474 SCIENCE PROGRESS 



In general form, the central problem may be thus stated : Standing in face of 

 the whole world of mental activity, actual or possible, let us proceed to analyse 

 all complexes of thought with which we meet, so as to exhibit them as composed 

 of simpler forms ; these forms again let us reduce to greater simplicity ; in the 

 course of this investigation, having observed that the processes, or schemata, of 

 thought in one domain resemble those of another (the variations being found in 

 the differences of the objects referred to the schemata), and having observed, 

 moreover, that the processes most often consist of combinations of simpler 

 processes, or reiterations of such processes, we are at length brought to ask the 

 question, as to whether it be possible to continue the analysis until a limit be 

 reached at which no further analysis is possible, and then, examining with the 

 closest scrutiny the mental processes that occur at that limit, we ask — is it possible 

 to formulate these processes, to define their character with precision, to show that 

 they are necessary to the simplest modes of thought, and that they are sufficient 

 to explain the most complex mental operations ; and that consequently, by 

 retracing the steps of the analysis and representing the course of the thoughts in 

 synthetic forms, we may show that by the combination of these fundamental pro- 

 cesses the constitution of any possible synthesis in the realm of thought may 

 be exhibited ? 



Stated in these terms the problem appears abstract and intangible. The 

 abstract character arises from the extreme generality of the expressions, the word 

 " generality " being here used, in the sense usual in mathematics, not of loose- 

 ness nor vagueness, but as embracing all particular cases. When particular cases 

 are examined, that is to say, when the system involved in the solution is applied 

 to concrete examples, then the fecundity of the method will be evident ; we will 

 find here a powerful instrument of thought applicable to all domains. 



The intangibility of the question has been such that in the whole literature of 

 psychology there are extremely few instances of formulation of the problem in any 

 manner similar to that here given. Certainly it is possible, once the system is 

 grasped, to trace the correspondences it presents to those of Aristotle and Kant. 

 Neither of these philosophers, however, found a principle of division to guide the 

 research ; there is no attempt to prove that the categories are both necessary and 

 sufficient ; the analysis in both cases is tentative and weak. 



Certainly the task of tracing down all complex syntheses to their elemental 

 forms would be hopeless. Convinced of this, therefore, I sought other means of 

 attack. Certain suggestions came to me which proved to be not independent 

 of each other, and at length I obtained a starting-point. One of these was that 

 since we must trace all forms of thought to the simplest, we should concentrate 

 our gaze upon simple modes, and make a beginning with any of these selected 

 with as much judgment as possible, at the same time looking out at that level for 

 a principle of division. I determined to examine with persistent attention simple 

 movements of the mind, so as to discover the minutest wheelwork of the mechan- 

 ism, and thus to gain power to trace out the successive steps of the working. 

 This method suggested to me the expression " putting the microscope on the 

 thoughts." Some of these simple forms I found in the study of the axioms of 

 geometry. 



Another suggestion that arose was that, as I could trace most algebraical 

 methods to combinations of the familiar processes of addition, subtraction,' multi- 

 plication, division, and finally to addition and its inverse operation, together with 

 a system of symbolification, it became laudable to scrutinise in the microscopical 

 manner indicated the process of addition. From this I was led to a study, an 

 intensive examination, of the processes involved in counting. 



