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. It is an example of jumping to conclusions. 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. 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.
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.
Faulty generalization is also a mode of thinking that takes the experiences of one person or one group, and incorrectly extends it to another.
- 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.
- 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.
Underpowered generalization is an informal fallacy of faulty generalization, which involves reaching an inductive generalization based on insufficient evidence—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 survey from a small sample group that fails to sufficiently represent an entire population. 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").
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.
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
- Accident (fallacy) – Informal fallacy
- Association fallacy
- Availability bias
- Blind men and an elephant – Parable from the ancient Indian subcontinent, whence it has been widely diffused
- Cherry picking (fallacy)
- Cognitive distortion – Exaggerated or irrational thought pattern
- Confirmation bias – Tendency of people to favor information that confirms their beliefs or values
- Converse accident – Informal fallacy
- Generalization (logic)
- Generalization error – In machine learning, a measure of how accurately an algorithm is able to predict outcome values for previously unseen data
- Hypercorrection – Non-standard language usage from the over-application of a perceived prescriptive rule
- Package-deal fallacy
- Pooh-pooh – Fallacy in informal logic
- Problem of induction – Epistemological question of whether inductive reasoning leads to definitive knowledge understood in the classic philosophical sense
- Statistical significance – Concept in inferential statistics
- Stereotype – Generalized belief about a particular category of people
- Straw man – Type of informal fallacy
- Syllogism – Type of logical argument that applies deductive reasoning
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