induction

n.

1. 1. The act or an instance of inducting.
   2. A ceremony or formal act by which a person is inducted, as into office or military service.
2. Electricity.
   1. The generation of electromotive force in a closed circuit by a varying magnetic flux through the circuit.
   2. The charging of an isolated conducting object by momentarily grounding it while a charged body is nearby.
3. Logic.
   1. The process of deriving general principles from particular facts or instances.
   2. A conclusion reached by this process.
4. Mathematics. A two-part method of proving a theorem involving an integral parameter. First the theorem is verified for the smallest admissible value of the integer. Then it is proven that if the theorem is true for any value of the integer, it is true for the next greater value. The final proof contains the two parts.
5. The act or process of inducing or bringing about, as:
   1. Medicine. The inducing of labor, whereby labor is initiated artificially with drugs such as oxytocin.
   2. Medicine. The administration of anesthetic agents and the establishment of a depth of anesthesia adequate for surgery.
   3. Biochemistry. The process of initiating or increasing the production of an enzyme, as in genetic transcription.
   4. Embryology. The process by which one part of an embryo causes adjacent tissues or parts to change form or shape, as by the diffusion of hormones or other chemicals.
6. Presentation of material, such as facts or evidence, in support of an argument or proposition.
7. A preface or prologue, especially to an early English play.

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induction

An effect in electrical systems in which electrical currents store energy temporarily in magnetic fields before that energy is returned to the circuit.

The process of generating an electric current in a circuit from the magnetic influence of an adjacent circuit as in a transformer or capacitor.

Electrical induction is also the principle behind the write head on magnetic disks and earlier read heads. To create (write) the bit, current is sent through a coil that creates a magnetic field which is discharged at the gap of the head onto the disk surface as it spins by. To read the bit, the magnetic field of the bit "induces" an electrical charge in the head as it passes by the gap. See inductor.

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noun

1. The act or process of formally admitting a person to membership or office: inaugural, inauguration, initiation, installation, instatement, investiture. See accept/reject.
2. Compulsory enrollment in military service: conscription, draft, levy. See give/take/reciprocity.
3. A short section of preliminary remarks: foreword, introduction, lead-in, overture, preamble, preface, prelude, prolegomenon, prologue. See start/end, words.

n

Definition: taking in, initiation
Antonyms: blackballing, expulsion, rejection

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n

The act or process of inducing or causing to occur.

n. enlistment into military service.

See the Introduction, Abbreviations and Pronunciation for further details.

Using the observation of particular initial cases in order to infer a general law from them. The researcher devises a general law to fit the observations—such as ‘what goes up must come down’—and then searches for examples which disprove that law; if any are found, the law is reformulated until it fits these exceptions. When no new discrepancies can be found (although this is a rather subjective decision), the generalization is accepted. Compare with deduction.

induction, an older word for the prologue or introduction to a work. The introductory episode of Shakespeare's The Taming of the Shrew, for example, is called the induction.

1. In air conditioning, the entrainment of air in a room by the flow of a stream of primary air from an air outlet.
2. The process by which current in one conductor induces an electric current in a nearby conductor.

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The term is most widely used for any process of reasoning that takes us from empirical premises to empirical conclusions supported by the premises, but not deductively entailed by them. Inductive arguments are therefore kinds of ampliative argument, in which something beyond the content of the premises is inferred as probable or supported by them. Induction is, however, commonly distinguished from arguments to theoretical explanations, which share this ampliative character, by being confined to inference in which the conclusion involves the same properties or relations as the premises. The central example is induction by simple enumeration, where from premises telling that Fa, Fb, Fc…, where a, b, c, are all of some kind G, it is inferred that Gs from outside the sample, such as future Gs, will be F, or perhaps that all Gs are F. If this, that, and the other person deceive them, children may well infer that everyone is a deceiver. Different but similar inferences are those from the past possession of a property by some object to the same object's future possession of the same property, or from the constancy of some law-like pattern in events and states of affairs to its future constancy: all objects we know of attract each other with a force inversely proportional to the square of the distance between them, so perhaps they all do so, and always will do so.

The rational basis of any such inference was challenged by Hume, who believed that induction presupposed belief in the uniformity of nature, but that this belief had no defence in reason, and merely reflected a habit or custom of the mind. Hume was not therefore sceptical about the propriety of processes of induction, but sceptical about the role of reason in either explaining it or justifying it. Trying to answer Hume and to show that there is something rationally compelling about the inference is referred to as the problem of induction. It is widely recognized that any rational defence of induction will have to partition well-behaved properties for which the inference is plausible (often called projectible properties) from badly behaved ones for which it is not (see Goodman's paradox). It is also recognized that actual inductive habits are more complex than those of simple enumeration, and that both common sense and science pay attention to such factors as variations within the sample giving us the evidence, the application of ancillary beliefs about the order of nature, and so on (see Mill's methods). Nevertheless, the fundamental problem remains that any experience shows us only events occurring within a very restricted part of the vast spatial and temporal order about which we then come to believe things. See also confirmation, explanation, falsification, vindication.

A process of reasoning in which a general statement suggesting a regular association between two or more variables is derived from a series of specific empirical observations.

A term encompassing a variety of forms of inference, commonly, but not always, in contrast to deduction. If 'proposition' is defined as a thought expressible by a grammatical sentence having either prescriptive or descriptive force, 'inference' may be defined as a transition in thought between one or more propositions (premisses) and a further proposition (conclusion), where the premisses purport to be reasons for the conclusion. The conclusions of deductive inferences cannot be rejected without contradicting the thoughts contained in the premisses, and in this sense are already contained in the premisses. Deductive inferences were consequently classified by C. S. Peirce as 'explicative', while inferences whose conclusions were not already implicit in their premisses were called 'ampliative'. 'Induction' is sometimes used in the sense of 'ampliative inference'. Classically, however, following Aristotle's use of 'epagōgē' (from the Latin translation of which we have 'induction'), the term applies to a subclass of ampliative inferences, namely those in which the conclusion is more general (applies to a wider range of instances) than the premisses.

The root idea of a movement in thought from particular to general has given rise to the practice of applying the term 'induction' to two forms of inference which are in fact deductive. The first of these is complete induction (in Aristotle, 'deduction from induction, ex epagōgēs sullogismos'), where the premisses are all less general than the conclusion, but collectively exhaust the instances covered by the conclusion. If chimpanzees, gorillas, humans, etc. are found species by species to react in a certain way to a certain virus, and these species exhaust the class of primates, one may conclude that all primates react in this way to the given virus. The second is the large family of proof procedures used by mathematicians on a variety of order structures, the simplest example of which is numerical induction: if (1) F is a property of the number one and (2) if F is a property of the number n, then it is a property of n+1, then (1) and (2) together entail that F is a property of all (natural) numbers.

The narrower classical idea of induction as inference from particular to general excludes certain ampliative inferences involving probability, e.g. inferring that x is F from the high probability that a member of a class, C, to which x belongs, will be F. It also excludes ampliative inference from one or more descriptions of an individual case to some further descriptions of that case. (Where the further description stands as the best explanation of why the first descriptions apply to that case, Peirce distinguished what he regarded as a scientifically vital form of inference, and which he called 'hypothesis' or 'abduction'.)

It is clear from this account that ampliative inferences are by definition not deductions and hence not deductively valid. Where, in other words, an induction is not complete — that is, the cases covered in the premisses do not exhaust those referred to in the conclusion (e.g. when concluding that all chimpanzees react in a certain way to a certain virus on the basis of having examined any number, n, of chimpanzees) — the premisses may all be true and the conclusion false, and the inference may be reasonable but unfortunately misleading. This gives rise to the so-called problem of induction, but from a purely logical standpoint it can appear to be a matter of lamenting the fact that not all of the inferences which we make have the rigour and compulsion of deductions, coupled, perhaps, with the insinuation that only deductive inferences are rationally grounded. But, against the insinuation, it is far from obvious why good reasons for a conclusion must preclude its negation on pain of contradiction. It is clearly possible to distinguish good from bad reasoning which is not in this way absolutely compelling.

From the standpoint of certain epistemological presuppositions, however, the problem is acute. If we assume, as is done in traditional empiricism, that all our knowledge is founded on (sensory) observations of individual instances, inductive inference presents itself as the only, however doubtful, means at our disposal for building on this modest foundation the vast edifice of our beliefs about the natural world. Unless there are general statements whose truth can be known a priori, all premisses of our deductions must be reached by induction; and every attempt to infer what holds for some unobserved or unobservable case on the basis of what has been observed must explicitly or implicitly appeal to a general proposition, which can only rest on induction from observed cases.

But the most, it is held, we are able to observe in individual cases are certain similarities among them, and it seems reckless in the extreme to expect such similarities to appear elsewhere unless we can identify some cause or constraint which ensures that a pattern we have observed will occur elsewhere. However, in seeking such a causal constraint in what we observe, all we will find are further patterns of similarities in the features of what we observe which are constantly conjoined. We can find, in other words, no basis for a causal constraint which is not itself in need of the very justification that we are seeking to provide.

David Hume, who is the classic source for this problem (although he did not formulate it using the word 'induction'), considered whether a global principle such as the uniformity of nature could underwrite our inferences from observed to unobserved cases. But such a global principle seems a non-starter: nature is uniform only in certain respects, and in other respects is highly variable. This is reflected in our practice of making inductive inferences. In some cases it is reasonable to generalize on the basis of very few instances; in others a very large number of observed instances is no basis at all for a generalization. Traditional empiricism tends to obscure this difference because it presents all inductive inferences as ultimately proceeding by 'simple enumerations', which have to be assessed in the absence of any background of established beliefs and experimental techniques. Popular and oversimplified views of Karl Popper's response to Hume, namely that science does not rely on induction but on finding exceptions to its generalizations, are likewise based on the notion that induction is simply a matter of projecting a similarity in our experience of part of a class of cases onto the whole of that class (e.g. of expecting what we have observed in some chimpanzees to hold of all chimpanzees which have yet to be observed). In fact we move no closer to real science by saying that the aim is rather to find exceptions to such attempts at superficial generalization.

Francis Bacon rejected the procedure of applying a global principle as 'childish', insisting that induction must proceed 'by proper rejections and exclusions'. The underlying principle of this genuine Baconian induction (known as 'eliminative induction') is the control we exercise over the circumstances of our observations. We must, in other words, move beyond simply projecting our observations to cases not yet observed and project in the form of experimental hypotheses, which ascribe a network of links between circumstances, which can be varied, and phenomena, which we can observe. We have observed a link between heavy smoking and lung cancer, but do not yet know how the circumstances may be varied so as to interfere with the link (and therefore cannot yet explain why many heavy smokers do not get lung cancer). In this spirit Peirce defined induction as 'the operation of testing a hypothesis by experiment'.

J. S. Mill's 'four methods of experimental inquiry' were designed to help identify the laws and causal factors governing phenomena. We need (i) to find what is common among the differences in the instances that we have observed ('method of agreement') and (ii) to compare the instances in which the phenomena occur with those in which they do not ('method of difference'). We can (iii) 'subduct' from the phenomena all portions which we can assign to known causes and the remainder will be the effects of causes still to be determined ('method of residues'). And we can (iv) look for functional relations between variations in phenomena ('method of concomitant variations'). The application of such methods and the testing of the hypotheses which they yield evidently involve a procedure of thought which goes well beyond the projection of superficial similarities (expecting future crows to be black because all observed crows have been black); it requires an account of the causal mechanism, which we can then test by creating circumstances which would very likely not occur in nature without our intervention.

Arguably, traditional empiricism generalized inadequately on the procedures by which all humans learn about their environment. Some things are learned by simple habituation, developing a uniform response to similar stimuli, but a great deal of human learning involves interfering with the environment.

Such a response to traditional empiricism and the problem it has with induction will, however, appear to beg the question unless at the same time one calls into question the assumptions that observation consists in the passive reception of sensory qualities and that the concepts we apply to what we observe derive wholly from this source rather than, in a large and important part, from the control we are able to exercise over what we observe. Bacon, for one, saw that induction properly conducted (i.e. as experimental inquiry) needed to be used not only 'to discover axioms but also in the formation of notions'. If we allow that induction is a procedure through which we develop our concepts of what is or is not a (natural) possibility the traditional problem of induction appears in a quite different light.

(Published 1987)

— J. E. Tiles

Bibliography
• Bacon, F. (1620). The New Organon (1960 edn.), esp. Bk. I.
• Hume, D. (1739–40). A Treatise of Human Nature (1888 edn.), Bk. I, pt. iii.
• Mill, J. S. (1843). A System of Logic (1879 edn.), Bk. III.
• Peirce, C. S. (1955). Philosophical Writings of Peirce. Ed. J. Buchler, chs. 11–15.
• Swinburne, R. (ed.) (1974). The Justification of Induction.

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1. the process or act of inducing, or causing to occur, especially the production of a specific morphogenetic effect in the embryo through evocators or organizers, or the production of anesthesia or unconsciousness or parturition by use of appropriate agents.
2. the generation of an electric current or magnetic properties in a body because of its proximity to an electrified or magnetized object.

• i. period — the time from exposure to a non-infectious agent to the first appearance of the disease. Analogous to the incubation period but for non-infectious pathogenic agents.

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Dansk (Danish)
n. - induktion, indsættelse, indkaldelse, indsugning

Nederlands (Dutch)
inductie, installatie, opwekking (m.n. van weeën), oproep voor militaire dienst (V.S.)

Français (French)
n. - (Élec, Math, Philos, Tech) induction, (Méd) déclenchement (d'un accouchement), installation, (US, Mil) incorporation

Deutsch (German)
n. - Induktion, Amtseinführung, Herbeiführen, Auslösung, (Mil.) Einberufung

Ελληνική (Greek)
n. - επαγωγή, πρώτη γνωριμία, (προ)εισαγωγή, μύηση, (μτφ.) μπάσιμο, εγκατάσταση σε αξίωμα, ανάρρηση, (ηλεκτρ.) αυτεπαγωγή

Italiano (Italian)
induzione, installazione

Português (Portuguese)
n. - indução (f) (Log.), introdução (f), raciocínio (m)

Русский (Russian)
индукция, официальное введение в должность

Español (Spanish)
n. - inducción, admisión, instalación, iniciación

Svenska (Swedish)
n. - induktion (filos., fys. el. matem.), framkallande, anförande, installation, introduktion, inkallelse (amer. mil.)

中文（简体）(Chinese (Simplified))
就职, 入会, 就职仪式, 征召

中文（繁體）(Chinese (Traditional))
n. - 就職, 入會, 就職儀式, 徵召

한국어 (Korean)
n. - 유도, 귀납법, 전제, (성직) 취임식

日本語 (Japanese)
n. - 引き入れること, 誘導, 感応, 就任式, 入隊式, 帰納, 帰納法, 序幕, 緒言

العربيه (Arabic)
‏(الاسم) تنصيب, استقراء‏

עברית (Hebrew)
n. - ‮הכנסה לתפקיד, גיוס, השראה, זירוז לידה, התגייסות לצבא (ארה"ב), אינדוקציה, הסקת חוק כללי ממקרים פרטיים (לוגיקה), יצירת השראה מגנטית או חשמלית ע"י קירוב גוף מחושמל או ממוגנט, הצגה רשמית של תפקיד חדש, הפשטה‬

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