98 PROFESSOR DE MORGAN, ON THE SYMBOLS OF LOGIC, 



Introduction of Contraries. 



(.) Universal negative, with particular terms, 

 and affirmative form in common lan- 

 guage. 

 All things are either Xs or Ys. 



) ( Particular affirmative, with universal terms, 

 and negative form in common language. 



Some things are neither Xs nor Ys. 



Invention of predicates. 



(.) Particular negative with particular terms, 

 not used in common language. 



Some Xs are not some Ys. 



) ( Universal affirmative with universal terms, 

 being declaration of identity in common 

 language. 



All Xs are all Ys. 



My objections to this system as promulgated by Sir William Hamilton (F. L. p. 302) may 

 be developed as follows : 



First, the fundamental propositions of a logical system should be independent of each other, 

 so that no one of them should be a compound of two others. Now X)(Y, or ' X and Fare 

 identical names,' is really compounded of X)) Y and X(( Y. If we once grant a complex propo- 

 sition, why this one only, when there are others, out of which, as I have shewn, a separate system 

 of complex syllogism may be constructed ? 



To say that the mode of inventing propositions yields no other, is not an answer : for it 

 is the mode itself which is attacked in its results. Every syllogism in which )( occurs, is 

 either a strengthened form, or the resultant of two other syllogisms. 



Secondly, one object of formal logic being to provide form of enunciation for all truth, 

 and form of denial for all falsehood, it is clear that every falsehood which can be enunciated as 

 a truth should be deniable within the forms of the science. Now the simple denial of )( is the 

 disjunctive assertion ').) or (,(*. Though it happen that I can prove one of these to be true, 

 without knowing which, yet the power of denying in an elementary form the elementary pro- 

 position )( is refused me. A philologist asserts the Greek words A and B to be identical in 

 meaning : he says " All A is all B." One passage of Homer, and one of Hesiod, both contain 

 the doubtful word G, having two possible explanations, the first of which makes Homer assert 

 that some As are not Bs, while the second makes Hesiod assert that some Bs are not As. The 

 premises being admitted, the resulting denial of the simple proposition of Sir William Hamilton's 

 system is only obtainable by a dilemma, or, as it were, metasyllogism. 



Thirdly, the proposition (.), or 'Some Xs are not some Fs,' has no fundamental proposition 

 which denies it, and not even a compound of other propositions. It is then open to the above 

 objection : and to others peculiar to itself. It is what I have called (F. L. p. 153) a spurious 

 proposition, as long as either of its names applies to more than one instance. And the denial 

 is as follows : ' There is but one X, and but one Y, and X is F.' Unless we know beforehand 

 that there is but one soldier, and one animal, and that soldier the animal, we cannot deny 

 that ' some soldiers are not some animals.' Whenever we know enough of X and F to bring 

 forward ' Some Xs are not some Fs' as what could be conceived to have been false, we know 

 more, namely, • No X is F,' which, when X and F are singular, is true or false with 'Some Xs 

 are not some Fs.' 



