The use of “is-not” (or “are-not”) as a Copula.
Is it better to say “John is-not in-the-house” or “John is not-in-the-house”? “Some of my acquaintances are-not men-I-should-like-to-be-seen-with” or “Some of my acquaintances are men-I-should-not-like-to-be-seen-with”? That is the sort of question we have now to discuss.
[pg172]This is no question of Logical Right and Wrong: it is merely a matter of taste, since the two forms mean exactly the same thing. And here, again, “The Logicians” seem to me to take much too humble a position. When they are putting the final touches to the grouping of their Proposition, just before the curtain goes up, and when the Copula——always a rather fussy ‘heavy father’, asks them “Am I to have the ‘not’, or will you tack it on to the Predicate?” they are much too ready to answer, like the subtle cab-driver, “Leave it to you, Sir!” The result seems to be, that the grasping Copula constantly gets a “not” that had better have been merged in the Predicate, and that Propositions are differentiated which had better have been recognised as precisely similar. Surely it is simpler to treat “Some men are Jews” and “Some men are Gentiles” as being both of them, affirmative Propositions, instead of translating the latter into “Some men are-not Jews”, and regarding it as a negative Propositions?
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.