SCIENCE AND RELIGION. 445 



not contradictory. If one should say that there is in the universe a 

 circular triangle, we should deny it, not because the concept of a tri- 

 angle is irreconcilable with the concept of a circle, as consistent in the 

 same figure, which is quite true, but because they are contradictory. 

 What is irreconcilable to you may be reconcilable to another mind, 

 because "irreconcilable" indicates the relation of the concept to the 

 individual intellect ; but what is contradictory to the feeblest is con- 

 tradictory to tlie mightiest mind, because " contradictory" represents 

 the relation of the concepts to one another. 



In the definition of a person there is nothing to exclude infinity, 

 and in the definition of infinite there is nothing to exclude personality. 

 There is no more exclusion between " person " and " infinite " than 

 between "line" and "infinite;" and yet we talk of infinite lines, 

 knowing the irreconcilability of the ideas, but never regarding them 

 as contradictory. 



Writers of great ability sometimes fall into this indiscrimination. 

 For instance, a writer whom 1 greatly admire, Dr. Hill, former Presi- 

 dent of Harvard College, in one paragraph (on "The Uses of Mathesis," 

 in JBiUiotheca Sacra)^ seems twice to employ " contradictory " in an 

 illogical sense, even when he is presenting an illustration which goes 

 to show most clearly that in other sciences, as well as in theology, 

 there are propositions which we cannot refuse to accept, because they 

 are not contradictory, although they are irreconcilable ; in other 

 M'ords, that there are irreconcilable concepts which are not contra- 

 dictory, for we always reject one or the other of two contradictory 

 concepts or propositions. 



That is so striking an illustration of the mystery of the infinite 

 that I will reproduce it. On a plane imagine a fixed line, pointing 

 north and south. Intersect this at an angle of ninety degrees by 

 another line, pointing east and west. Let this latter rotate at the 

 point of intersection, and at the beginning be a foot long. At each 

 approach of the rotating line toward the stationary line let the former 

 double its length. Let each approach be made by bisecting the angle. 

 At the first movement the angle would be forty-five degrees, and the 

 line two feet in length ; at the second, the angle twenty-two and one- 

 half degrees, and the line four feet ; at the third, the angle eleven and 

 one-fourth degrees, and the line eight feet ; at the fourth, the angle 

 five and five-eighths degrees, and the line sixteen feet ; at the fifth, the 

 angle two and thirteen-sixteenths degrees, and the line thirty-two feet, 

 and so on. Now, as this bisecting of the angle can go on indefinitely 

 before the rotating line can touch the stationary line at all its points, 

 it follows that before such contact the rotating line will have a length 

 which cannot be stated in figures, and which defies all human compu- 

 tation. It can be mathematically demonstrated that a line so rotating, 

 and increasing its length in the inverse ratio of its angle with the me- 

 ridian, will have its end always receding from the meridian and ap- 



