238 H. M'COLL ON THE GROWTH AND 



interchanged. The fact, however, that conditionals and dis- 

 junctives are frequently confounded in ordinary untechni- 

 cal language, is no reason why they should be so in formal or 

 symbolical logic. Even if I have not succeeded in satis- 

 factorily proving that a : h and c^ -\-h are not synonymous, 

 it is safest, I think, to adopt my view in actual practice. 

 Let it be observed that the hypothesis of non- equivalence 

 commits one to less, and therefore involves less risk to the 

 inferred conclusions. My critics admit with me that 

 [a:h) : {a' + i) is a correct formula; but they would also add 

 the formula a' + b : {a:b), the validity of which I deny. If 

 I am wrong, I am open to the charge of seeking to deprive 

 logic of a new formula which might possibly prove useful, 

 but whose utility has yet to be proved. If my opponents 

 are wrong, they are open to the graver charge of seeking 

 to introduce an erroneous formula, which not only can 

 render no service in reasoning, but might even seriously 

 endanger our conclusions. 



As this article is an attempt to explain and illustrate 

 the laws which necessitate the growth, and the principles 

 which determine the form, of a symbolical language, I 

 hope it will not be considered either irrelevant or egotis- 

 tical, if I give a brief account of the development of my 

 own method. By " my own method " I mean simply the 

 method which I discovered (including those features which 

 it has in common with the prior methods of others), as 

 well as those characteristics which are peculiar to itself. 

 What these are I leave to others to decide. The question 

 is certainly irrelevant to the expressed object of this 

 article ; and its discussion would only provoke the natural 

 impatience of the reader. I only mention this at all in 

 order to explain that I use the possessive pronoun my 

 merely as a convenient abbreviation, and in a sense which 

 cannot possibly give oflFence to any of my fellow workers. 



