Page:Mind (New Series) Volume 12.djvu/378

 364 HUGH MACCOLL : SYMBOLIC SEASONING. Just as A : B, or its synonym (AB') 1 ', implies A' + B, so AB', the denial of the latter, implies (AB') 171, the denial of the former. I did not enter upon the preceding discussion from any wish to provoke a controversy, but in order to remove mis- understandings. I find that several logicians are in error as to the precise meanings of my symbols and the relation in which my system stands to others that symbolically more or less resemble it. My main object has been to show that these resemblances of mere form hide important differences in matter, method, and limits of application. To effect this object without, at the same time, pointing out what, rightly or wrongly, I regard as serious defects in all the other symbolic systems of which I have any knowledge was im- possible. But I have attacked no particular system ; the faults that I have indicated are faults which they appear to have in common, and from which indeed my own earlier researches were not wholly free, though the central principle of these was sound and forms an important factor of the better and far more comprehensive system into which they have since developed. Modern symbolic logic, unlike the venerable logic of the schools, is a progressive science ; it can lay claim to no finality or perfection. But, in the form which I have given it, it has now one great merit which it never possessed before ; it has become a practical science ; it can actually be applied as an instrument of research. As regards utility, logic used to be contrasted, much to its disadvantage, with mathematics ; but now that the mathe- matician is obliged to hand over to the logician the dis- entanglement of some of his most difficult problems, he can no longer with justice or consistency look down upon the science of the latter and call it useless and inapplicable.