478 



Mb DE morgan, ON THE SYLLOGISM, No. V. AND 



This basis of thought may now be introduced in my former papers as the mathematical 

 substratum of the metaphysical notion : I need not enter into details. Both the systems of 

 secondary relations may be adapted to it. In the second of the systems given above pp 

 is the mathematical reading ; ww the metaphysical ; pw the physical ; and wp the con- 

 traphysical : according to the phraseology of my third paper. 



I need hardly say that, in like manner as any individuals may be selected, and con- 

 stituted a class, so those same individuals may be distinguished by a term which denotes 

 an attribute: we cannot put on a class-mark without acquiring a right to treat that mark 

 as designative of a concept. When we pass from the arithmetical abacus to the use of 

 terms of relation, mathematical or metaphysical, as species, dependent, &c. we shake our- 

 selves free of many of the questions which I have discussed. Before we come to this point 

 we feel a want as to (.) and )( of which we are inclined to complain until we see that 

 only defective correlation prevented our feeling the corresponding want as to ).( and ( ) 

 in another wing of the subject. I have frequently heard it made an objection to X(-) Y 

 that it appears as 'Everything is either X or Y', of disjunctive character and apparently 

 affirmative quality. So long as we have a copula either of identification or inclusion, we 

 cannot read either (■) or ) ( by part and part. For this objection, as an objection, I have 

 never cared : those who acknowledge the existence, and admit the entrance, of a privative 

 term must needs confess that X))Y and x (•) Y are equivalent. But I have always 

 respected the complaint as merely directed against a blemish, and have awaited the time 

 when further consideration would provide further explanation. The reader will see that this 

 time has now arrived: the forms ).( and () are subject to precisely the same difficulties 

 with reference to whole and whole. The following table of correlative readings will illus- 

 trate this. 



X)-(Y. 



No part of X is any part of Y. 



Any part of X is not included in (and does 

 not include) any part of Y. 



Some whole of X is external of some whole 

 of Y. 



Every penultimate is whole either of X or 

 of Y. 



Every penultimate includes either X or Y. 



Every individual is not included in some pen- 

 ultimate either of X or of Y. 



X(.)Y. 

 No whole of X is any whole of Y. 

 Any whole of X does not include (and is not 



included in) any whole Y. 

 Some part of X is complement of some part 



of Y. 

 Every individual is part either of X or of Y. 



Every individual is included in either X or Y. 

 Every penultimate does not include some in- 

 dividual either of X or of Y. 



And so we might proceed, never failing to translate a reading of either proposition into a 

 reading of the other, strictly correlative in every detail. 



I shall close this paper by attempting to procure for the quantification of the predicate an 

 honourable acquittal from the charge of having disturbed the peace of the logical world. It 

 has never been the subject of discussion, except by myself in the investigation of the 

 numerical syllogism ; an investigation of which the truth remains unquestioned, and in 



