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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 ...
For example, one might argue that it is valid to use inductive inference in the future because this type of reasoning has yielded accurate results in the past. However, this argument relies on an inductive premise itself—that past observations of induction being valid will mean that future observations of induction will also be valid.
The classical model of scientific inquiry derives from Aristotle, [3] who distinguished the forms of approximate and exact reasoning, set out the threefold scheme of abductive, deductive, and inductive inference, and also treated the compound forms such as reasoning by analogy.
Though Solomonoff's inductive inference is not computable, several AIXI-derived algorithms approximate it in order to make it run on a modern computer. The more computing power they are given, the closer their predictions are to the predictions of inductive inference (their mathematical limit is Solomonoff's inductive inference). [12] [13] [14]
The validity of an inference depends on the form of the inference. That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference. An inference can be valid even if the parts are false, and can be invalid even if some parts are true.
Some have argued that although inductive inference is often obscured by language—as in news reporting that experiments have proved a substance is safe—and that enumerative induction ought to be tempered by proper clarification, inductive inference is used liberally in science, that science requires it, and that Popper is obviously wrong. [107]
The history of scientific method considers changes in the methodology of scientific inquiry, not the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of ...
If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance save one in common, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or cause, or an indispensable part of the cause, of the phenomenon.