Deduction

Definition (Ernest H. Hutten)
Definition (Vincent E. Barry and Douglas J. Soccio)
Classification (Richard E. Mayer)
Function (Deobold B. Van Dalen)
Features (Abraham Kaplan)
Features (Wesley C. Salmon)
Features (Vincent E. Barry and Douglas J. Soccio)
Distinction-induction (Deobold B. Van Dalen)
Distinction-induction (Irving M. Copi)
Distinction-induction (Barbara Minto)
Related Concepts: Axiom (Morris Kline)
Related concepts: Syllogism (Aristotle)
Related concepts: Syllogism (John Stuart Mill)
Related concepts: Syllogism (Deobold B. Van Dalen)

Definition

[1962] Ernest H. Hutten, The Origins of Science. An inquiry into the foundations of western thought, Allen & Unwin, London
“By deduction, ... the content of the derived sentence remains, at best, the same as that of the premiss; otherwise, it decreases. This is what we mean by ‘deduction’, for we say that the method brings out what is contained in the premisses. That is, by a logical procedure like deduction we can never gain content, only lose it.” (Chapter XII, p. 156)

[1988, Third Edition] Vincent E. Barry and Douglas J. Soccio, Practical Logic. Holt, Rinehart and Winston, New York,
“A deductive argument is one whose conclusions is claimed to follow from its premises with logical certainty. In other words, in a proper deductive argument, it’s logically impossible for the argument’s premises to be true and its conclusion false.” (Chapter 1, p. 11)

Classification

[1992, Second Edition] Richard E. Mayer , Thinking, Problem Solving, Cognition, W. H. Freeman & Co. New York (1) Categorical syllogism
      All A are B; all B are C; Therefore all A are C.
(2) Linear syllogism
      A is greater than B; B is greater than C; therefore A is greater than C.
(3) Conditional syllogism
      If p then q; p is true; therefore q is true.
(from Chapter 5, p. 117)

Functions

[1979, First edition 1962] Deobold B. Van Dalen, Understanding Educational Research. An Introduction, McGraw-Hill Book Company, New York
“... researchers move back and forth between the operational, inductive activities of observing, defining, and accumulating facts and the conceptual, deductive activities of theorizing about facts and their relations to one another.” (Chapter 3, p. 53)

Features

[1964] Abraham Kaplan , The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania
“... the scientist, by a combination of careful observation, shrewd guesses, and scientific intuition arrives at a set of postulates governing the phenomena in which he is interested; from these he deduces observable consequences; he then tests these consequences by experiment, and so confirms or disconfirms the postulates, replacing them, where necessary, by others, and so continuing.” (Chapter 1, pp. 9-10)

[1973, Second Edition] Wesley C. Salmon, Logic, Prentice-Hall, Englewood Cliffs, New Jersey
- “I - If all of the premises are true, the conclusion must be true.”
- “II - All of the information or factual content in the conclusion was already contained, at least implicitly, in the premises.” (Chapter 1, p. 14)

[1988, Third Edition] Vincent E. Barry and Douglas J. Soccio , Practical Logic, Holt, Rinehart and Winston, New York
“When the premises of an argument logically entail a conclusion the argument is called valid. Validity, strictly speaking, applies only to deductive arguments.”
“A deductive argument that is sound is one that is true and valid.” (Chapter 13, p. 291)

Distinction deduction-induction

[1979, First edition 1962] Deobold B. Van Dalen , Understanding Educational Research. An Introduction, McGraw-Hill Book Company, New York
“Both deductive and inductive arguments have advantages and disadvantages. A deductive argument does not guarantee that the conclusion is true, but if the two premises are true, the deductive argument arrives at a conclusion that is necessarily true. The conclusion of the deductive argument, however, does not probe beyond that which is already known [in the premises]. In an imperfect inductive argument, the conclusion does contain information that is not present, even implicitly, in one of the premises (the observed instances). This type of argument is absolutely necessary if scholars are to extend knowledge. Through imperfect induction, however, an investigator merely arrives at conclusions of varying degree of probability. If all the premises (observed instances) are true, the conclusion is probably but not necessarily true. The possibility always exists that some unexamined instance of the class does not agree with the conclusion.” (Chapter 1, p. 12)

[1982, Sixth Edition] Irving M. Copi , Introduction to Logic. Macmillan, New York
“We characterize a deductive argument as one whose conclusion is claimed to follow from its premisses with absolute necessity not being a matter of degree and not depending in any way upon whatever else may be the case. And in sharp contrast we characterize an inductive argument as one whose conclusion is claimed to follow from its premisses only with probability, this probability being a matter of degree and dependent upon what else may be the case.”
(Chapter 1, p. 54)

[1991] Barbara Minto, The Pyramid Principle. B C A, London
“C. S. Peirce’s insight was that in any reasoning process you always deal with three distinct entities:
- A Rule (a belief about the way the world is structured)
- A Case (an observed fact that exists in the world)
- A Result (an expected occurrence given the application of the Rule in this Case).
The way in which you can consider yourself to be reasoning at any one time is determined by where you start in the process and what additional fact you know.
To illustrate the differences:
Deduction (1 Rule, 2 Case, 3 Result)
- Rule: If you put the price too high sales will go down.
- Case: You have put the price too high.
- Result: Therefore sales will go down.
Induction (1 Case, 2 Result, 3 Rule)
- Case: We have put the price up.
- Result: Sale have gone down.
- Rule: The reason sale have gone down is probably that the price was too high.
Abduction (1 Result, 2 Rule, 3 Case)
- Result: Sales have gone down.
- Rule: One reason sales go down is that the price is too high.
- Case: Let me check whether in fact the price is too high.”
(Appendix, p. 154)

Related Concept : Axiom

[1953] Morris Kline , Mathematics in Western Culture, Penguin, Harmondsworth, 1972
“To undertake the deductive process he [Euclid] needed premises for, as Aristotle points out : “It is not everything that can be proved, otherwise the chain of proof would be endless. You must begin somewhere, and you start with things admitted but undemonstrable. These are first principles common to all sciences which are called axioms or common opinions.”
“In the selection of axioms Euclid displayed great insight and judgement.”
“The extraordinary merit of Euclid’s selection is that though they are immediately acceptable they are no mere superficialities, for they lead to profound consequences. Moreover, he was able to choose a very limited number, ten in all, and yet secure the construction of the whole system of geometry.” (Chapter IV, pp. 62-63)

Related Concept : Syllogism

[IV century B. C.] Aristotle, Analytica Priora. Britannica World Library, Chicago, 1990
“A syllogism is discourse (lógos) in which, certain things being stated, something other than what is stated follows of necessity from their being so.
I mean by the last phrase that they produce the consequence, and by this, that no further term is required from without in order to make the consequence necessary.” (Book I, 24b, 20)

[1891, First Published 1843] John Stuart Mill , A System of Logic. Longmans, Green, and Co., London
“The value ... of the syllogistic form and of the rules for using it correctly does not consist in their being the form and the rules according to which our reasoning are necessarily, or even usually, made but in their furnishing us with a mode in which those reasonings may always be represented, and which is admirably calculated, if they are inconclusive, to bring their inconclusiveness to light.” (Book II, § 5)

[1979, First edition 1962] Deobold B. Van Dalen , Understanding Educational Research. An Introduction, McGraw-Hill Book Company, New York
“The categorical syllogism has severe limitations. The content of the conclusion of the syllogism cannot exceed the content of the premises, A categorical syllogism deduces the consequences of preexisting knowledge; it does not enable scholars to gain new knowledge or to make new discoveries. A second weakness of deductive reasoning lies in the possibility that one or more of the premises are not materially true. When the validity of a deductive argument is checked, questions are raised not about the content (truth or falsity) of the statements but about the forms of the arguments.” (Chapter 1, p.9)

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