vi.] THE INDIRECT METHOD OF INFERENCE. 95 



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 : 1 



" By him who stampt The Four upon the Mind, 

 The Four, the fount of Nature's ernlless stream." 



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. 



To a person who has once comprehended the extreme 

 significance and utility of the Logical Alphabet the 

 indirect process of inference becomes reduced to the 

 repetition of a few uniform operations of classification, 

 selection, and elimination of contradictories. Logical 

 deduction, even in the most complicated questions, 

 becomes a matter of mere routine, and the amount of 



1 Whewell, History of the Inductive Sciences, vol. i. p. 222. 



