Inductive reasoning
method of reasoning in which a body of observations is synthesized to hypothesize a general principle
Inductive reasoning refers to a variety of methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but at best with some degree of probability. 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 premises provided.
Types
The types of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. There are also differences in how their results are regarded.
Inductive generalization
A generalization (more accurately, an inductive generalization) proceeds from premises about a sample to a conclusion about the population. The observation obtained from this sample is projected onto the broader population.
The proportion Q of the sample has attribute A.
Therefore, the proportion Q of the population has attribute A.
For example, if there are 20 balls—either black or white—in an urn: to estimate their respective numbers, a sample of four balls is drawn, three are black and one is white. An inductive generalization may be that there are 15 black and five white balls in the urn. However this is only one of 17 possibilities as to the actual number of each color of balls in the urn (the population) — there may have been 19 black and just 1 white ball, or only 3 black balls and 17 white, or any mix in between. The probability of each possible distribution being the actual numbers of black and white balls can be estimated using techniques such as Bayesian inference, where prior assumptions about the distribution are updated with the observed sample, or maximum likelihood estimation (MLE), which identifies the distribution most likely given the observed sample.
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