We need not quote any less authority, and perhaps could not quote a greater, 

 than Professor Cassius J. Keyser, of Columbia" University, to tell you that 

 mathematics is nothing more nor less than applied logic. 



When Immanuel Kant tells us that space and time are forms of intuition, 

 he is saying as clearly as he can make language express it that they are not 

 intuitions at all. They are but the forms. They are as the moulds of the 

 designer into which the artisan may pour any and all sorts of material. Space 

 and time are the immaterial moulds to which all intuitional empiricism must 

 conform. This Kantian interpretation seems so clear that it would appear 

 needless to remind one of it; yet the president of one of the greatest universities 

 in this country, in a work upon Kant, says, and says without qualification, that 

 Kant tells us that space and time are intuitions. 



It is in this purely formal sense that we must regard matter as it really 

 is; and every new stride in physics and chemistry is carrying us nearer such a 

 goal. There is a well-known interpretation of our sense of personal identity 

 that may serve to illustrate the method by which we may better understand the 

 probable nature of matter. The problem here referred to is, how is it possible 

 that we can, and do, throughout life, maintain our sense of personal identity, 

 even when the entire mental and moral constitution has been fundametally 

 changed, and science has conclusively demonstrated that, in the course of every 

 few years, every cell in the body has been renewed.'' The explanation offered 

 is, that what the cell transmits is simply and solely its form; and it is this 

 form, or form memory, that maintains the continuity of personal identity. It 

 is, doubtless, in some such sense that we should regard the nature of what we 

 know as material substance. 



The most fundamental fact In the phenomena of heredity is not variation, 

 but persistency of type. It may be granted that the tendency to vary is ever 

 present, and that it is the indisputable foundation of all evolution; but to beem 

 our study of vital inheritance with the phenomena of variation is much like 

 beginning psychological research with the aberrations of the Insane and the 

 feeble-minded. As long as we assume that matter Is materialistic, there appears 

 no escape from some form or modification of the pre-formation theory, with all 

 the absurdities and irreconcilable contradictions that it entails. Weismann is 

 assuredly right in saying that we can make no progress by the use of material 

 units; but we certainly do not avoid or escape such units by simply beginning 

 our investigations, as he suggested, "at some point higher up." All combinations 

 of such units would still be material, and would be as inadequate as ever to 

 explain the intricate phenomena of heredity. To assume that such things as 

 "ids," "biophores," "determinants," or any other vital factors, under whatever 

 names they may masquerade, are material entities, in the ordinary acceptation 

 of the word, is but to fall into inextricable difficulties; difficulties which Weismann 

 himself seemed to foresee and sought vainly to avoid. 



If we assume that the bases of the germ-plasm are material units, there 

 is no escape fgrom the conclusion that the germ-plasm Is handed down through 

 an infinite series of successive generations, and in just such form as may be 

 necessary to preserve the continuity of type. It is doubtful whether any bio- 

 logist really believes such a thing; yet his materialistic assumptions absolutely 

 necessitates such a conclusion. 



For want of a- better term, we may designate as form-tendency the con- 

 necting link between parent and offspring. This form-tendency performs the 

 same office in maintaining the continuity of type as that which Weismann 

 assigned to the selective principle in the germ; but with this added advantage, 

 that, while Wesimann's germinal selection implies some sort of choice, the form 

 impress operates through rigorous mathematical necessity. The phenomena of 

 heredity are subject to the same laws of mathematical necessity as those which 

 govern the various groupings of eletrons that determine elemental qualities. 

 Just as in personal identity the sense is preserved solely through the form 

 relation, so it is in vital Inheritance nothing is transmitted but the form necessary. 

 It little matters what names we employ by which to designate the complex 

 groupings and combinations of elemental forms that make manifest thephenomena 



