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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 ...
All horses are the same color is a falsidical paradox that arises from a flawed use of mathematical induction to prove the statement All horses are the same color. [1] There is no actual contradiction, as these arguments have a crucial flaw that makes them incorrect. This example was originally raised by George Pólya in a 1954 book in ...
Mind projection fallacy – assuming that a statement about an object describes an inherent property of the object, rather than a personal perception. Moralistic fallacy – inferring factual conclusions from evaluative premises in violation of fact–value distinction (e.g.: inferring is from ought).
In mathematics, proof by contrapositive, or proof by contraposition, is a rule of inference used in proofs, where one infers a conditional statement from its contrapositive. [15] In other words, the conclusion "if A , then B " is inferred by constructing a proof of the claim "if not B , then not A " instead.
Circular reasoning (Latin: circulus in probando, "circle in proving"; [1] also known as circular logic) is a logical fallacy in which the reasoner begins with what they are trying to end with. [2] Circular reasoning is not a formal logical fallacy, but a pragmatic defect in an argument whereby the premises are just as much in need of proof or ...
A formal fallacy, deductive fallacy, logical fallacy or non sequitur (Latin for "it does not follow") is a flaw in the structure of a deductive argument that renders the argument invalid. The flaw can be expressed in the standard system of logic. [ 1 ] Such an argument is always considered to be wrong.
Proof by example. 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 ...
A faulty generalization is an informal fallacy wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances of that phenomenon. It is similar to a proof by example in mathematics. [1] It is an example of jumping to conclusions. [2] For example, one may generalize about all people or all ...
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