17. SUMMARY.
(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.