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In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof. [1] [2] The structure, argument form and formal form of a proof by example generally proceeds as follows ...
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. [55]
An argument that actually contains premises that are all the same as the assertion is thus proof by assertion. This fallacy is sometimes used as a form of rhetoric by politicians, or during a debate as a filibuster. In its extreme form, it can also be a form of brainwashing. [1] Modern politics contains many examples of proofs by assertion.
List of fallacies with clear examples, infidels.org; Interactive Syllogistic Machine A web based syllogistic machine for exploring fallacies, figures, and modes of syllogisms. Logical Fallacies and the Art of Debate, csun.edu; Stephen Downes Guide to the Logical Fallacies, onegoodmove.org; Explain fallacies, what they are and how to avoid them ...
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
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.
Overgeneralization is a fallacy occurring when a statistic about a particular population is asserted to hold among members of a group for which the original population is not a representative sample. For example, suppose 100% of apples are observed to be red in summer.
Proving a negative or negative proof may refer to: Proving a negative, in the philosophic burden of proof; Evidence of absence in general, such as evidence that there is no milk in a certain bowl; Modus tollens, a logical proof; Proof of impossibility, mathematics; Russell's teapot, an analogy: inability to disprove does not prove