Induction

Definition (Vincent E. Barry and Douglas J. Soccio)
Definition (Encyclopedia of World Problems and Human Potential)
Definition (Stephen F. Barker)
Definition (Richard E. Mayer)
Classification (Irving M. Copi)
Classification (Vincent E. Barry and Douglas J. Soccio)
Function (George Pólya)
Function (R. Harré)
Features (Alfred North Whitehead)
Features (Max Wertheimer)
Features (Alfred North Whitehead)
Features (Max Wertheimer)
Features (Wesley C. Salmon)
Distinction induction-deduction (Deobold B. Van Dalen)
Distinction induction-deduction (Wesley C. Salmon)
Distinction induction-deduction (Louise E. Rorabacher; Georgia Dunbar and Clement Dunbar)
Related Concepts: Analogy (George Pólya)
Related Concepts: Analogy (Vincent E. Barry and Douglas J. Soccio)
Related concepts: Probability (Abraham Kaplan)

Definition

[1988, Third Edition] Vincent E. Barry and Douglas J. Soccio, Practical Logic. Holt, Rinehart and Winston, New York
“An inductive argument is one whose conclusion is claimed to be more or less probable, but not certain."
An inductive argument that’s justified is one whose premises lend its conclusion a high degree of probability.” (Chapter 1, p. 12)

VV. AA. Encyclopedia of World Problems and Human Potential. Union of International Associations eds. K. G. Saur, München, Second Edition
"1. Any inference whose premises do not entails its conclusions.
2. Inference from particular instances of conjunctions of characteristics that a conjunction may be held to be universal." (KC0014)

[1989, First published 1965] Stephen F. Barker, The Elements of Logic, McGraw-Hill, New York
“An inductive argument has to have a conclusion embodying empirical conjectures about the world that do not follow deductively what its premises say - in an inductive argument the conclusion is not wholly ‘contained in’ its premises. Consequently, in an inductive argument the truth of the premises cannot absolutely ensure the truth of the conclusion, and the argument cannot be demonstrative in the way that valid deduction is. But if the premises of an inductive argument are true and the reasoning is good, then it is reasonable to believe the conclusion; the conclusion is probably true.” (Chapter 7, p. 181)

[1992, Second Edition] Richard E. Mayer, Thinking, Problem Solving, Cognition, W. H. Freeman & Co. New York
“... inductive thinking ... involves inducing or formulating or extrapolating a rule based on limited information.”
“Inductive thinking ... can never result in a provable rule because new information may come along that violates the induced rule; since induced rules are based on a limited set of information, they require the thinker to go beyond the information, to generalize.” (Chapter V, p. 116)

Classification

[1982, Sixth Edition] Irving M. Copi, Introduction to Logic. Macmillan, New York
“Typical kinds of inductive argument are the following.
First are those that proceed by analogy, in which two or more things acknowledged to resemble each other in some respects are inferred to resemble each other in some further respect also.
Second are those that proceed by generalization, in which from the premiss that a number of things of a given kind all have some further characteristic, it is inferred that all things of that kind have that characteristic.
Third are those that infer a causal connection between events or characteristics that have been observed to go together regularly.” (Chapter 1, p. 54)

[1988, Third Edition] Vincent E. Barry and Douglas J. Soccio, Practical Logic. Holt, Rinehart and Winston, New York,
- Strong or Univeral Generalizations : “A strong, or universal, generalization is a statement that asserts that something is true of all members of a class.” (e.g. ‘all humans are vertebrates’).
- Weak or Particular Generalization : "A weak, or particular, generalization is a statement that asserts that something is true of some members of a class." (e.g. 'students who come to class prepared do better than those who don't').
- Statistical Generalizations : “A statistical generalization is a statement that asserts that something is true of a percentage of a class.” (e.g. ‘Seventy five per cent of voters favours a reduction in property taxes').
(Chapter 9, pp. 182-183)

Functions

[1990, First published 1945] George Pólya, How to Solve It, Penguin Books, Harmondsworth
“Induction tries to find regularity and coherence behind the observations. Its most conspicuous instruments are generalization, specialization, analogy.” (Part III, p. 117)

[1963] R. Harré, An Introduction to the Logic of the Sciences, Macmillan & Co. London
“Economy of thought is an obvious aim in description and generalization clearly satisfies it without loss of adequacy, for in a general statement the least that we do is to sum up the information conveyed by many particular statements.”
“There is still another job which generalizations do for us. They play an important part in reasoning for our rules of inference are derived from them.”
“... when a thing has been identified as a member of a class we may also ascribe to it the further property which our generalizations ascribes to members of the class." (Chapter 1, pp. 15-17)

Features

[1928] Alfred North Whitehead, Science and the Modern World. Cambridge University Press, Cambridge
“... I do not hold induction to be in its essence the derivation of general laws.
It is the divination of some characteristics of a particular future from the known characteristics of a particular past. The wider assumption of general laws holding for all cognizable occasions appears a very unsafe addendum to attach to this limited knowledge.” (Chapter III, p. 56)

[1968, First Published 1945] Max Wertheimer , Productive Thinking, Tavistock Publications, London, 1968
"It is widely believed that inductive logic adds to the classical rules and operations the emphasis on:
- empirical observations
- careful gathering of facts
- studying problems empirically
- introducing experimental methods
- correlating facts
- developing crucial tests."
(Introduction, p. 8)

[1973, Second Edition] Wesley C. Salmon , Logic, Prentice-Hall, Englewood Cliffs, New Jersey
- “I - If all the premises are true, the conclusion is probably true but not necessarily true”.
- “II - The conclusion contains information not present, even implicitly, in the premises.”
(Chapter 1, p. 14)

[1989, First published 1965] Stephen F. Barker, The Elements of Logic, McGraw-Hill, New York
“An inductive argument establishes a high probability for its conclusion, provided that it is possible to regard the conclusion as a hypothesis supplying the best explanation of the data contained in the premises.”
(Chapter 7, p. 209)

Distinction induction-deduction

[1979, First published 1962] Deobold B. Van Dalen, Understanding Educational Research. An Introduction McGraw-Hill Book Company, New York
“... inductive reasoning has been devised to complement deductive reasoning as a means of searching for knowledge. In inductive reasoning, an inquiry is initiated by observing particular instances (concrete facts). From an examination of these facts, a general conclusion is established about the whole class to which these particular instances belong. General conclusions that are arrived at through induction may be used as major premises for deductive inferences.” (Chapter 1, p. 10)

[1973, Second Edition] Wesley C. Salmon , Logic, Prentice-Hall, Englewood Cliffs, New Jersey
“Deductive and inductive arguments fulfil different functions. The deductive argument is designed to make explicit the content of the premises; the inductive argument is designed to extend the range of our knowledge.” (Chapter 1, p. 15)

[1988, Ninth Edition] Louise E. Rorabacher; Georgia Dunbar and Clement Dunbar , Assignments in Exposition. Harper & Row, New York
“With inductive reasoning we add one piece of information to another until we have enough evidence to draw a conclusion.”
“With deductive reasoning we use earlier conclusions, reached inductively by ourselves or others, to answer new questions about material.” (Unit 14, p. 290)

Related Concepts : Analogy

[1990, First Published 1945] George Pólya , How to Solve It, Penguin Books, Harmondsworth
“Inference by analogy appears to be the most common kind of conclusion, and it is possibly the most essential kind. It yields more or less plausible conjectures which may or may not be confirmed by experience and stricter reasoning. The chemist, experimenting on animals in order to foresee the influence of his drugs on humans, draws conclusions by analogy.” (Part III, p. 43)

[1988, Third Edition] Vincent E. Barry and Douglas J. Soccio, Practical Logic. Holt, Rinehart and Winston, New York
"An argument from analogy is an inductive argument in which a known similarity that two things share is used as evidence for concluding that the two things are similar in other respects.” (Chapter 9, p. 189)
“There are four factors that affect the strength of analogies :
1) The number of entities involved. “Ordinarily, the more instances lying at the base of the analogy, the greater the likelihood of its conclusion.”
2) The number of relevant likenesses. “The more relevant likenesses among the instances, the stronger the analogical argument and more likely its conclusion.”
3) The number of differences. “The more strengthening differences between the things compared, the stronger the analogical argument itself.” (e.g. different drivers with different styles of driving, driving in different weather conditions, being happy with a certain make of car). “The more weakening differences, or disanalogies, between the things compared, the weaker the analogical argument itself.”
4) The strength of the conclusion relative to the premises. "The greater the margin for error [allowed] in the analogical conclusion, the stronger the argument.”
(Chapter 9, pp. 191-192)

Related Concept : Probability

[1964] Abraham Kaplan , The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania
“... inductive logic is now generally agreed to rest on some theory of probability however that be interpreted. The conclusions of an inductive inference are never established absolutely, but only to some degree or other. To just what degree depends, inescapably, on the premises from which it is inferred - that is, on the state of our knowledge.” (Chapter VI, p. 233)

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