588 



SCIENCE. 



[N. S. Vol. XX. No. 514. 



seems to underlie all arbitrary spaces, as 

 their foundation, a good deal of the solid 

 material of empirical knowledge, gained 

 by human beings through contact with an 

 environing world, the environing character 

 of which seems to be quite independent of 

 the freedom of their thought. However 

 that may be, it is evident, I think, that the 

 generalization of the principle involved in 

 this idea of the freedom of thought in 

 framing its conception of space, would, if 

 extended to logic, give us a science of 

 knowledge which would have no necessary 

 relation to the real things of experience, 

 although these are the things with which all 

 concrete knowledge is most evidently con- 

 cerned. It would inform us about the con- 

 clusions which necessarily follow from ac- 

 cepted conceptions, but it could not inform 

 us in any way about the real truth of these 

 conclusions. It would, thus, always leave 

 a gap between our knowledge and its ob- 

 jects which logic itself would be quite 

 impotent to close. Truth would thus be- 

 come an entirely extra-logical matter. So 

 far as the science of knowledge is con- 

 cerned, it -would be an accident if knowl- 

 edge fitted the world to which it refers. 

 Such a conception of the science of knowl- 

 edge is not the property of a few mathe- 

 maticians exclusively, although they have, 

 perhaps, done more than others to give it 

 its present revived vitality. It is the 

 classic doctrine that logic is the science 

 of thought as thought, meaning thereby 

 thoi^ght in independence of any specific 

 ob.ject whatever. 



In regard to' this doctrine, I would not 

 even admit that such a science of knowl- 

 edge is possible. You can not, by a process 

 of generalization or free construction, rid 

 thought of connection with objects; and 

 there is no such thing as a general content 

 or as eontent-in-general. Generalization 

 simply reduces the richness of content and, 

 consequently, of implication. It deals with 



concrete subject-matter as much and as di- 

 rectly as if the content were individual and 

 specialized. 'Things equal to the same 

 thing are equal to each other,' is a truth, 

 not about thought, but about things. The 

 conclusions about a fourth dimension fol- 

 low, not from the fact that we have thought 

 of one, but from the conception about it 

 which we have framed. Neither general- 

 ization nor free construction can reveal the 

 operations of thought in transcendental 

 independence. 



It may be urged, however, that nothing 

 of this sort was ever claimed. The bond- 

 age of thought to content must be admitted, 

 but generalization and free construction, 

 just because they give us the power to vary 

 conditions as we please, give us thinking 

 in a relative independence of content, and 

 thus show us how thought operates irre- 

 spective of, although not independent of, 

 its content. The binomial theorem oper- 

 ates irrespective of the values substituted 

 for its symbols. But I can find no gain in 

 this restatement of the position. It is true, 

 in a sense, that we may determine the way 

 thought operates irrespective of any spe- 

 cific content by the processes of generaliza- 

 tion and free construction; but it is im- 

 portant to know in what sense.- Can we 

 claim that such irrespective operation 

 means that we have discovered certain log- 

 ical constants, which now stand out as the 

 distinctive tools of thought? Or does it 

 rather mean that this process of varying 

 the content of thought as we please reveals 

 certain real constants, certain ultimate 

 characters of reality, which no amount of 

 generalization or free construction can 

 possibly alter? The second alternative 

 seems to me to be the correct one. Whether 

 it is or not may be left here undecided. 

 What I wish to emphasize, is the fact that 

 the decision is one of the things of vital 

 interest for logic, and properly belongs in 

 that science. Clearly, we can never know 



