AN OBJECTIVE STUDY OF MATHEMATICAL 
INTELLIGENCE*. 
By WILLIAM BROWN, M.A., Oxford ; Lecturer on Psychology, King's 
College, London. 
I. Introductory. 
One of the most pressing needs of the psychology of the present day is a 
theory of reasoning, full, concrete, and capable of practical application. If we turn 
to the chapters on reasoning in any of the standard text-books, we find a vagueness 
and diffidence strongly contrasting with the wealth of detail and confident generali- 
sation prominent in the chapters on lower mental processesf. This state of affairs 
is due in part, doubtless, to the desire not to encroach on the territory of the 
logician, in part to the complexity of the processes concerned, — most of all, 
however, to the insufficiency of the method employed, viz. that of unaided intro- 
spection. That this is so, is clear from the fact that the psychology of thought 
has even a longer history than that of most of the simpler mental processes, and 
yet has made far less progress. 
The unsatisfactory character of the generally-accepted introspective account 
has been recently brought into prominence by considerations, separately conclusive, 
yet quite independent of one another. These originate from the three distinct 
realms of normal psychology, psychopathology, and applied psychology of education, 
respectively. 
(1) In normal psychology the evidence is derived from certain experiments, 
among which those of Thorndike, Woodworth, Winch, Watt, and Ach are of chief 
importance. They all point to the fact that mental imagery, or, in more general 
terms, sensory content of any kind, is not an indispensable factor in cognitive 
process, and, even when present, is of small efficiency. Thorndike J compared 
* Read before the British Psychological Society, March 13, 1909. Considerable changes have since 
been made in the methods of evaluating the results. 
+ A recent notable exception is J. E. Miller's The Psychology of Thinking, Macmillan, 1909. 
X E. L. Thorndike: "On the Function of Visual Images," Journal of Philosophy, Psychology, 
and Scientific Methods, Vol. iv. No. 12, p. 321, June 6, 1907. 
