316 LOGIC 



gives only an apparent freedom from experience. Moreover, there is 

 no reason for saying that a implies b unless it does so either really or 

 by supposition. If a really implies 6, then the implication is clearly 

 not a matter of thinking it; and to suppose the implication is to feign 

 a reality, the implications of which are equally free from the processes 

 by which they are thought. Ultimately, therefore, logic must take 

 account of real implications. We cannot avoid this through the use 

 of a symbolism which virtually implies them. Implication can have 

 a logical character only because it has first a metaphysical one. 



The supposition underlying the conception of logic I have been 

 examining is, itself, open to doubt and seriously questioned. That 

 supposition was the so-called freedom of thought. The argument 

 has already shown that there is certainly a very definite limit to this 

 freedom, even when logic is conceived in a very abstract and formal 

 way. The processes of knowledge are bound up with their contents, 

 and have their character largely determined thereby. When, more- 

 over, we view knowledge in its genesis, when we take into considera- 

 tion the contributions which psychology and biology have made to 

 our general view of what knowledge is, we seem forced to conclude 

 that the conceptions which we frame are very far from being our own 

 free creations. They have, on the contrary, been laboriously worked 

 out through the same processes of successful adaptation which have 

 resulted in other products. Knowledge has grown up in connection 

 with the unfolding processes of reality, and has, by no means, freely 

 played over its surface. That is why even the most abstract of all 

 mathematics is yet grounded in the evolution of human experience. 



In the remaining parts of this paper, I shall discuss further the 

 claims of psychology and biology. The conclusion I would draw 

 here is that the field of logic cannot be restricted to a realm where 

 the operations of thought are supposed to move freely, independent 

 or irrespective of their contents and the objects of a real world; 

 and that mathematics, instead of giving us any support for the 

 supposition that it can, carries us, by the processes of symbolization 

 and formal implication, to recognize that logic must ultimately find 

 its field where implications are real, independent of the processes 

 by which they are thought, and irrespective of the conceptions we 

 choose to frame. 



II 



The processes involved in the acquisition and systematization of 

 knowledge may, undoubtedly, be regarded as mental processes and 

 fall thus within the province of psychology. It may be claimed, 

 therefore, that every logical process is also a psychological one. The 

 important question is, however, is it nothing more? Do its logical 

 and psychological characters simply coincide? Or, to put the ques- 



