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1 A form of reasoning, also called empirical induction, in which a general law or principle is inferred from particular instances that have been observed. Many people believe that this form of reasoning works in practice, and it is widely believed to form the basis of all empirical sciences, but the Scottish philosopher David Hume (1711–76) showed in A Treatise of Human Nature in 1739 that induction is logically invalid: from the premise All swans that have been observed are white it is not valid to conclude that Therefore, all swans are white. There is a missing premise, that All swans have been observed, which is not true and could never be true of any universal proposition in science that is supposed to apply throughout time and space. Hume pointed out that the uniformity of nature might justify induction, in the form of the premise Future observations will resemble past observations, but this could be justified only by a question-begging appeal to induction itself, and in any event it is not true in general—for example, there are black swans in Australia. This apparent inconsistency is called the problem of induction or Hume's problem, and it is solved by the insight that empirical evidence is used to falsify rather than to confirm hypotheses. See also falsifiability, Goodman's paradox, Hempel's paradox, hypothetico-deductive method. Compare deduction.

2 A mathematical technique, also called mathematical induction, for proving that a statement or proposition (1) is true in general, or (equivalently) that each of an infinite sequence of statements is true, by proving that the first statement in the sequence is true, and then that if any one of the statements is true it follows that the next one is also true.

3 Indirect generation of a sensory experience without direct stimulation of the corresponding sensory receptors, by stimulation of adjacent or related sensory processes. See colour induction, induced motion, visual induction, warmth contrast.

4 The name given by the Russian physiologist Ivan Petrovich Pavlov (1849–1936) to positive induction, in which the response to an excitatory conditioned stimulus is increased if it is immediately preceded by an inhibitory one, and to negative induction, in which the response to an inhibitory conditioned stimulus is increased if it is immediately preceded by an excitatory one.

5 The process whereby morphogenic differentiation is stimulated in a developing embryo by Müllerian inhibiting substance, testosterone, or other hormones or substances.

6 A formal process of introduction to membership of a group or organization.

7 A shortened name for enzyme induction. induce vb. inductive adj. [From Latin inducere to lead in, from in in+ducere, inductum to lead+-ion indicating an action, process, or state]

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