408 



PROFESSOR DE MORGAN, ON THE STRUCTURE OF THE SYLLOGISM, ETC. 



(1.) The two terms may be identical, or F ) y¥ and X)V. Let this be denoted by D. 

 Taking the order XV, we have, to constitute D, the proposition J, a. And denoting coexistence by 

 + , as before, we may write D = A + a. 



(2.) A' may be entirely contained in, but not repletive of, Y, or we may have X) l' and Y : X. 

 Let X be now called a subidentiual of }', and let D^ denote this form. We have then D^= A + o. 



(3.) X may entirely contain 1', and more; or Y ) X and X : Y. Let A' be now called a 

 superidentical of 1', and let D' denote this form. We have then D' = a + O. 



(4.) X may be the contrary of Y, both together tilling up the universe of the proposition witli- 

 <iut anything in common ; or X .Y and j- . y. Let this form be called C : we have then C = E + e. 



(5.) X and Y may have nothing incommon, but may not together fill up the universe of the 

 proposition; or X. F and .xy. Let them be called subcontraries, and let C^ denote this form. 

 We have then C^ = E + i. 



(6.) A'and F may have something in common, and may together fill up the universe; or XY 

 and X . y. Let these be called supercontraries, and let C' denote the form. We have then C' = e + I. 



(7.) Each of the two may have something in common with the other and something not in 

 common, both together not filling up the universe; or XY, xy, X : Y, Y : X. I cannot propose 

 any name for this case with whicli I am in any degree satisfied : but as all the particular forms 

 are here concerned, I will for the present call X and F in this case complete particulars each of the 

 other. Let P represent this form ; we have tlien P=I+0+i + o. 



In arranging for a syllogism, let the order be XY, ZY, XZ, the conclusion being described by 

 what .V is as related to Z, X coming from the first premiss ; and both terms of the conclusion being 

 described with respect to the middle term, F. On examining the cases in which complete premises 

 give a complete conclusion, I find as follows. 



1. If one of the concluding terms be a complete particular of the middle term, there is no 

 complete conclusion except when the other concluding terra is either identical with or contrary to 

 the middle term. And then each concluding term is a complete particular of the other. 



2. The following table shows tlie result of all the other cases. 



X 



This is a table of double entry, in which from the description of X and Z with respect to F, we 

 see set down that of A" with respect to Z, when one can be affirmed: and, when nothing can be affirm- 

 ed, all that can be denied, in parentheses. Thus, if AT be a supercontrary of F, and Z a subcontrary, 

 X must be a superidentical of Z. But if X and Z be both subidenticals of F, it may be denied that 

 X is either the contrary or a supercontrary of Z. 



I will not lengthen this addition by putting down in words all the rules wliich are expressed in 

 the preceding table. 



A. DE MORGAN. 



University College, London, 



February 27, 1847. 



