THE FIELD OF LOGIC 315 



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 

 irrespective of, although not independent of, its content. The bino- 

 mial theorem operates 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 specific content by the processes of generalization 

 and free construction; but it is important to know in what sense. 

 Can we claim that such irrespective operation means that we have 

 discovered certain logical 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 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 con- 

 struction; logic must become other than simply mathematical or 

 symbolic. 



There is another sense in which the determination of the operations 

 of thought irrespective of its specific content is interpreted in con- 

 nection with the exaltation of generalization and free construction. 

 Knowledge, it is said, is solely a matter of implication, and logic, 

 therefore, is the science 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 are themselves related to the 

 real things of the world. If, for instance, a implies &, then, if a is 

 true, 6 is true, and this quite irrespective of the real truth of a or 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 6, 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 misconception. For even so-called formal 

 implication gets its significance only on the supposed truth of the 

 terms with which it deals. We suppose that a does imply b, 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 generalization and nothing more. The formal statement 



