INFLUENCE OF ABSTRACT THOUGHT 19 



Minor, Egypt, and Lower Italy, where Pythagorean 

 influence was particularly strong. His chief interest 

 lay in speculation. For him there were two worlds, 

 the world of sense and the world of ideas. The senses 

 deceive us ; therefore, the philosopher should turn his 

 back upon the world of sensible impressions, and 

 develop the reason. In his Dialogues he outlined a 

 course of training and study, the professed object of 

 which was to educate a class of philosophers. (Strange 

 to say, Plato's curriculum, planned originally for the 

 intellectual elite, still dictates in our schools the edu- 

 cation of millions of boys and girls whose careers do 

 not call for a training merely of the reason.) 



Over the porch of his school, the Academy at 

 Athens, were inscribed the words, " Let no one who is 

 unacquainted with geometry enter here." It was not 

 because it was useful in everyday life that Plato laid 

 such insistence on this study, but because it increased 

 the students' powers of abstraction and trained the 

 mind to correct and vigorous thinking. From his 

 point of view the chief good of geometry is lost unless 

 we can through it withdraw the mind from the par- 

 ticular and the material. He delighted in clearness 

 of conception. His main scientific interest was in 

 astronomy and mathematics. We owe to him the 

 definition of a line as " length without breadth," and 

 the formulation of the axiom, " Equals subtracted 

 from equals leave equals." 



Plato had an immediate influence in stimulating 

 mathematical studies, and has been called a maker 

 of mathematicians. Euclid, who was active at AJex- 

 andria toward the end of the fourth century B.C., was 

 not one of Plato's immediate disciples but shared the 



