314 LOGIC 



experience or not; the properties of it and the conclusions reached 

 about it may hold in the real world or they may not; for the mind is 

 free to construct its conception and definition of space in accordance 

 with its own aims. Whether geometry is to be ultimately a science 

 of this type must be left, I suppose, for the mathematicians to decide. 

 A logician may suggest, however, that the propriety of calling all 

 these conceptions " space " is not as clear as it ought to be. Still 

 further, there seems to underlie all arbitrary spaces, as their founda- 

 tion, 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 concerned. It would inform us about the conclusions 

 which necessarily follow from accepted 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 

 objects which logic itself would be quite impotent to close. Truth 

 would thus become an entirely extra-logical matter. So far as the 

 science of knowledge is concerned, it would be an accident if knowledge 

 fitted the world to which it refers. Such a conception of the science 

 of knowledge is not the property of a few mathematicians 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 thought in inde- 

 pendence of any specific object whatever. 



In regard to this doctrine, I would not even admit that such a 

 science of knowledge is possible. You cannot, by a process of general- 

 ization or free construction, rid thought of connection with objects; 

 and there is no such thing as a general content or as content-in- 

 general. Generalization simply reduces the richness of content and, 

 consequently, of implication. It deals with concrete subject-matter 

 as much and as directly as if the content were individual and spcial- 

 ized. " 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 follow, not from the fact that we have thought 

 of one, but from the conception about it which we have framed. 

 Neither generalization 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 bondage of thought to content must be admitted, but 



