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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 ...
Argument from ignorance. Argument from ignorance (from Latin: argumentum ad ignorantiam), also known as appeal to ignorance (in which ignorance represents "a lack of contrary evidence"), is a fallacy in informal logic. The fallacy is committed when one asserts that a proposition is true because it has not yet been proven false or a proposition ...
Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.
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 ...
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 ...
The argument from authority is a logical fallacy, [2] and obtaining knowledge in this way is fallible. [3][4] However, in particular circumstances, it is sound to use as a practical although fallible way of obtaining information that can be considered generally likely to be correct if the authority is a real and pertinent intellectual authority ...
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).
Affirming a disjunct. Affirming a disjunct is a fallacy. The formal fallacy of affirming a disjunct also known as the fallacy of the alternative disjunct or a false exclusionary disjunct occurs when a deductive argument takes the following logical form: [1] A or B. A.