=http://www.nizkor.org/features/fallacies/hasty-generalization.html | url-status=dead | archive-url=https://web.archive.org/web/20081217061525/http://www.nizkor.org/features/fallacies/hasty-generalization.html | archive-date=2008-12-17 }}</ref><ref>{{Cite web|url=http://www.ditext.com/fearnside/1.html|title=Fallacy|website=www.ditext.com|access-date=2019-12-05}}</ref>  Its opposite fallacy is called [[slothful induction]], which consists of denying a reasonable conclusion of an inductive argument (e.g. "it was just a coincidence").

===Examples===

Hasty generalization usually follows the pattern:

#X is true for A.
#X is true for B.
#Therefore, X is true for C, D, E, etc.

For example, if a person travels through a town for the first time and sees 10 people, all of them children, they may erroneously conclude that there are no adult residents in the town.

Alternatively, a person might look at a number line, and notice that the number 1 is a [[square number]]; 3 is a [[prime number]], 5 is a prime number, and 7 is a prime number; 9 is a square number; 11 is a prime number, and 13 is a prime number. From these observations, the person might claim that all odd numbers are either prime or square, while in reality, 15 is an example that disproves the claim.

===Alternative names===
The fallacy is also known as:
*Illicit generalization
*Fallacy of insufficient sample
*Generalization from the particular
*Leaping to a conclusion
*Blanket statement
*Hasty induction
*Law of small numbers
*Unrepresentative sample
*''[[Secundum quid]]''

When referring to a generalization made from a single example, the terms "fallacy of the lonely fact",<ref name="Fischer">{{Cite book |first=David Hackett |last=Fischer |title=Historians' Fallacies: Toward a Logic of Historical Thought |year=1970 |publisher=HarperCollins |isbn=978-0-06-131545-9 |url=https://archive.org/details/historiansfallac00fisc |url-access=registration |pages=[https://archive.org/details/historiansfallac00fisc/page/109 109]–110}}</ref> or the "fallacy of proof by example", might be used.<ref>{{cite web |url=http://www.auburn.edu/~marchjl/fallacies.htm |title=Logical Fallacies |first=Jamie |last=Marchant |access-date=2011-04-26 |url-status=dead |archive-url=https://archive.is/20120630223544/http://www.auburn.edu/~marchjl/fallacies.htm |archive-date=2012-06-30 }}</ref><ref name=":0" />

When evidence is intentionally excluded to bias the result, the fallacy of exclusion—a form of [[selection bias]]—is said to be involved.<ref name="UnrepresentativeSample">{{cite web | title=Unrepresentative Sample | url=http://www.changingminds.org/disciplines/argument/fallacies/unrepresentative_sample.htm | access-date=2008-09-01 | url-status=live | archive-url=https://web.archive.org/web/20080415203831/http://changingminds.org/disciplines/argument/fallacies/unrepresentative_sample.htm | archive-date=2008-04-15 }}</ref>

==See also==
{{columns-list|colwidth=22em|
* {{annotated link|Accident (fallacy)}}
* {{annotated link|Association fallacy}}
* {{annotated link|Availability bias}}
* {{annotated link|Blind men and an elephant}}
* {{annotated link|Cherry picking (fallacy)}}
* {{annotated link|Cognitive distortion}}
* {{annotated link|Confirmation bias}}
* {{annotated link|Converse accident}}
* {{annotated link|Generalization (logic)}}
* {{annotated link|Generalization error}}
* {{annotated link|Hypercorrection}}
* {{annotated link|Package-deal fallacy}}
* {{annotated link|Pooh-pooh}}
* {{annotated link|Problem of induction}}
* {{annotated link|Statistical significance}}
* {{annotated link|Stereotype}}
* {{annotated link|Straw man}}
* {{annotated link|Syllogism}}
}}

==References==
<references />

{{Fallacies}}

[[Category:Inductive fallacies]]