*a*B*cdef* *ab*CDEF *ab*CDE*f* *ab*CD*e*F *ab*CD*ef* *ab*C*d*EF *ab*C*d*E*f* *ab*C*de*F *ab*C*def* *abc*DEF *abc*DE*f* *abc*D*e*F *abc*D*ef* *abcd*EF *abcd*E*f* *abcde*F *abcdef* In a theoretical point of view we may conceive that the Logical Alphabet is infinitely extended. Every new quality or circumstance which can belong to an object, subdivides each combination or class, so that the number of such combinations, when unrestricted by logical conditions, is represented by an infinitely high power of two. The extremely rapid increase in the number of subdivisions obliges us to confine our attention to a few qualities at a time. When contemplating the properties of this Alphabet I am often inclined to think that Pythagoras perceived the deep logical importance of duality; for while unity was the symbol of identity and harmony, he described the number two as the origin of contrasts, or the symbol of diversity, division and separation. The number four, or the *Tetractys*, was also regarded by him as one of the chief elements of existence, for it represented the generating virtue whence come all combinations. In one of the golden verses ascribed to Pythagoras, he conjures his pupil to be virtuous:[77] “By him who stampt *The Four* upon the Mind, *The Four*, the fount of Nature’s endless stream.” [77] Whewell, *History of the Inductive Sciences*, vol. i. p. 222. Now four and the higher powers of duality do represent in this logical system the numbers of combinations which can be generated in the absence of logical restrictions. The followers of Pythagoras may have shrouded their master’s doctrines in mysterious and superstitious notions, but in many points these doctrines seem to have some basis in logical philosophy. *The Logical Slate.*