For instance, supposing someone says: “All my friends have colds”; someone else may add: “No one can sing who has a cold”; then the third person draws the conclusion, which is: “None of my friends can sing,” and the perfect logical argument would read as follows:
1. Premise—“All my friends have colds.”
2. Premise—“No one can sing who has a cold.”
3. Conclusion—“None of my friends can sing.”
That is what is called a perfect syllogism, and in Chapter IV, which he calls Hit or Miss, Lewis Carroll has collected a hundred examples containing the two Premisses which need the Conclusion. Here are some of them. Anyone can draw her own conclusions:
Pain is wearisome;
No pain is eagerly wished for.
In each case the student is required to fill up the third space.
No bald person needs a hairbrush;
No lizards have hair.
No unhappy people chuckle;
No happy people groan.
All ducks waddle;
Nothing that waddles is graceful.
Some oysters are silent;
No silent creatures are amusing.
Umbrellas are useful on a journey;
What is useless on a journey should be left behind.
No quadrupeds can whistle;
Some cats are quadrupeds.
Some bald people wear wigs;
All your children have hair.
The whole book is brimful of humor and simple everyday reasoning that the smallest child could understand.
Another “puzzle” book of even an earlier date is “A Tangled Tale”; this is dedicated—
TO MY PUPIL.
Belovéd pupil! Tamed by thee,
Addish, Subtrac-, Multiplica-tion,
Division, Fractions, Rule of Three,
Attest the deft manipulation!
Then onward! Let the voice of Fame,
From Age to Age repeat the story,
Till thou hast won thyself a name,
Exceeding even Euclid’s glory!
In the preface he says: “This Tale originally appeared as a serial in The Monthly Packet, beginning in April, 1880. The writer’s intention was to embody in each Knot (like the medicine so deftly but ineffectually concealed in the jam of our childhood) one or more mathematical questions, in Arithmetic, Algebra, or Geometry, as the case might be, for the amusement and possible edification of the fair readers of that Magazine.