November 4, 1904.] 



SCIENCE. 



589 



the significance of ultimate constants for 

 our thinking until we know what their real 

 character is. To determine that character 

 we must most certainly pass out of the 

 realm of generalization and free construc- 

 tion; logic must become other than simply 

 mathematical or symbolic. 



There is another sense in which the de- 

 termination of the operations of thought 

 irrespective of its specific content is inter- 

 preted in connection with the exaltation 

 of generalization and free construction. 

 Knowledge, it is said, is solely a matter of 

 implication, and logic^ therefore, is the sci- 

 ence of implication simply. If this is so, 

 it would appear possible to develop the 

 whole doctrine of implication by the use 

 of symbols, and thus free the doctrine from 

 dependence on the question as to how far 

 these symbols were themselves related to 

 the real things of the world. If, for in- 

 stance, a implies h, then, if co, is true, h is 

 true, and this quite irrespective of the real 

 truth of a ov b. It is to be urged, however, 

 in opposition to this view, that knowledge 

 is concerned ultimately only with the real 

 truth of a and h, and that the implication 

 is of no significance whatever apart from 

 this truth. There is no virtue in the mere 

 implication. Still further, the supposition 

 that there can be a doctrine of implication 

 simply, seems to be based on a misconcep- 

 tion. For even so-called formal implica- 

 tion gets its significance only on the sup- 

 posed truth of the terms with which it 

 deals. We suppose that a does imply h, 

 and that a is true. In other words, we can 

 state this law of implication only as we 

 first have valid instances of it given in 

 specific, concrete cases. The law is a gen- 

 eralization and nothing more. The formal 

 statement gives only an apparent freedom 

 from experience. Moreover, there is no 

 reason for saying that a implies i unless 

 it does so either really or by supposition. 

 If a really implies i, 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 equal- 

 ly free from the processes by which they 

 are thought. Ultimately, therefore, logic 

 must take account of real implications. 

 We can not 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 concep- 

 tion of logic I have been examining is, 

 itself, open to doubt and seriously ques- 

 tioned. 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, moreover, we view knowledge in its 

 genesis, when we take into consideration 

 the contributions which psychology and 

 biology have made to our general view of 

 what knowledge is, we seem forced to con- 

 clude that the conceptions which we frame 

 are very far from being our own free crea- 

 tions. They have, on the contrary, been 

 laboriously worked out through the same 

 processes of successful adaptation which 

 have resulted in other products. Knowl- 

 edge 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 evolu- 

 tion of human experience. 



In the remaining parts of this paper, I 

 shall discuss further the claims of psychol- 

 ogy and biology. The conclusion I would 

 draw here is, that the field of logic can not 

 be restricted to a realm where the opera- 

 tions of thought are supposed to move 

 freely, independent or irrespective of their, 

 contents and the objects of a real world; 



