Lewis Carroll

“ we can but stand aside, and let them Rush upon their Fate! There is scarcely anything of yours, upon which it is so dangerous to Rush, as your Fate. You may Rush upon your Potato-beds, or your Strawberry-beds, without doing much harm: you may even Rush upon your Balcony (unless it is a new house, built by contract, and with no clerk of the works) and may survive the foolhardy enterprise: but if you once Rush upon your Fate—why, you must take the consequences! ”

“ A 'Proposition' is a sentence stating that some, or none, or all, of the Things belonging to a certain class, called the 'Subject', are also Things belonging to a certain other class, called the 'Predicate'. For example, "some new Cakes are not nice", that is (written in full) "some new Cakes are not nice Cakes"; where the class "new Cakes" is the Subject, and the class "not-nice Cakes" is the Predicate. ”

“ Let us begin with
"Some new Cakes are nice."
But before doing so, a remark has to be made--one that is rather important, and by no means easy to understand all in a moment: so please to read this VERY carefully.
The world contains many THINGS (such as "Buns", "Babies", "Beetles". "Battledores". &c.) ; and these Things possess many ATTRIBUTES (such as "baked", "beautiful", "black", "broken", &c.: in fact, whatever can be "attributed to", that is "said to belong to", any Thing, is an Attribute) . ”

“ No one, who is not pale, looks poetical. All spiders spin webs;
Some creatures, that do not spin webs, are savage. None of my cousins are just;
All judges are just. John is industrious;
No industrious people are unhappy. Umbrellas are useful on a journey ”

“ Let us now write out, all together, our two Premisses and our brace of Conclusions.
"All Dragons are uncanny; All Scotchmen are canny. &there4 All Dragons are not-Scotchmen; All Scotchmen are not-Dragons."
Let me mention, in conclusion, that you may perhaps meet with logical treatises in which it is not assumed that any Thing EXISTS at all, by "some x are y" is understood to mean "the Attributes x, y are COMPATIBLE, so that a Thing can have both at once", and "no x are y" to mean "the Attributes x, y are INCOMPATIBLE, so that nothing can have both at once". ”

“ Now let us make another agreement--that a red counter in a compartment shall mean that it is 'OCCUPIED', that is, that there are SOME Cakes in it. (The word 'some,' in Logic, means 'one or more' so that a single Cake in a compartment would be quite enough reason for saying "there are SOME Cakes here") . ”

“ Pain is wearisome;
No pain is eagerly wished for. No bald person needs a hair-brush;
No lizards have hair. All thoughtless people do mischief;
No thoughtful person forgets a promise. I do not like John ”

“ How much easier it is, when you want to play a Game, to find ONE Player than twenty-two. At the same time, though one Player is enough, a good deal more amusement may be got by two working at it together, and correcting each other's mistakes. ”

“ No dishonest men are trustworthy."
and were to ask him what Conclusion followed, he would probably say "None at all! Your Premisses offend against TWO distinct Rules, and are as fallacious as they can well be!" Then suppose you were bold enough to say "The Conclusion is 'No men who cheat are trustworthy'," I fear your Logical friend would turn away hastily--perhaps angry, perhaps only scornful: in any case, the result would be unpleasant. I ADVISE YOU NOT TO TRY THE EXPERIMENT!
"But why is this?" you will say. "Do you mean to tell us that all these Logicians are wrong?" ”

“ The Attribute, which occurs in the Middle Term or Terms, disappears in the Conclusion, and is said to be "eliminated", which literally means "turned out of doors".
Now let us try to draw a Conclusion from the two Premisses--
"Some new Cakes are unwholesome; No nice Cakes are unwholesome."
In order to express them with counters, we need to divide Cakes in THREE different ways, with regard to newness, to niceness, and to wholesomeness. For this we must use the larger Diagram, making x mean "new", y "nice", and m "wholesome". ”

“ You will find these seven words——Proposition, Attribute, Term, Subject, Predicate, Particular, Universal——charmingly useful, if any friend should happen to ask if you have ever studied Logic. Mind you bring all seven words into your answer, and your friend will go away deeply impressed——'a sadder and a wiser man'. ”

“ This is because "nice" and "not-nice" make what we call an 'EXHAUSTIVE' division of the class "new Cakes": i.e. between them, they EXHAUST the whole class, so that all the new Cakes, that exist, must be found in one or the other of them.
And now suppose you had to represent, with counters the contradictory to "no Cakes are new", which would be "some Cakes are new", or, putting letters for words, "some Cakes are x", how would you do it? ”

“ Gold is heavy;
Nothing but gold will silence him. Some pigs are wild;
There are no pigs that are not fat. No emperors are dentists;
All dentists are dreaded by children. All, who are not old, like walking ”

“ Some dreams are terrible;
No lambs are terrible. No rich man begs in the street;
All who are not rich should keep accounts. No thieves are honest;
Some dishonest people are found out. All wasps are unfriendly ”

“ All battles are noisy; What makes no noise may escape notice. No Jews are mad; All Rabbis are Jews. There are no fish that cannot swim; Some skates are fish. All passionate people are unreasonable; Some orators are passionate. ”

“ For example, if the Premisses are "some m are x" and "no m are y'", the class of "m-Things" is 'the Middle Term.'
If an Attribute occurs in one Premiss, and its contradictory in the other, the Terms containing them may be called 'the Middle Terms'. For example, if the Premisses are "no m are x'" and "all m' are y", the two classes of "m-Things" and "m'-Things" may be called 'the Middle Terms'.
24. Because they can be marked with CERTAINTY: whereas AFFIRMATIVE Propositions (that is, those that begin with "some" or "all") sometimes require us to place a red counter 'sitting on a fence'. ”

“ I mean that misers actually exist. If I wished to avoid making this assertion, and merely to state the law that miserliness necessarily involves selfishness, I should say "no misers are unselfish" which does not assert that any misers exist at all, but merely that, if any did exist, they would be selfish. ”

“ When a man cannot make up his mind which of two parties he will join, he is said to be "sitting on the fence"—not being able to decide on which side he will jump down.
13. "Some are " and "no are ".
14. A Proposition, whose Subject is a single Thing, is called 'Individual'. For example, "I am happy", "John is not at home". These are Universal Propositions, being the same as "all the I's that exist are happy", "all the Johns, that I am now considering, are not at home". ”

“ I charm in vain; for never again,
All keenly as my glance I bend,
Will Memory, goddess coy,
Embody for my joy
Departed days, nor let me gaze
On thee, my fairy friend! ”

“ You see, we must give up the "Cakes" now, or our cupboards will be of no use to us. We must take, as our 'Universe', some class of things which will include Dragons and Scotchmen: shall we say 'Animals'? And, as "canny" is evidently the tribute belonging to the 'Middle Terms', we will let stand for "canny", for "Dragons", and for "Scotchmen". So that our two Premisses are, in full,
And these may be expressed, using letters for words, thus:
The first Premiss consists, as you already know, of two parts:
"Some are ,"
and "No are ." ”

“ Some old misers are thin. All ducks waddle;
Nothing that waddles is graceful. No Professors are ignorant;
Some ignorant people are conceited. Toothache is never pleasant;
Warmth is never unpleasant. Bores are terrible ”

“ All uneducated men are shallow;
All these students are educated. All my cousins are unjust;
No judges are unjust. No country, that has been explored, is infested by dragons;
Unexplored countries are fascinating. No misers are generous ”

“ But if, in the above example, the writer had drawn the Conclusion "All misers are selfish" (that is, "All y are x") , this would be going BEYOND his legitimate rights (since it would assert the EXISTENCE of y, which is not contained in the Premisses) , and you would very properly say "Fallacious Conclusion!"
Now, when you read other treatises on Logic, you will meet with various kinds of (so-called) 'Fallacies' which are by no means ALWAYS so. For example, if you were to put before one of these Logicians the Pair of Premisses
"No honest men cheat ”

“ Some grasses are blades. No dictatorial person is popular;
She is dictatorial. Some sweet things are unwholesome;
No muffins are sweet. No military men write poetry;
No generals are civilians. Bores are dreaded;
A bore is never begged to prolong his visit. All owls are satisfactory;
Some excuses are unsatisfactory. All my cousins are unjust;
All judges are just. Some buns are rich;
All buns are nice. No medicine is nice;
No pills are unmedicinal. Some lessons are difficult ”

“ Mark, on a large Diagram, the following Pairs of Propositions: then mark a small Diagram, &c. These are, in fact, Pairs of Premisses for Syllogisms: and the results, read off from the small Diagram, are the Conclusions.
No exciting books suit feverish patients; Unexciting books make one drowsy. Some, who deserve the fair, get their deserts; None but the brave deserve the fair. No children are patient; No impatient person can sit still. All pigs are fat; No skeletons are fat. No monkeys are soldiers; All monkeys are mischievous. ”

“ There is 'no information' for the smaller Diagram; so no Conclusion can be drawn.
0 0 1 1
Let "creatures" be Universe; = "that run well"; = "fat"; = "greyhounds".
No are ;
Some are . ∴ Some are .
i.e. Some greyhounds are not fat.
1 — 0 0
Let "persons" be Universe; = "soldiers"; = "that march"; = "youths".
All are ;
Some are .
There is 'no information' for the smaller Diagram; so no Conclusion can be drawn.
0 0 0 1 0 1 0 1 1
Let "food" be Universe; = "sweet"; = "sugar"; = "salt".
All are ;
All are . ∴ All are .
All are . i.e. Sugar is not salt.
Salt is not sugar. ”

“ Thirdly, take "all are ", which consists of the two partial Propositions "some are " and "no are ". Here, of course, the treatises mean less than we do in the first part, and more than we do in the second. But the two operations don't balance each other—— any more than you can console a man, for having knocked down one of his chimneys, by giving him an extra door-step.
If you meet with Syllogisms of this kind, you may work them, quite easily, by the system I have given you: you have only to make 'are' mean 'are capable of being', and all will go smoothly. ”

“ Now this contains two 'TERMS'--"new Cakes" being one of them, and "nice (Cakes) " the other. "New Cakes," being the one we are talking about, is called the 'SUBJECT' of the Proposition, and "nice (Cakes) " the 'PREDICATE'. Also this Proposition is said to be a 'PARTICULAR' one, since it does not speak of the WHOLE of its Subject, but only of a PART of it. The other two kinds are said to be 'UNIVERSAL', because they speak of the WHOLE of their Subjects--the one denying niceness, and the other asserting it, of the WHOLE class of "new Cakes". ”