XXX.] CLASSIFICATION. 697 



of things admits of numerical discrimination. It would 

 seem absurd to arrange things according as tliey Iiave one 

 degree of the quality or not one degree, two degrees or not 

 two desrees, and so on. The elements are classified accord- 

 ing as the atom of each saturates one, two, three, or more 

 atutns of a monad element, such as chlorine, and they are 

 called accoidingly monad, dyad, triad, tetrad elements, and 

 so on. Jt would be useless to apply the bifid arrangement, 



thus : — 



Element 



Mouad 



Dyad 



The reason of this is that, by the nature of number (p. 157} 

 every number is logically discriminated from every other 

 }iurnber. There can thus be no logical confusion in a nume- 

 rical arrangement, and the series of numbers indefinitely 

 e.xtended is also exhaustive. Every thing admitting of a 

 quality expressible in numbers must find its place some- 

 wl.;ire in the series of numbers. The chords in musio 

 correspond to the simpler numerical ratios and must adndt 

 of complete exhaiistive classification in respect to the 

 complexity of the latios forming them. Plane I'cctilinear 

 figures niiiy be classified according to the numbers of their 

 8id;*3, as triangles, quadrilateral figures, pentagons, hexagons, 

 hep^iagons, &c. Tlie bifurcate arrangement is not false when 

 apjtlied to such series of objects; it is even necessarily 

 involved in the airangement which we do a])ply, so that 

 its formal statement is needless and tedious. Tlie same 

 may be said of the division of portions of space. Keid 

 and Kames endeavoured to cast ridicule on, the bifurcate 

 arrangement^ by proposing to classify the parts of Englatul 

 into Middlesex and what is not Middlesex, dividing tlie 

 latter again into Kent and what is not Kent, Sussex and 



' George Benthaiii, Outline 0/ a New ISysteihi of Logic, p. 1 1 5. 



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