Faulty generalization

In logic and reasoning, a faulty generalization, similar to a proof by example in mathematics, is a 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.[1][2] It is an example of jumping to conclusions.[3] For example, one may generalize about all people or all members of a group, based on what they know about just one or a few people:

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

Faulty generalizations may lead to further incorrect conclusions. One may, for example, conclude that citizens of country X are genetically inferior, or that poverty is the fault of the poor.

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.[4] 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.[3]

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 (often unrepresentative or biased), to a conclusion about the population itself.[4]

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.
  • Fallacy of unrepresentative samples is a fallacy where a conclusion is drawn using samples that are unrepresentative or biased.[5]
  • 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.[6]

Hasty generalization
"Over-extension" redirects here. For the error common in language-learning, see Errors in early word use.

Hasty generalization is an informal fallacy of faulty generalization, which involves reaching an inductive generalization based on insufficient evidence[4]—essentially making a rushed conclusion without considering all of the variables. In statistics, it may involve basing broad conclusions regarding the statistics of a survey from a small sample group that fails to sufficiently represent an entire population.[2][7][8] 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:

  1. X is true for A.
  2. X is true for B.
  3. 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 which 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",[9] or the "fallacy of proof by example", might be used.[10][1]

When evidence is intentionally excluded to bias the result, the fallacy of exclusion—a form of selection bias—is said to be involved.[11]

gollark: It has not.
gollark: I should probably just disavow all knowledge of heavpoot.
gollark: I see.
gollark: How do they KNOW they tried to modify their memories?
gollark: Order beer and convert it to bee.

See also

References
  1. "The Definitive Glossary of Higher Mathematical Jargon — Proof by Example". Math Vault. 2019-08-01. Retrieved 2019-12-05.
  2. "Hasty Generalization". logicallyfallacious.com. Retrieved 2019-12-05.
  3. Dowden, Bradley. "Hasty Generalization". Internet Encyclopedia of Philosophy. Retrieved 2019-12-05.
  4. Nordquist, Richard. "Logical Fallacies: Examples of Hasty Generalizations". ThoughtCo. Retrieved 2019-12-05.
  5. Dowden, Bradley. "Fallacies — Unrepresentative Sample". Internet Encyclopedia of Philosophy. Retrieved 2019-12-05.
  6. Fischer, D. H. (1970), Historians' Fallacies: Toward A Logic of Historical Thought, Harper torchbooks (first ed.), New York: HarperCollins, pp. 110–113, ISBN 978-0-06-131545-9, OCLC 185446787
  7. "Fallacy: Hasty Generalization (Nizkor Project)". Archived from the original on 2008-12-17. Retrieved 2008-10-01.
  8. "Fallacy". www.ditext.com. Retrieved 2019-12-05.
  9. Fischer, David Hackett (1970). Historians' Fallacies: Toward a Logic of Historical Thought. HarperCollins. pp. 109–110. ISBN 978-0-06-131545-9.
  10. Marchant, Jamie. "Logical Fallacies". Archived from the original on 2012-06-30. Retrieved 2011-04-26.
  11. "Unrepresentative Sample". Archived from the original on 2008-04-15. Retrieved 2008-09-01.
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