82 PROFESSOR DE MORGAN, ON THE SYMBOLS OF LOGIC, 



distinguished as X% X 2 X 3 &c, the universal 'Every X is Y' affirms that X l is F, and that 

 X 2 is F, and that X 3 is P", e£ ccetera. But the particular ' some Xs are not Fs' only declares 

 that either X x is not F, or that X 2 is not F, or that X 3 is not F, aut ccetera. Nor do I here 

 narrow the meaning of the particular : as used in logic, this species of proposition does not 

 necessarily affirm nor deny of more than one. 



5. The distinction of universal and particular may be made that of convertible and incon- 

 vertible. This is the only case in which I have had to search for a meaning to make the 

 system good : in all the other cases, perception of the instance preceded that of the general 

 analogy ; I believe my work on logic will shew this of nearly all. Now convertibility 

 and inconvertibility are only expressions of identity and non-identity : and it may be easily 

 shewn that the universal is the identity of (followed by the right to convert) two names; 

 and the particular the non-identity. Let U be the name of everything in the universe of 

 the proposition : and let X, Y be a name which includes everything that is either X, or F, 

 or both. Then the universal t. Every X is F' affirms the convertibility of w,Y and £7; while 

 ' some Xs are not Fs ' denies it. 



6. On the connexion of universal and particular with conclusive and inconclusive, I have 

 already spoken. 



7. The distinction of universal and particular is that of singular and plural. All books 

 of logic affirm that the singular proposition is universal. But the manner in which logi- 

 cians have treated the universal proposition as singular, in effect, if not in name, will be 

 the material of a curious chapter in the history of logic, when written. Some of them have 

 seen their own tendency, and have made ' Man is animal ' to be a proposition of a distinct 

 species from ' Every man is an animal.' The universal proposition treats the subject col- 

 lectively, and makes one singular notion of the whole : the particular makes, or may make, two 

 groups, of indefinite proportions to the whole, and affirms or denies of one, neither affirming nor 

 denying of the other. 



8. Sir William Hamilton has very effectively forced the attention of logicians to the 

 manner in which their universal and particular are definite and indefinite. I shall presently 

 insist on this same distinction as that of indefinite and definite, and that with particular relation 

 to Sir William Hamilton's system. 



If, instead of taking universal and particular as the standard relation, I had chosen 

 affirmative and negative, the principle for which I contend would have appeared more clearly, 

 perhaps: but at the same time it would have appeared to state nothing but what everybody 

 knows. Surely, one would remark, all oppositions stand to one another in an affirmatory and 

 negatory relation, so that affirmation and negation are the root of them all, and as things 

 which are connected with the same are connected with one another, it follows that all opposite 

 relations are connected with one another. This is perfectly true, and fully admitted : never- 



