380 PROFESSOR DE MORGAN, ON THE STRUCTURE OF THE SYLLOGISM, 



and the sino-ino- tree in the eastern fable: but surely, with as much justice, man may be predicated 

 of the Shakspeare who wrote Paradise Lost, or the Cassar who conquered Darius. 



In the next place, it is not true that the aorist or indefinite character of the mere contrary 

 actually exists in the use which we make of language. Writers on logic, it is true, do not find 

 elbow-room enouo'h in anything less than the whole universe of possible conceptions : but the 

 universe of a particular assertion or argument may be limited in any matter expressed or under- 

 stood. And this without limitation or alteration of any one rule of logic. Let every one of the 

 possible points of space have one or more of the names X, Y, &c. : then if we can say, " No X is F," 

 of course we can say " No Y is A'." But this is equally true if, by an understanding to that 

 effect, the universe of our proposition be one square described in a certain plane. Divide the points 

 of this square into Xs and not-Xs, and the not-X is no more an aorist term than the X. 



By not dwelling upon this power of making what we may properly (inventing a new technical 

 name) call the nniveme of a proposition, or of a name, matter of express definition, all rules 

 remainintj- the same, writers on logic deprive themselves of much useful illustration. And, more 

 than this, they give an indefinite negative character to the contrary, as Aristotle did when he said 

 that not-man was not the name of anything. Let the universe in question be " man f then 

 Briton and alien are simple contraries; alien has no meaning of definition except not-Briton. But 

 we cannot say that either term is positive or negative, except correlatively. As to a claim of right 

 to be considered a prisoner of war, for instance, alien is the positive term, and Briton the negative 

 one. We separate formal logic from language, if we refuse to admit this. In many cases, 

 the lano-uao-e has the term which signifies the contrary, and wants the direct term : as in the 

 word parallels, for example. To this day the word intersectors has not found its way into the 

 idiom of o-cometry. In one case we give a name to the tiling of course, and define the exception by 

 means of a contrary : in another we find it more convenient to reverse the process. I hold that the 

 system of formal logic is not well fitted to our mode of using language, until the rules of direct and 

 contrary terms are associated : the words direct and contrary being merely correlative. Those who 

 teach Alo-ebra know how difficult it is to make the student fully aware that a may be the negative 

 quantity, and - a the positive one. There is a want of the similar perception in regard to direct 

 and contrary terms. 



Throuo-hout this paper, I shall use the small letters .c, ij, z, &c. for names contrary to tho.se 

 represented by the capitals X, Y, Z, &c. Thus " every thing in the universe is either X or ,r," 

 " No X is .r," &c. are identical propositions. 



Section II. Ov the simple propositioi/. 



Thkre is no need to dwell on the usual matters given as to the distinction of universal and 

 i)articular, or of positive and negative. But, I think it cannot be denied, that the distinctions may, 

 for loo-ical ]iurposes, be considered as accidents of language. Any proposition which is either of the 

 four in one language, may be either of the others in another. Our language has, say the names X and 

 1', and suppose that " Every A' is y" is true. Another language translates X by X', but has no 

 term for Y, but only y' for its contrary ; the proposition is then " No X' is y'." In a third 

 lannuage Xs have no specific name; they appear but as individuals of the name .V": the proposition 

 is then " Some X"s are F"s." But if the last language had only possessed the name y", it would 

 have been " Some X"s are not y's." 



^'ery often, having established such a proposition as " Some Xs are I's," we, for that reason, 

 distinguish those Xs by a separate name, Z : and then we have " Every Z is Y." If language 

 were copious enough, particular propositions would seldom occur : and the idioms of every tongue 

 are probably infiuenccd by its power of supplying universal terms, or of converting particulars into 

 the form of universals. 



