INDUCTIVE REASONING.
(1) Inductive and Deductive Reasoning Distinguished.
(2) The “Inductive Hazard.”
Essential in world’s progress.
Cultivated and regulated in school.
(3) Complexity of the Problem of Induction.
(4) Various Conceptions of Induction.
Quotations from prominent authorities.
(5) Induction and Deduction Contiguous Processes.
(6) Induction an Assumption.
A mode of inference; A method.
(7) Universal Causation.
Law stated and illustrated.
Conditions all induction.
(8) Uniformity of Nature.
Defined and illustrated.
Conditions all induction.
Empirical.
(9) Inductive Assumptions Justified.
(10) Three Forms of Inductive Research.
(1) Enumeration (2) Analogy (3) Analysis.
Illustrated.
Conditions determine form followed.
(11) Induction by Simple Enumeration.
Defined and illustrated.
Outcome threefold—these illustrated.
(12) Induction by Analogy.
Two conceptions.
Analogy by type or example. Illustrations representative.
Error of analogy.
Suggestiveness of analogy.
Value of analogy.
Requirements of a true analogy. Three.
(13) Induction by Analysis.
Importance.
Defined and illustrated.
(14) Perfect Induction.
Defined and illustrated.
Its use.
Method of Socrates.
(15) Traduction.
Defined and illustrated.
Three methods compared.
(1) Reasoning is the process of deriving a judgment from two antecedent judgments. The syllogism is a common form of expressing the process of reasoning.
Inductive reasoning is reasoning from less general premises to a more general conclusion.
Deductive reasoning is reasoning from more general premises to a less general conclusion.
The inductive syllogism is not supposed to conform to the canons of the deductive syllogism.
(2) Positing in the conclusion more than is indicated in the premises involves what is known as the “inductive hazard.”
The inductive hazard which is another expression for the spirit of discovery, should be fostered in the school room since it has been one of the great forces in human progress; but this venturesome spirit must be regulated by rules, principles, and systematic procedure, or low ideals of recklessness and inaccuracy will result.
(3) The problem of induction is more complex than that of deduction; because the former is a comparatively new subject, and also is more closely related to the activities of life.
(4) The opinion relative to the exact nature of induction, though varied, may be summed up in the thought of its being the process which leads to general truths, derived from the observation of individual facts.
(5) Induction and deduction are contiguous processes which go to make up the more general process of thinking. Where induction ceases, deduction naturally commences; induction discovers new knowledge, deduction clarifies it.
(6) Induction as a general process may be treated as a mode of inference or as a method. In either case the conclusion comprehends more than is contained in the premises.
Since no imperfect induction is absolutely free from doubt, on what ground are we justified in making any inductive assumptions? The answer follows:
(7 and 8) “Nothing can occur without a cause and every cause has its effect,” is the law of universal causation; while the law of the uniformity of nature is “the same antecedents are universally followed by the same consequents.” These two laws justify inductive assumptions, and, in a sense, condition all thinking.
(9) Uniformity of nature gives man confidence, while universal causation arouses his curiosity. With these two weapons he is willing to “march into the unknown.”
(10) As the process of universalizing individual experiences, induction assumes the three forms of simple enumeration, analogy and analysis. The form adopted is not always elective but is controlled largely by the exigency of the case. Some topics lend themselves to all three modes.
(11) Induction by simple enumeration consists in observing many instances which exemplify the uniformity under consideration. Complete enumeration gives the so called perfect inductive inference; incomplete but uncontradicted enumeration leads to empirical truths; while incomplete and contradictive enumeration involves a mere calculation of chances.
(12) Induction by analogy assumes that if two (or more) things resemble each other in certain respects, they belong to the same type, and, therefore, any fact known of the one, may be affirmed of the other.
A most common form of analogy is reasoning by type or example. In this it is assumed that if two or more things are of the same type, they resemble each in every essential property. The type must be truly representative. A second form of analogy is reasoning by marks of resemblance. This second form often leads to egregious error.
Analogy is especially valuable in suggesting hypotheses and in giving training in originality and initiative.
A true analogy demands that the points of resemblance be representative; that they outweigh the points of difference, and that no disagreement be incompatible.
(13) Induction by analysis is the process of dividing a whole into its parts with a view of deriving a generalization relative to the nature and causal connection of these parts.
Induction by analysis makes use of the hypothesis, of observation and experiment, including Mill’s five methods.
(14) A perfect induction is one in which the premises enumerate all of the instances denoted by the conclusion. It is serviceable in inspiring care and accuracy in the establishment of generalizations.
(15) Traduction is the process of reasoning to a conclusion which is neither less general nor more general than the premises.
Traduction includes reasoning from particular to particular or from general to general. Perfect induction is in reality a form of traduction.
Induction, though the most useful form of inference, is the most untrustworthy; whereas traduction is just the reverse of this.
(1) Define and illustrate reasoning.
(2) Distinguish by definition and illustration between inductive and deductive reasoning.
(3) Explain the “inductive hazard” and show its use to man.
(4) “For twenty centuries Aristotle’s Deductive Logic was the logician’s bible.” Explain this.
(5) Show that induction and deduction are contiguous processes.
(6) Distinguish between induction as a mode of inference and induction as a method.
(7) State and explain the law of universal causation. Illustrate fully.
(8) Make evident that a cause may involve many antecedents.
(9) State and explain by illustration the law of uniformity of nature.
(10) Verify by illustration the notion that the “fact of causation” conditions all induction.
(11) Which of the two laws is empirical, “causation” or “uniformity”? Why?
(12) Show that induction is a form of thinking.
(13) Why should the law of uniformity of nature convince man that nature is honest? Illustrate.
(14) Show that the law of universal causation stirs the spirit of discovery.
(15) Name and illustrate the three forms of induction.
(16) Why is it that the tendencies of the investigator often determine the inductive form which he adopts?
(17) Explain by illustration the three-fold outcome of induction by simple enumeration.
(18) Selecting some class room experience, illustrate analogy by example or type.
(19) Define and exemplify types as used in logic.
(20) Remark upon the errors incident to analogy.
(21) Summarize the advantages which induction by analogy offers.
(22) State and exemplify the requirements of true analogies.
(23) Indicate the superiority of induction by analysis over the other two forms. Illustrate.
(24) Define and illustrate perfect induction.
(25) Under what circumstances is perfect induction justified?
(26) Define and illustrate traduction.
(27) Indicate the various forms of traduction.
(1) Show the connection between illicit minor and the “inductive hazard.”
(2) Show by illustration that time tends to universalize truth.
(3) “Induction and not deduction is the natural method of the child mind.” Prove the correctness of this statement.
(4) “Induction is the process of inference by which we get at general truths from particular facts or cases.” Prove that this is not strictly correct according to definition.
(5) As related to establishing general truths, what are the special functions of induction and deduction?
(6) Show that an inductive inference must of necessity be more or less uncertain.
(7) Is there any distinction between the laws of universal causation and sufficient reason? Hyslop’s Elements of Logic, page 329.
(8) Show that universal causation and uniformity of nature are complementary laws. Hyslop, p. 330.
(9) Relate the “fact of causation” to the laws of thought.
(10) Distinguish between empirical and “a priori” laws.
(11) When Harvey discovered the circulation of the blood, what form of induction did he use?
(12) What form of reasoning did Columbus follow in proving that the earth is spherical?
(13) “It is said that the greatness of Darwin was due largely to his habit of never ignoring an exception.” Justify by illustration the truth of this assertion.
(14) In analogical reasoning by example, under what conditions would one illustration be as convincing as many?
(15) “Considering the similarities and differences, the weight of the argument favors Mars’ habitability.” Suppose the proportion of probability were something like this—Resemblances: Differences = 8:7; wherein might the conclusion be erroneous?
(16) Mention a mark or characteristic which would make the habitability of Mars incompatible?
(17) Select a topic for investigation which is peculiarly adapted to enumeration; to analogy; to analysis.
(18) “The uniformities we expect to find in the world take two main aspects, one of which is indicated by the term thing and the other by the term circumstance.” Aikin’s Principles of Logic, 1905; p. 233. In the light of the two fundamental laws of universal causation and uniformity of nature explain and illustrate the quotation.
(19) Explain the principle of teleology as related to analogy. Hibben, 1908; p. 317.