1 64 SCIENCE PROGRESS 



grinding has been attacked so often and defended so seldom 

 that in theory it should be quite slain; but I have an impression 

 that most of the testimonials I have read recently contain 

 reference to Mr. A.'s success in preparing his pupils for 

 examination ; I doubt whether things have changed perceptibly 

 for the better. Most teachers still regard a good examination 

 average as the most real test of success ; the " mathematical 

 outlook" developed under these circumstances is likely to be 

 a sharp outlook for a probable question. This will continue 

 to be the dominant feature in our system until the time comes 

 when a teacher is trusted to examine his own class. In the 

 meantime there is a minority who sow for a harvest to be 

 reaped elsewhere than in the examination room. What are 

 their ideals ? 



A section — perhaps the larger section— are victims of a 

 psychological theory ; the theory being that in the class-room 

 you can develop certain powers or faculties that admit of 

 being carried over and transferred to the activities of real life. 

 Some hold that the memory can be so trained and developed, 

 though it is fair to add that memory training is commonly 

 attempted through the medium of literary rather than of 

 mathematical studies; respectable teachers of mathematics 

 fight shy of much memory work. However this may be, it 

 is probably impossible to increase the general retentiveness 

 of the memory by any kind of exercise ; the memory is not 

 analogous to a muscle. To come nearer to mathematical 

 practice, it is almost universally assumed that the study of 

 the Euclidean and other derived systems of formal geometry 

 cultivate the so-called " logical faculty." Such studies do no 

 doubt attain their object when the subject-matter is geometry : 

 by studying formal geometry I became more wary in approaching 

 a geometrical argument and more skilful in detecting fallacies 

 in such an argument. But did I become more logical in the 

 reasonings of actual life ? I should like to answer in the 

 affirmative but some evidence ought to be forthcoming before 

 this answer is given. I should like to see evidence that 

 mathematicians actually are more logical beings than their 

 fellow men (apart altogether from the question of whether it 

 is well to be logical). I should also like to see a psychological 

 discussion of this logic business ; it might be found that the 

 word " logical " is used in more senses than one. If a trained 



