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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.
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.
A statistical syllogism (or proportional syllogism or direct inference) is a non-deductive syllogism. It argues, using inductive reasoning , from a generalization true for the most part to a particular case.
For example, when predicting how a person will react to a situation, inductive reasoning can be employed based on how the person reacted previously in similar circumstances. It plays an equally central role in the sciences , which often start with many particular observations and then apply the process of generalization to arrive at a universal ...
As an example of the method of difference, consider two similar countries. Country A has a centre-right government, a unitary system and was a former colony. Country B has a centre-right government, a unitary system but was never a colony.
Because statisticians often associate statistical inference with induction, Popper's philosophy is often said to have a hidden form of induction. For example, Mayo wrote "The falsifying hypotheses ... necessitate an evidence-transcending (inductive) statistical inference. This is hugely problematic for Popper". [61]