Lewis Carroll

“ First, then, a Proposition in I may be understood as asserting, or else as not asserting, the existence of its Subject. (By “existence” I mean of course whatever kind of existence suits its nature. The two Propositions, “dreams exist” and “drums exist”, denote two totally different kinds of “existence”. A dream is an aggregate of ideas, and exists only in the mind of a dreamer: whereas a drum is an aggregate of wood and parchment, and exists in the hands of a drummer.) ”

“ 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. ”

“ It will give you clearness of thought——the ability to see your way through a puzzle——the habit of arranging your ideas in an orderly and get-at-able form——and, more valuable than all, the power to detect fallacies, and to tear to pieces the flimsy illogical arguments, which you will so continually encounter in books, in newspapers, in speeches, and even in sermons, and which so easily delude those who have never taken the trouble to master this fascinating Art. ”

“ We may think of a certain Class, not the Class “Things,” and may imagine that we have picked out from it all the Members of it which possess a certain Adjunct not possessed by the whole Class. This Adjunct is said to be ‘peculiar’ to the smaller Class so formed. In this case, the Class thought of is called a ‘Genus’ with regard to the smaller Class picked out from it: the smaller Class is called a ‘Species’ of the larger: and its peculiar Adjunct is called its ‘Differentia’. ”

“ 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? ”

“ Pairs of Concrete Propositions, proposed as Premisses: Conclusions to be found. 1. I have been out for a walk;
I am feeling better.
2. No one has read the letter but John;
No one, who has not read it, knows what it is about.
3. Those who are not old like walking;
You and I are young.
4. Your course is always honest;
Your course is always the best policy.
5. No fat creatures run well;
Some greyhounds run well.
6. Some, who deserve the fair, get their deserts;
None but the brave deserve the fair. ”

“ Thus, the Proposition “Some merchants are misers” is of the right kind, since “merchants” and “misers” are Specieses of the same Genus “men”; and since the Name “merchants” conveys the idea of the Attribute “mercantile”, and the name “misers” the idea of the Attribute “miserly”, each of which ideas is not conveyed by the other Name. ”

“ And, all the while, you have been leaving unexplored a perfect mine of wealth. Once master the machinery of Symbolic Logic, and you have a mental occupation always at hand, of absorbing interest, and one that will be of real use to you in any subject you may take up. ”

“ Every logician, Aldrichian or otherwise, accepts it as an established fact that “Some x are y” may be legitimately converted into “Some y are x.”
But is it equally clear that the Proposition “If there were any x, some of them would be y” may be legitimately converted into “If there were any y, some of them would be x”? I trow not.
The example I have already used——of a Boys’ School pg171with a non-existent First Class——will serve admirably to illustrate this new flaw in the theory of “The Logicians.” ”

“ A person, who has no power of expression and who cannot influence others, is certainly not a woman;
pg191 (18) People, who are popular and worthy of praise, either are public benefactors or else are unassuming.
Univ. “persons”; a = able to keep a secret; b = clear-headed; c = constantly talking; d = deserving praise; e = exhibited in shop-windows; h = expressing oneself well; k = fit to be an M.P.; l = influential; m = never-to-be-forgotten; n = popular; r = public benefactors; s = unassuming; t = using one’s influence for good objects; v = well-educated; w = women ”

“ Mental recreation is a thing that we all of us need for our mental health; and you may get much healthy enjoyment, no doubt, from Games, such as Back-gammon, Chess, and the new Game “Halma”. But, after all, when you have made yourself a first-rate player at any one of these Games, you have nothing real to show for it, as a result! ”

“ That is the sort of question we have now to discuss.
pg172This 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!” ”

“ Just as a Class is said to be Real, or Unreal, according as there is, or is not, an existing Thing in it, so also a Name is said to be Real, or Unreal, according as there is, or is not, an existing Thing represented by it.
[Thus, “Town lit with gas” is a Real Name: “Town paved with gold” is an Unreal Name.]
Every Name is either a Substantive only, or else a phrase consisting of a Substantive and one or more Adjectives (or phrases used as Adjectives) . ”

“ An implication is, therefore, contained in the conclusion, which is not justified by the premisses.”
This seems to me entirely clear and convincing. Still, “to make sicker”, I may as well throw the above (soi-disant) Syllogism into a concrete form, which will be within the grasp of even a non-logical Reader.
Let us suppose that a Boys’ School has been set up, with the following system of Rules:—
“All boys in the First (the highest) Class are to do French, Greek, and Latin. All in the Second Class are to do Greek only. All in the Third Class are to do Latin only.” ”

“ Hence the Trio is a Syllogism; the two Propositions, “No x are m” and “No y are m′”, are its Premisses; the Proposition “No x are y” is its Conclusion; the Terms m and m′ are its Eliminands; and the Terms x and y are its Retinends.
Hence we may write it thus:—
“No x are m;
No y are m′.
∴ No x are y”.
As a second specimen, let us take the Trio
“All cats understand French;
Some chickens are cats.
Some chickens understand French”.
These, put into normal form, are
“All cats are creatures understanding French;
Some chickens are cats.
Some chickens are creatures understanding French”. ”

“ The Proposition may be written
“No | not-brave persons | are | persons deserving of the fair”.
7. Univ. is “persons”. The phrase “looks poetical” evidently belongs to the Predicate; and the Subject is the Class, of persons, whose peculiar Attribute is “not-pale”.
The Proposition may be written
“No | not-pale persons | are | persons who look poetical”.
8. Univ. is “persons”.
The Proposition may be written
“Some | judges | are | persons who lose their tempers”.
9. Univ. is “persons”. The phrase “never neglect” is merely a stronger form of the phrase “am a person who does not neglect”. ”

“ pg166In opposition to this view, I maintain that any writer of a book is fully authorised in attaching any meaning he likes to any word or phrase he intends to use. If I find an author saying, at the beginning of his book, “Let it be understood that by the word ‘black’ I shall always mean ‘white’, and that by the word ‘white’ I shall always mean ‘black’,” I meekly accept his ruling, however injudicious I may think it. ”

“ No bride-cakes are wholesome;
What is unwholesome should be avoided.
28. John is industrious;
No industrious people are unhappy.
29. No philosophers are conceited;
Some conceited persons are not gamblers. ”

“ So long as you are conscious that all the land you have passed through is absolutely conquered, and that you are leaving no unsolved difficulties behind you, which will be sure to turn up again later on, your triumphal progress will be easy and delightful. ”

“ A clear-headed person, who has influence and uses it for good objects, is a public benefactor;
(15) A public benefactor, who is unassuming, is not the sort of person whose photograph is in every shop-window ”

“ Two Nullities, with Like Eliminands asserted to exist, yield an Entity, in which both Retinends change their Signs.
In order to help the Reader to remember the peculiarities and Formulæ of these three Figures, I will put them all together in one Table.
I will now work out, by these Formulæ, as models for the Reader to imitate, some Problems in Syllogisms which have been already worked, by Diagrams, in Book V., Chap. II.
(1) [see p. 64] “No son of mine is dishonest;
People always treat an honest man with respect.”
Univ. “men”; m = honest; x = my sons; y = treated with respect. ”

“ It may be well to explain what I mean by the complete Conclusion of a Syllogism or a Sorites. I distinguish their Terms as being of two kinds——those which can be eliminated pg186 (e.g. the Middle Term of a Syllogism) , which I call the “Eliminands,” and those which cannot, which I call the “Retinends”; and I do not call the Conclusion complete, unless it states all the relations among the Retinends only, which can be deduced from the Premisses.
1.
All the boys, in a certain School, sit together in one large room every evening. ”

“ After the six friends, named in Problem 5, had returned from their tour, three of them, Barry, Cole, and Dix, agreed, with two other friends of theirs, Lang and Mill, that the five should meet, every day, at a certain table d’hôte. Remembering how much amusement they had derived from their code of rules for walking-parties, they devised the following rules to be observed whenever beef appeared on the table:—
(1) If Barry takes salt, then either Cole or Lang takes one only of the two condiments, salt and mustard: if he takes mustard, then either Dix takes neither condiment, or Mill takes both. ”

“ A Class, containing two or more Members, is sometimes regarded as one single Thing. When so regarded, it may possess an Adjunct which is not possessed by any Member of it taken separately.
[Thus, the Class “The soldiers of the Tenth Regiment,” when regarded as one single Thing, may possess the Attribute “formed in square,” which is not possessed by any Member of it taken separately.] ”

“ People, who can talk for ever and are fit to be Members of Parliament, deserve praise;
(9) Any one, who can keep a secret and who is unassuming, is a never-to-be-forgotten public benefactor;
(10) A woman, who benefits the public, is always popular ”

“ Whenever all the English are singing “Rule Britannia,” and some of the Scotch are not dancing reels, none of the Germans are playing chess;
(10) Whenever some of the English are singing “Rule Britannia”, and some of the Monitors are asleep, some of the Irish are not fighting;
(11) Whenever some of the Monitors are awake, and some of the Eleven are not oiling their bats, some of the Scotch are dancing reels ”

“ Whenever you find two men, who differ in Politics and in their views of Society, and who are not both of them ugly, you may be sure that they look well when walking together;
(5) Ugly men, who look well when walking together, are not both of them free from self-consciousness ”

“ People, who benefit the public, but do not use their influence for good purpose, are not fit to go into Parliament;
(5) People, who are worth their weight in gold and who deserve praise, are always unassuming ”

“ People, who are worth their weight in gold, who never leave off talking, and whom it is impossible to forget, are just the people whose photographs are in all the shop-windows;
(12) An ill-educated woman, who is not clear-headed, is not fit to go into Parliament ”

“ Formulæ for solving Problems in Syllogisms.
When once we have found, by Diagrams, the Conclusion to a given Pair of Premisses, and have represented the Syllogism in subscript form, we have a Formula, by which we can at once find, without having to use Diagrams again, the Conclusion to any other Pair of Premisses having the same subscript forms. ”