Inductive reasoning is a way of thinking that uses comparisons to reach conclusions.

Inferences made from one or more premises are typically processed in four stages: (1) observation (the collection of facts); (2) analysis (the classification of the collected facts and then the organization of them into identifiable patterns); (3) inference (the inference of generalizations from the valid patterns); and (4) confirmation (the testing of the inference through further observations).

Inductive reasoning was known to have been used by English philosopher and scientist Francis Bacon (1561–1626) when he used its methods to understand nature via unbiased, neutral observations. Induction was later derived from the mathematical study of probability by French mathematician and physicist Blaise Pascal (1623–1662) and French lawyer and mathematician Pierre de Fermat (1601–1665) during the middle part of the seventeenth century.

From its conception to the early nineteenth century, probability was used primarily to draw statistical conclusions from large populations and to assess the risks in games of chance. De Laplace widened the usefulness of probability with his theoretical work in science, which helped to create inductive reasoning, along with other methods of probability.

When inductive reasoning is used, the approach is usually founded on Bayes' theorem, also called Bayes’ rule, which is a theorem of probability first developed by English statistician and philosopher Thomas Bayes (1702–1761). The theorem was first published by Bayes in 1764 in “An Essay Toward Solving a Problem in the Doctrine of Chances.”

In essence, Bayes’ theorem finds the actual (real) probability of an event based on the results of tests, along with the known error rates (such as false positives and false negatives). It uses a simple mathematical formula for calculating conditional probabilities.

In inductive arguments, conclusions contain more information than in the premises; thus, the amount of knowledge is greater in the conclusion than in its related premises. For such arguments, if the premises are assumed to be true, then it is still possible for the conclusion to be false. For the most part, premises within inductive reasoning support its conclusion in one of two ways: strong inductive argument or weak inductive argument.

A strong inductive argument is one in which the premises support the conclusion so that it is probable that the conclusion is true (however, it is still possible for the premises to be true and the conclusion to be false). An inductive argument that is strong and has all true premises is called a cogent argument. A weak inductive argument is the other possibility. In this case, the premises are assumed to be true but it is not probable that the conclusion is true. An example of a cogent argument begins with the premise that “All known stars are round,” and results in the conclusion that “Therefore, all stars are probably round.”

When children, for example, use inductive thinking or reasoning, they engage in the evaluation and comparison of facts to reach a conclusion. Inductive reasoning progresses from observations of individual cases to the development of a generality. For example, if children put their hand into a bag of candy and withdraw three pieces, all of which are blue, they may conclude that all the candy is blue. However, it is still possible for the next piece of candy withdrawn from the bag not to be blue.

Inductive reasoning (which is based on observations) is often confused with deductive thinking (or deduction, which is based on theory); in the latter, general principles or conditions are applied to specific instances or situations. In deduction, the conclusion of a deductive argument is certaintly true, whereas the conclusion of an inductive argument is deemed probably true.

Generally, inductive reasoning is widely used in science, such as in psychology, to form hypotheses and theories. Further, deductive reasoning allows those hypotheses and theories to be applied to specific situations.

*See also* Deductive reasoning
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Harman, Gilbert, and Sanjeev Kulkarni. *Reliable Reasoning: Induction and Statistical Learning Theory*. Cam-bridge: MIT Press, 2007.

Lipson, Marc, and Seymour Lipschutz. *Probability*. New York: McGraw-Hill, 2011.

Bradford, Alina. “Deductive Reasoning vs. Inductive Reasoning.” Live Science. http://www.livescience.com/21569deduction-vs-induction.html (accessed August 6, 2015).

Dartmouth College. “Logical Basis of Hypothesis Testing in Scientific Research.” http://www.dartmouth.edu/~bio125/logic.Giere.pdf (accessed August 6, 2015).

American Psychological Association, 750 First St. NE, Washington, DC, 20002, (202) 336-5500, (800) 3742721, http://www.apa.org .

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