PROBLEMS EMPHASIZED BY PR A GMATISM 4°9 



VI 



Some of the studies that I thus suggest may be of a nature to be 

 treated by the methods of experimental psychology proper. I do not 

 see 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 deduc- 

 tive 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 con- 

 versely. 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 discus- 

 sion 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 syllo- 

 gism, briefly restated by her in Baldwin's " Dictionary " and elsewhere, 

 involves a deductive use of a construction which almost any psychol- 

 ogist 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 com- 

 plex 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 



VOL. LXXXIII. — 28. 



