(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.