Page:Mind (New Series) Volume 6.djvu/526

 510 HUGH MACCOLL: SYMBOLIC SEASONING. Another three-divisional scheme would be the following : We might agree to make  a (x, y) assert that the formula  (x, y) is true for all values of x and y ;  n (x, y} that it is true for no values of x and y ; and <' (x, y} that it is true for some value or values of x or y, or both, but not for all. These three schemes might, in like manner, be united into a twenty-seven-divisional scheme of symbolic logic ; and so on ad libitum,. It is evident that a logic of 3" dimensions, constructed on these lines, though complicated for high values of n, would be in no way transcendental, like the geometry of a four-dimensional or w-dimensional space, but would be founded upon, and give results in accordance with, the daily and ordinary facts of our consciousness and experience. [The problem discussed on page 502 has been discussed by its pro- poser in MIND for January, 1895. EDITOR.]