90 PROFESSOR DE MORGAN, ON THE SYMBOLS OF LOGIC, 



Section III. 



ON THE SYMBOLIC FORMS OF THE EXTENSION OF THE ARISTOTELIAN SYSTEM IN 



WHICH CONTRARIES ARE ADMITTED. 



This system is, by consequence, not by assumption, one in which any term, be it subject 

 or predicate, may have either kind of quantity, universal or particular, in any proposition, 

 affirmative or negative. Sir William Hamilton's system has the same peculiarity, as the 

 basis of invention for the forms of predication : that is, the accidental form of my system is 

 the substantial form of his, so far as these terms are applicable. 



I did not make this point of agreement between the two systems prominent in my work on 

 formal logic, for the following reasons. In the memoir printed by this Society, in which 

 all my interest in novelty of quantification was directed to the algebraical form of numerically 

 definite propositions, this complete distribution of all the quantifications, existing in the system 

 of contraries, was overlooked. So much so, that no one could conclude from my words* more 

 than that, with eight forms of predication, and knowledge of the doctrine of combinations, I 

 must have seen the necessity of this alternative — either two forms of predication with the same 

 terms and the same quantities, or a distribution of all possible pairs of quantifications. But I 

 have no remembrance of even this alternative suggesting itself. 



When the discussion with Sir William Hamilton turned all my attention to the question 

 whether he had or had not the numerical system, and, subsequently, to the comparison 

 of his system (F. L. pp. 300 — 302) with the numerical one, it became evident of course, that 

 the complete distribution of quantifications is incidental to the system of contraries. But I did 

 not mention this explicitly in my work (pp. 63, 293) : because, as the controversy was then 

 unfinished, I neither wished to dwell upon an irrelevant quantification (that which is assumed 

 and constructed, not that which can be derived, being the subject-matter of the dispute), such 

 as might mislead the reader of the controversy, nor to appear as insinuating that I had 

 published to the Society, before I had had any correspondence with my opponent, a system 

 containing by derivation the whole extent of quantification, the invention of which was in the 

 subject-matter of the discussion. Such insinuation would have been untrue : for though the 

 system I now write upon does contain that extent of quantification, and though it was published 

 (to the Society) before I had any knowledge even of the fact of Sir William Hamilton having 

 a system of his own, yet I can most distinctly affirm that all my perception of complete quanti- 

 fication of both terms was derived from the algebraical form of numerical quantification. 



The universal and particular affirmative may be made the bases of all the modes of 

 predication : the others arising out of the various substitutions of contraries in them. The 

 following are then the eight forms, with reference to the order XY. 



* As follows, in the fourth page of my paper "... every 

 proposition speaks in different ways of each term and its con- 

 trary; making one particular or universal, according as the 



other is universal or particular.. ..And of the two terms and 

 their contraries, each proposition speaks universally of two, 

 and particularly of two." 



