91 



venient to introduce them for the time), and represents the proposi- 

 tion by the symbols of quantity only, and the presence or absence of 

 a sign of negation. Secondly, instead of making the symbols of uni- 

 versal and particular absolute, he gives one symbol, ), to a universal 

 subject and a particular predicate, and another, (, to a particular 

 subject and a universal predicate: a dot [.} signifying negation. 

 Thus X)-(Y, or simply )•(, represents 'No X is Y': X(-(Y, or (•(, 

 represents ' Some Xs are not any Ys :' X() Y represents ' Some Xs 

 are Ys.' Of the second circumstance above mentioned, Mr. De 

 Morgan believes that it makes the rules easier, and knows that it 

 makes the notation more suggestive. 



Retaining in mind the order XY, YZ, XZ, which is the only figure 

 used in tbe classification (being the first with inverted order of pre- 

 mises), the syllogism is to be denoted by the junction of the prepo- 

 sitional symbols. Thus )))) = )) denotes 'Every X is Y, every Yis 

 Z, therefore every X is Z.' When this is to be read in any figure, 

 the subject-quantities are to have their symbols thickened, the second 

 premise being read first : thus in the four figures, in order, will be 

 seen such symbols as |||l, |H|, ||j|, ||||. 



Section III. On the symbolic forms of the extension of the Aristo- 

 telian system in which contraries are introduced. — This system is the 

 one which was completed and published to the Society before any 

 correspondence with Sir William Hamilton. Mr. De Morgan re- 

 marks that it contains (incidentally, not designedly) every distribu- 

 tion of quantifications ; and gives his reasons for not dwelling on this 

 fact while the controversy was unfinished, with his statement that it 

 had not struck him when the controversy began. Mr. De Morgan 

 frequently distinguishes this system from Sir W. Hamilton's by calling 

 the former that of introduction of contraries, the latter that of inven- 

 tion of predicates. For distinctness, it may be stated that Mr. De 

 Morgan's other, or numerically definite system (the one concerned in 

 the discussion), does not appear in the present paper, except as matter 

 of allusion. 



The forms of predication in this system are as follows, with refer- 

 ence to the order XY, x and y being not X and not Y. 



Universals. 



Affirmative / A > X » Y Every X is Y 



Affirmative j A , x))y or X((Y Every Y is X 



Negative 1 E > X ^ or X H Y No X is Y 



i\e b au\ e | El ^ )y Qr X q Y Everything is X or Y or both. 



Particulars. 

 fl, X()Y Some Xs are Ys 



\l l x()y or X)(Y Some thingsare neither Xs nor Ys 

 *, .. \O l X()y orX(-(Y Some Xs are not Ys 

 negative | Q1 ^ y orX) . )Y Some Ys are not Xs. 



Various rules of connexion are given, being all translations of 

 those in the work on Formal Logic, except a classification of the par- 

 ticulars by probability, answering to that of universals. Thus of 

 X))Y and X(-) Y, each makes the other impossible : of their con- 



Affirmative 



