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Inductive reasoning refers to a variety of methods of reasoning in which broad generalizations or principles are derived from a set of observations. [1] [2] Unlike deductive reasoning (such as mathematical induction), where the conclusion is certain, given the premises are correct, inductive reasoning produces conclusions that are at best probable, given the evidence provided.
In inductive reasoning, one makes a series of observations and infers a claim based on them. For instance, from a series of observations that a woman walks her dog by the market at 8 am on Monday, it seems valid to infer that next Monday she will do the same, or that, in general, the woman walks her dog by the market every Monday.
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.
Despite its name, mathematical induction is a method of deduction, not a form of inductive reasoning. In proof by mathematical induction, a single "base case" is proved, and an "induction rule" is proved that establishes that any arbitrary case implies the next case.
Uniformity conjecture: diophantine geometry: n/a: Unique games conjecture: number theory: n/a: Vandiver's conjecture: number theory: Ernst Kummer and Harry Vandiver: Virasoro conjecture: algebraic geometry: Miguel Ángel Virasoro: Vizing's conjecture: graph theory: Vadim G. Vizing: Vojta's conjecture: number theory: ⇒abc conjecture: Paul ...
Some plausible reasoning methods due to George Polya. George Polya in his two volume book titled Mathematics and Plausible Reasoning [3] [4] presents plausible reasoning as a way of generating new mathematical conjectures. To Polya, “a mathematical proof is demonstrative reasoning but the inductive evidence of the physicist, the ...
Despite its name, mathematical induction differs fundamentally from inductive reasoning as used in philosophy, in which the examination of many cases results in a probable conclusion. The mathematical method examines infinitely many cases to prove a general statement, but it does so by a finite chain of deductive reasoning involving the ...
Francis Bacon, articulating inductivism in England, is often falsely stereotyped as a naive inductivist. [11] [12] Crudely explained, the "Baconian model" advises to observe nature, propose a modest law that generalizes an observed pattern, confirm it by many observations, venture a modestly broader law, and confirm that, too, by many more observations, while discarding disconfirmed laws. [13]