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Hasty generalization (fallacy of insufficient statistics, fallacy of insufficient sample, fallacy of the lonely fact, hasty induction, secundum quid, converse accident, jumping to conclusions) – basing a broad conclusion on a small or unrepresentative sample.
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 ...
Generalizing quickly and sloppily (hasty generalization) (secundum quid) Using an argument's connections to other concepts or people to support or refute it, also called "guilt by association" (association fallacy) Claiming that a lack of proof counts as proof (appeal to ignorance) In humor, errors of reasoning are used for comical purposes.
The fallacy can take many forms, such as cherry picking, hasty generalization, proof by assertion, and so on. [1] The fallacy does not mean that every single instance of sense data or testimony must be considered a fallacy, only that anecdotal evidence, when improperly used in logic, results in a fallacy.
Together with the axiom of choice (see below), these are the de facto standard axioms for contemporary mathematics or set theory.They can be easily adapted to analogous theories, such as mereology.
The connection of generalization to specialization (or particularization) is reflected in the contrasting words hypernym and hyponym.A hypernym as a generic stands for a class or group of equally ranked items, such as the term tree which stands for equally ranked items such as peach and oak, and the term ship which stands for equally ranked items such as cruiser and steamer.
[16]: 147 The generalization, in this case, ignores that insanity is an exceptional case to which the general rights of property do not unrestrictedly apply. Hasty generalization , on the other hand, involves the converse mistake of drawing a universal conclusion based on a small number of instances.
The full generalization rule allows for hypotheses to the left of the turnstile, but with restrictions.Assume is a set of formulas, a formula, and () has been derived. The generalization rule states that () can be derived if is not mentioned in and does not occur in .