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Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations. [1] [2] This article is concerned with the inductive reasoning other than deductive reasoning (such as mathematical induction), where the conclusion of a deductive argument is certain, given the premises are correct; in contrast, the truth of the ...
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.
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]
This raises the broader question of the relation of probability theory to inductive reasoning. Karl Popper argued that probability theory alone cannot account for induction. His argument involves splitting a hypothesis, H {\displaystyle H} , into a part that is deductively entailed by the evidence, E {\displaystyle E} , and another part.
Old knowledge-building methods were often not based in facts, but on broad, ill-proven deductions and metaphysical conjecture. Even when theories were based in fact, they were often broad generalisations and/or abstractions from few instances of casually gathered observations.
Backward induction is the process of determining a sequence of optimal choices by reasoning from the endpoint of a problem or situation back to its beginning using individual events or actions. [1] Backward induction involves examining the final point in a series of decisions and identifying the optimal process or action required to arrive at ...
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 ...