Page:Popular Science Monthly Volume 83.djvu/413

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Some of the studies that 1 thus suggest may he of a nature to be treated by the methods of experimental psychology proper. I do not sec why the psychological process of solving deductive problems that really illustrate the fecundity of deduction should not be, in certain cases, proper objects for detailed introspection. Let me mention a few possible cases. The one-sided strip of paper and a. considerable number of related geometrical forms, may be made the topic of more or less direct experimental inquiry. Trained observers might undertake to solve such problems, namely, as deductive problems proper, that is, as problems of working out what conclusions follow from what premises. The deductive process proper could be separated in such cases from the special empirical materials used. And if the process is brief enough, or can be sufficiently well divided into stages to be the subject of introspection, there is much that is new to discover.

Let me mention another case of an extremely simple process of deduction of a type of which elementary mathematics is full, the process being one that involves a genuine ideal experiment, and a genuine deduction. Almost anybody knows that if the sum of the digits of a number is divisible by nine, the number is divisible by nine, and conversely. Now let the psychological student be asked, if he does not already know the solution of the problem, Why, granting the ordinary principles of number, the numbers expressed in any decadic system must have this property. Let the ideal construction by which the problem is solved in a given case be a topic of introspection. The result could easily throw a light upon the psychology of reasoning which no discussion of the misused syllogism could possibly produce.

But the syllogism itself does indeed involve deductive processes that have a genuine fecundity. Mrs. Ladd-Franklin's theory of the syllogism, briefly restated by her in Baldwin's "Dictionary" and elsewhere, involves a deductive use of a construction which almost any psychologist can grasp with comparatively little trouble. The nature of the proof of the identity of the ordinary syllogism with Mrs. Ladd-Franklin's reconstruction, can be grasped by a process probably too complex to admit of any strictly experimental control. Yet if one once becomes familiar with this process and with repeated operations of it under controlled conditions, he would have material for the psychology of deduction.

There is another very fascinating problem in the psychology of deduction which has been almost wholly neglected. In my address before the Psychological Association years ago I called attention to the psychology of order as a problem still awaiting discussion. So far as I know, the problem has been little considered by psychologists since that time. But here is an aspect which presents curious phenomena. The