468 Mr DE morgan, ON THE SYLLOGISM, No. V. AND 



X(( )) ))Y = X))Y Any part of X is some part of Y 

 X ) ) ( ( ( ( Y = X ) ) Y Some whole of X is any whole of Y 

 X ( ( (■( ) ) Y = X (.( Y Some part of X is not any part of Y 

 X))))((Y=X((Y Any whole of X is not some whole of Y 

 X(( (( ))Y = X((Y Some part of X is any part of Y 

 X)) )) ((Y = X((Y Any whole of X is some whole of Y 

 X(())))Y=X))Y Any part of X is not some part of Y 

 X)) (•( (( Y = X)-) Y Some whole of X is not any whole of Y 

 X(( )■( )) Y = X)(Y Any part of X is not any part of Y 

 X)) {') i(~Y = o? Every class is either some whole of X or of Y 



X((()))Y = X()Y Some part of X is some part of Y 

 X)) )(((Y denies "o? Some class is neither whole of X nor of Y 

 X(( (•) ))Y= o? Every class is either some part of X or of Y 



X)))-(((Y=X()Y Any whole of X is not any whole of Y 

 X(()( ))Y denies s » Some class is neither part of X nor of Y 

 X))()((Y = X)(Y Some whole of X is some whole of Y 



This table selects all the cases in which the primaries are either genus and genus, or 

 species and species ; genus and species are called whole and part. The readings by part and 

 part form a system analogous to that of Hamilton, and differing only from it in this, that 

 the restrictive affirmed and denied is singular and penultimate contrariety, instead of singular 

 identity. Both systems are only portions of larger wholes ; and in both, other sections 

 balance the irregularities of the sections here under review. And both give this lesson, that 

 no system is complete until all its circumstances exhibit complete balance ; any appearance of 

 irregularity in one of the aliquot parts being thrown into symmetry by an inverted irregu- 

 larity in another part. 



Taking the last table as a whole, and dismissing the restrictives to their proper sphere, we 

 see that each unbalanced proposition has a reading of either kind ; while each balanced pro- 

 position has only one reading. And we see — again, having seen the same in the full exem- 

 plar system, — that ) X or X ( is ' some part' or 'any whole' ; while X ) or ( X is ' any part' 

 or ' some whole'. 



In the preceding method the process of thought is absolute identification ; or its 

 denial : thus X ( ( ) ) ) )Y affirms of any species of X that it is strictly identical, coextensive 

 with, some species of Y. There is another set, of 512 cases, in which the comparison is 

 made by assertion or denial of one class being the precise external complement, or contrary, of 

 another: one instance would be 'Any species of X is the contrary of some species of Y'. 

 This system needs no more than a mention. I proceed to readings in which the copular 

 notion no longer insists on complete identification or its extreme contrary, but assumes one of 

 the eight terminally ambiguous forms: as seen in the presentation of 'Every X is Y' under 

 the form 'Any species of X is a species of any genus of Y\ I shall not lengthen this 

 • paper by a full discussion of the whole of this system : I shall confine myself to the cases in 

 which the primary relations are genus and species. And these words may be dispensed with, 

 since their correlatives are not to be employed : part and whole will be sufficient for the pur- 



