The fact is, "The Logicians" have somehow acquired a perfectly _morbid_ dread of negative Attributes, which makes them shut their eyes, like frightened children, when they come across such terrible Propositions as "All not-x are y"; and thus they exclude from their system many very useful forms of Syllogisms. Under the influence of this unreasoning terror, they plead that, in Dichotomy by Contradiction, the _negative_ part is too large to deal with, so that it is better to regard each Thing as either included in, or excluded from, the _positive_ part. I see no force in this plea: and the facts often go the other way. As a personal question, dear Reader, if _you_ were to group your acquaintances into the two Classes, men that you _would_ like to be seen with, and men that you would _not_ like to be seen with, do you think the latter group would be so _very_ much the larger of the two? For the purposes of Symbolic Logic, it is so _much_ the most convenient plan to regard the two sub-divisions, produced by Dichotomy, on the _same_ footing, and to say, of any Thing, either that it "is" in the one, or that it "is" in the other, that I do not think any Reader of this book is likely to demur to my adopting that course. pg173 § 4. _The theory that "two Negative Premisses prove nothing"._ This I consider to be _another_ craze of "The Logicians", fully as morbid as their dread of a negative Attribute. It is, perhaps, best refuted by the method of _Instantia Contraria_. Take the following Pairs of Premisses:-- "None of my boys are conceited; None of my girls are greedy". "None of my boys are clever; None but a clever boy could solve this problem". "None of my boys are learned; Some of my boys are not choristers". (This last Proposition is, in _my_ system, an _affirmative_ one, since I should read it "are not-choristers"; but, in dealing with "The Logicians," I may fairly treat it as a _negative_ one, since _they_ would read it "are-not choristers".) If you, dear Reader, declare, after full consideration of these Pairs of Premisses, that you cannot deduce a Conclusion from _any_ of them----why, all I can say is that, like the Duke in Patience, you "will have to be contented with our heart-felt sympathy"! [See Note (C), p. 196.] § 5. _Euler's Method of Diagrams._ Diagrams seem to have been used, at first, to represent _Propositions_ only. In Euler's well-known Circles, each was supposed to contain a class, and the Diagram consisted of two circles, which exhibited the relations, as to inclusion and exclusion, existing between the two Classes. _____ _/ ___ \_ / / y \ \ | \___/ | \_ x _/ \_____/