184 



Mk DE morgan, on the syllogism, No. Ill, 



In the opinion of Hegel, we are told, Ploucquet's logical calculus was the bitterest libel 

 ever vented against the science. So far as this refers to one particular calculus I need say 

 nothing : but, looking on the opinion as one having a general direction against symbols, it 

 ought to be noticed that every exact science is only so far exact as it knows how to express one 

 thing by one sign. Every science that has thriven has thriven upon its own symbols : logic, 

 the only science which is admitted to have made no improvements in century after century, is 

 the only one which has grown no symbols. To be presented with new marks by which to learn 

 new combinations is to be libelled, because there is a charge of imperfection, tending to destroy 

 credit. But both truth and utility may be pleaded to the indictment. Every little boy has 

 this libel vented against him, when he is first presented with his ABC : he does not feel it, be- 

 cause he is not come to his dignity. If logic, in her maturity, must be vexed with a horn-book, 

 the fault does not rest with those who offer it now, but with those who did not teach her the 

 alphabet when she was young. And I cannot help suspecting that the stern and decided 

 opposition which the follower of the ancients makes to the first introduction of symbols is the 

 feeling of the urchin whose chief objection to saying A was that he knew if he said it he should 

 be made to say B, as no doubt he would. 



VI. I shall now proceed to fundamental points, and to some criticism of the common 

 doctrines. Should I appear too free* in my remarks, I desire it may be remembered that my 

 former self is one of the parties assailed. In developing the opinion that all the writers on 

 logic have kept themselves too exclusively within what I now call the logico-mathematical 

 field, I do not claim to be an exception, save in a sentence here and there which may contain 

 a germ of my present views. I am especially to deal with the great distinction which is 

 gradually forcing its way into its proper place, usually called the distinction of extension and 

 comprehension. I do not adopt these terms. First, because, like denotation and connotation, 

 they are kindred words which might change places with the least possible violence. Secondly, 

 because the distinction of extension and intension occurs both in what is called extension, and 

 in what is called comprehension. Nor can objective and subjective be made the basis of the 

 distinction, for both are again in both, though the subjective rather predominates t in one 

 and the objective in the other. I distinguish the two sides of logic as the logico-mathe- 

 matical and the logico-metaphysical, frequently dropping the prefix logico. 



I symbolise extension and intension as follows. Let A, B, C, be names, no matter how 

 conceived ; let X be a name containing all that is signified by A, by B, and by C ; let Y be a 



* In this country, the study of logic has been, for a long 

 time past, and almost up to the present time, either the tradi- 

 tional practice of an old university, or the taste of an isolated 

 individual. A great amount of reaction iu its favour, all 

 things considered, has taken place in the last twelve years, as 

 evidenced by the publications on the subject. The conse- 

 quence is, even at Oxford, a commencement of considerable 

 diversity of opinion, and of plan of teaching: but, in the bulk 

 of the writings, we see the old system, variously patched, ex- 

 cept where a wider meaning is given to the word logic than it 

 usually bears, and it is taken for a science in which all human 

 knowledge is surveyed in its mode of acquisition. In sucli a 

 state of things, nothing is more desirable than the most decided 



and uncompromising attack from without, conducted on the 

 principle that a useful logic may exist, and directed to the 

 details of the common system, not to the question of its ge- 

 neral character. The dispute which has lasted so long has 

 assumed that if there be anything worth having, the common 

 books have it all ; a basis on which both sides have agreed that 

 this or nothing is their alternative. A change of question is 

 gradually, but far too gradually, taking place : any assault 

 which tends to expedite the fulness of this change must be a 

 benefit to the science. 



t I speak here only of the subjective distinction of sub- 

 ject and object. With the true objective, Logic has nothing 

 to do. 



