694 THE PRINCIPLES OF SCIENCE. [CHAP 



probably be made before we can resolve the question. Let 

 us now suppose that instead of eight objects and five 

 qualities, we have, say, five hundred objects and fifty 

 qualities. If we were to attempt the same method of 

 exhaustive grouping which we before employed, we should 

 have to arrange the five hundred objects in fifty different 

 ways, before we could be sure that we had discovered 

 even the simpler laws of correlation. But even the succes- 

 sive grouping of all those possessing each of the fifty 

 properties would not necessarily give us all the laws. 

 There might exist complicated relations between several 

 properties simultaneously, for the detection of which no 

 rule of procedure whatever can be given. 



Bifurcate Classification. 



Every system of classification ought to be formed on 

 the principles of the Logical Alphabet. Each superior 

 class should be divided into two inferior classes, distin- 

 guished by the possession and non-possession of a single 

 specified difference. Each of these minor classes, again, is 

 divisible by any other quality whatever which can be 

 suggested, and thus every classification logically consists 

 of an infinitely extended series of subaltern genera and 

 species. The classifications which we form are in reality 

 very small fragments of those which would correctly and 

 fully represent the relations of existing things. But if we 

 take more than four or five qualities into account, the 

 number of subdivisions grows impracticably large. Our 

 finite minds are unable to treat any complex group ex- 

 haustively, and we are obliged to simplify and generalise 

 scientific problems, often at the risk of overlooking 

 particular conditions and exceptions. 



Every system of classes displayed in the manner of the 

 Logical Alphabet may be called bifurcate, because every 

 class branches out at each step into two minor classes, 

 existent or imaginary. It would be a great mistake to 

 regard this arrangement as in any way a peculiar or 

 special method ; it is not only a natural and important 

 one, but it is the inevitable and only system which is 

 logically perfect, according to the fundamental laws of 

 thought. All other arrangements of classes correspond to 

 the bifurcate arrangement, with the implication that some 



