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If a range of factors are believed to cause a range of phenomena, and we have matched all the factors, except one, with all the phenomena, except one, then the remaining phenomenon can be attributed to the remaining factor. Symbolically, the Method of Residue can be represented as: A B C occur together with x y z B is known to be the cause of y
The proof of this is derived from a game between the induction and the environment. Essentially, any computable induction can be tricked by a computable environment, by choosing the computable environment that negates the computable induction's prediction. This fact can be regarded as an instance of the no free lunch theorem.
An inductive problem specifies a range of epistemically possible worlds over which to succeed and determines what sort of output would be correct, where correctness may embody both content and truth (or some analogous virtue like empirical adequacy). Each possible world produces an input stream which the inductive method processes sequentially ...
This is not the same as reliability, which is the extent to which a measurement gives results that are very consistent. Within validity, the measurement does not always have to be similar, as it does in reliability. However, just because a measure is reliable, it is not necessarily valid. E.g. a scale that is 5 pounds off is reliable but not valid.
That is, the mechanism by which the measurement is made is different; each method is dependent on an unrelated natural phenomenon. For example, the accuracy of laser range-finding measurements is based on the scientific understanding of lasers, while satellite pictures and metre-sticks (or yardsticks) rely
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]