296 



PART V.- WORKING STAGE. 



may be perhaps only of momentary and local importance; 

 (3) taking into account the broad historical, and geographical 

 aspects of the subject; (4) allowing for further developments 

 in the near and more distant future; (5) connecting the prob- 

 lem, if possible, with wider, and also with more fundamental, 

 considerations; and (6) weighing the comparative importance 

 of the problem in order to determine the approximate place 

 due to it at present in the domain of theory and practice. 



(ri) requires that we should compile a list of all the diffi- 

 culties involved in the solution of a problem, and also a list 

 of all reasonable solutions; and 



(o) demands that we should incessantly and schematically 

 re-examine for the special purpose of discovering new and 

 independent facts, and pursue this course, until varied efforts, 

 repeated at sundry intervals, yield nothing of moment. (See 

 Conclusion 24.) 



Methodical guidance of the above character is indispensable, 

 especially if subjective errors are to be weeded out and if the 

 enquiry is to be truly valid and exhaustive. In any particular 

 investigation auxiliary rules should be, of course, formulated. 



CONCLUSION 20. 

 Need of Searching for the Simplest Practicable Case. 



147. We should avoid plunging in medias res. If I desire, 

 for instance, as a beginner, to learn the principle of the addi- 

 tion (subtraction, multiplication, etc.) of vulgar (or other) frac- 

 tions, I ought not to write down a casual and arbitrary sum: 

 + T- 4- + ff I ought to select, instead, for study the sim- 

 plest possible example, say: y + y' 1 The more important and 

 complex the problem, the more imperative is it to start with 

 the simplest practicable case. In this manner a ready solution 

 will frequently be reached. Plato thus discussed a city instead 

 of an individual, as exemplifying the question of justice in a 

 simpler, because more conspicuous, form,' 2 and for the same 

 reason lecturers on physiology select the web of frogs, the ears 

 of guinea pigs, or the combs of fowls, to demonstrate the circula- 



1 The simplest practicable case should be made the foundation principle 

 in all teaching. Commencing with that case, the teacher would proceed to 

 the case slightly less simple, and so on. It is also a deduction from this 

 Conclusion that before passing from one stage to another, the scholar's 

 former task should be thoroughly assimilated. Also, in learning a language, 

 for instamce, the supreme difficulty of accurate vocalisation might be over- 

 come with relative ease by learning to enunciate, accent, and pronounce 

 correctly a single paragraph of three or four lines, carefully comparing the 

 enunciation, the accent, and the pronunciation with that of the language 

 known. This could be followed by practice with meaningless rhymed syl- 

 lables (e.g., ten, ben, len) and sets of syllables until proficiency is acquired. 



2 Plato, The Republic, bk. 2. 



