Page:Mind (New Series) Volume 12.djvu/369

 V. SYMBOLIC REASONING (V.). 1 BY HUGH MACCOLL. A RECENT controversy with a certain foreign logician has led me to examine with more care than I had hitherto done the points in which my symbolic logic resembles other modern systems, as well as the points in which it differs from them all. The result has been the discovery that the former are slight and superficial, while the latter are serious and funda- mental. So much is this the case that it is hardly an exaggeration to say that no single formula in my system has exactly the same meaning as the formula which is -supposed to be its equivalent in other systems. When both are valid, I usually find that mine is the more general and implies the other ; when they are not both valid, I invariably find that the valid formula is mine, and the defective formula that of other systems. Examples of this will be given presently ; meanwhile let me state the main points of difference. 1. Other logicians generally divide logic into two parts : the logic of class inclusion and the logic of propositions. Mine is one simple homogeneous system which comprises (either directly or as easy deductions), all the valid formulae of their two divisions, as well as many other valid formulae which their systems cannot even express. 2. My symbol of implication : they replace by some other, such as ^, or 4, or < , etc. I shall adopt the first of these three throughout as their general representative, it being more easily formed than the second, and less likely to lead to ambiguity^than the third. Now, this adoption of different symbols among logicians to express the same idea is a mere matter of taste or convenience, and if their symbol < (or its equivalent) really expressed the same idea as my symbol : , I should not mention this circumstance as one of the points of Difference. But their symbol -< never does express the same idea as my symbol :. 1 For IV. see MIND, July, 1902.