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SCIENCE 



[N. S. Vol. XXXVIII. No. i 



will say, with a process transcending con- 

 scious design. We are dealing with a proc- 

 ess deep in the nature and being of the 

 psychic world. Like a child, an idea, once 

 it is born, once it has come into the realm 

 of spiritual light, possibly long before such 

 birth, enters upon a career, a career, how- 

 ever, that, unlike the child's, seems to be 

 immortal. In most cases and probably in 

 all, an idea, on entering the world of con- 

 sciousness, is vague, nebulous, formless, 

 not at once betraying either what it is or 

 what it is destined to become. Ideas, how- 

 ever, are under an impulse and law of 

 amelioration. The path of their upward 

 striving and evolution — often a long and 

 winding way — leads towards precision and 

 perfection of form. The goal is mathe- 

 matics. Witness, for example, our lecturer 

 will say, the age-long ti'avail and aspiration 

 of the great concept now known as mathe- 

 matical continuity, a concept whose inner 

 structure is even now known and under- 

 stood only of mathematicians, though the 

 ancient Greeks helped in moulding its form 

 and though it has long been, if somewhat 

 blindly, yet constantly employed in natural 

 science as when a physicist, for example, or 

 an astronomer uses such numbers as e and w 

 in computation. Witness, again, how that 

 supreme concept of mathematics, the con- 

 cept of function, has struggled through 

 thousands of years to win at length its pres- 

 ent precision of form out of the nebulous 

 sense, which all minds have, of the mere 

 dependence of things on other things. Wit- 

 ness, too, he will say, the mathematical con- 

 cept of infinity, which prior to a half- 

 century ago was still too vague for logical 

 discourse, though from remotest antiquity 

 the great idea has played a conspicuous 

 role, mainly emotional, in theology, philos- 

 ophy and science. Like examples abound, 

 showing that one of the most impressive 

 and significant phenomena in the life of the 



psychic world, if we will but discern and 

 contemplate it, is the process by which 

 ideas advance, often slowly indeed but 

 surely, from their initial condition of 

 formlessness and indetermination to the 

 mathematical estate. The chemieization of 

 biology, the physicization of chemistry, the 

 mechanicization of physics, the mathema- 

 ticization of mechanics, these well-known 

 tendencies and drifts in science do but illus- 

 trate on a large scale the ubiquitous proc- 

 ess in question. 



At length, ladies and gentlemen, our 

 speaker will say, in the light of the last 

 consideration the deeper and larger aspects 

 of our subject are beginning to show them- 

 selves and there is dawning upon us a won- 

 derful vision. The nature, function and 

 life of the entire conceptual world seem to 

 come within the circle and scope of our 

 present enterprise. We are beginning to 

 see that to challenge the human worth of 

 mathematics, to challenge the worth of 

 rigorous thinking, is to challenge the worth 

 of all thinking, for now we see that mathe- 

 matics is but the ideal to which all think- 

 ing, by an inevitable process and law of the 

 human spirit, constantly aspires. We see 

 that to challenge the worth of that ideal is 

 to arraign before the bar of values what 

 seems the deepest process and inmost law 

 of the universe of thought. Indeed we see 

 that in defending mathematics we are really 

 defending a cause yet more momentous, 

 the whole cause, namely, of the conceptual 

 procedure of science and the conceptual 

 activity of the humein mind, for mathe- 

 matics is nothing but such conceptual pro- 

 cedure and activity come to its maturity, 

 purity and perfection. 



Now, ladies and gentlemen, our lecturer 

 will say, I can not in this course deal 

 explicitly and fully with this larger issue. 

 But, he will say, we are living in a day 

 when that issue has been raised ; we happen 



