Complete Works of Lewis Carroll
Page 108
An oyster may be crossed in love.
Oysters are not fossils.
15. All uneducated people are shallow;
Students are all educated.
No students are shallow.
16. All young lambs jump;
No young animals are healthy, unless they jump.
All young lambs are healthy.
17. Ill-managed business is unprofitable;
Railways are never ill-managed.
All railways are profitable.
18. No Professors are ignorant;
All ignorant people are vain.
No professors are vain.
19. A prudent man shuns hyænas;
No banker is imprudent.
No banker fails to shun hyænas.
20. All wasps are unfriendly;
No puppies are unfriendly.
Puppies are not wasps.
21. No Jews are honest;
Some Gentiles are rich.
Some rich people are dishonest.
22. No idlers win fame;
Some painters are not idle.
Some painters win fame.
23. No monkeys are soldiers;
All monkeys are mischievous.
Some mischievous creatures are not soldiers.
24. All these bonbons are chocolate-creams;
All these bonbons are delicious.
Chocolate-creams are delicious.
25. No muffins are wholesome;
All buns are unwholesome.
Buns are not muffins.
26. Some unauthorised reports are false;
All authorised reports are trustworthy.
Some false reports are not trustworthy.
27. Some pillows are soft;
No pokers are soft.
Some pokers are not pillows.
28. Improbable stories are not easily believed;
None of his stories are probable.
None of his stories are easily believed.
29. No thieves are honest;
Some dishonest people are found out.
Some thieves are found out.
30. No muffins are wholesome;
All puffy food is unwholesome.
All muffins are puffy.
31. No birds, except peacocks, are proud of their tails;
Some birds, that are proud of their tails, cannot sing.
Some peacocks cannot sing.
32. Warmth relieves pain;
Nothing, that does not relieve pain, is useful in toothache.
Warmth is useful in toothache.
33. No bankrupts are rich;
Some merchants are not bankrupts.
Some merchants are rich.
34. Bores are dreaded;
No bore is ever begged to prolong his visit.
No one, who is dreaded, is ever begged to prolong his visit.
35. All wise men walk on their feet;
All unwise men walk on their hands.
No man walks on both.
36. No wheelbarrows are comfortable;
No uncomfortable vehicles are popular.
No wheelbarrows are popular.
37. No frogs are poetical;
Some ducks are unpoetical.
Some ducks are not frogs.
38. No emperors are dentists;
All dentists are dreaded by children.
No emperors are dreaded by children.
39. Sugar is sweet;
Salt is not sweet.
Salt is not sugar.
40. Every eagle can fly;
Some pigs cannot fly.
Some pigs are not eagles.
EX8§ 8.
Sets of Abstract Propositions, proposed as Premisses for Soriteses: Conclusions to be found.
[N.B. At the end of this Section instructions are given for varying these Examples.]
1.
1. No c are d;
2. All a are d;
3. All b are c.
2.
1. All d are b;
2. No a are c′;
3. No b are c.
3.
1. No b are a;
2. No c are d′;
3. All d are b.
4.
1. No b are c;
2. All a are b;
3. No c′ are d.
5.
1. All b′ are a′;
2. No b are c;
3. No a′ are d.
6.
1. All a are b′;
2. No b′ are c;
3. All d are a.
7.
1. No d are b′;
2. All b are a;
3. No c are d′.
8.
1. No b′ are d;
2. No a′ are b;
3. All c are d.
9.
1. All b′ are a;
2. No a are d;
3. All b are c.
10.
1. No c are d;
2. All b are c;
3. No a are d′.
11.
1. No b are c;
2. All d are a;
3. All c′ are a′.
12.
1. No c are b′;
2. All c′ are d′;
3. All b are a.
13.
1. All d are e;
2. All c are a;
3. No b are d′;
4. All e are a′.
14.
1. All e are b;
2. All a are e;
3. All d are b′;
4. All a′ are c;
15.
1. No b′ are d;
2. All e are c;
3. All b are a;
4. All d′ are c′.
16.
1. No a′ are e;
2. All d are c′;
3. All a are b;
4. All e′ are d.
17.
1. All d are c;
2. All a are e;
3. No b are d′;
4. All c are e′.
18.
1. All a are b;
2. All d are e;
3. All a′ are c′;
4. No b are e.
19.
1. No b are c;
2. All e are h;
3. All a are b;
4. No d are h;
5. All e′ are c.
20.
1. No d are h′;
2. No c are e;
3. All h are b;
4. No a are d′;
5. No b are e′.
21.
1. All b are a;
2. No d are h;
3. No c are e;
4. No a are h′;
5. All c′ are b.
22.
1. All e are d′;
2. No b′ are h′;
3. All c′ are d;
4. All a are e;
5. No c are h.
23.
1. All b′ are a′;
2. No d are e′;
3. All h are b′;
4. No c are e;
5. All d′ are a.
24.
1. All h′ are k′;
2. No b′ are a;
3. All c are d;
4. All e are h′;
5. No d are k′;
6. No b are c′.
25.
1. All a are d;
2. All k are b;
3. All e are h;
4. No a′ are b;
5. All d are c;
6. All h are k.
26.
1. All a′ are h;
2. No d′ are k′;
3. All e are b′;
4. No h are k;
5. All a are e;
6. No b′ are d.
27.
1. All c are d′;
2. No h are b;
3. All a′ are k;
4. No c are e′;
5. All b′ are d;
6. No a are c′.
28.
1. No a′ are k;
2. All e are b;
3. No h are k′;
4. No d′ are c;
5. No a are b;
6. All c′ are h.
29.
1. No e are k;
2. No b′ are m;
3. No a are c′;
4. All h′ are e;
5. All d are k;
6. No c are b;
7. All d′ are l;
8. No h are m′.
30.
1. All n are m;
2. All a′ are e;
3. No c′ are l;
4. All k are r′;
5. No a are h′;
6. No d are l′;
7. No c are n′;
8. All e are b;
9. All m are r;
10. All h are d.
[N.B. In each Example, in Sections 8 and 9, it is possible to begin with any Premiss, at pleasure, and thus to get as many different Solutions (all of course yielding the same Complete Conclusion) as there are Premisses in the Example. Hence § 8 really contains 129 different Examples, and § 9 contains 273.]
EX9§ 9.
Sets of Concrete Propositions, proposed as Premisses for Soriteses: Conclusions to be found.
1.
(1) Babies are illogical;
(2) Nobody is despised who can manage a crocodile;
(3) Illogical persons are despised.
Univ. “persons”; a = able to manage a crocodile; b = babies; c = despised; d = logical.
2.
(1) My saucepans are the only things I have that are made of tin;
(2) I find all your presents very useful;
(3) None of my saucepans are of the slightest use.
Univ. “things of mine”; a = made of tin; b = my saucepans; c = useful; d = your presents.
3.
(1) No potatoes of mine, that are new, have been boiled;
(2) All my potatoes in this dish are fit to eat;
(3) No unboiled potatoes of mine are fit to eat.
Univ. “my potatoes”; a = boiled; b = eatable; c = in this dish; d = new.
4.
(1) There are no Jews in the kitchen;
(2) No Gentiles say “shpoonj”;
(3) My servants are all in the kitchen.
Univ. “persons”; a = in the kitchen; b = Jews; c = my servants; d = saying “shpoonj.”
5.
(1) No ducks waltz;
(2) No officers ever decline to waltz;
(3) All my poultry are ducks.
Univ. “creatures”; a = ducks; b = my poultry; c = officers; d = willing to waltz.
6.
(1) Every one who is sane can do Logic;
(2) No lunatics are fit to serve on a jury;
(3) None of your sons can do Logic.
Univ. “persons”; a = able to do Logic; b = fit to serve on a jury; c = sane; d = your sons.
7.
(1) There are no pencils of mine in this box;
(2) No sugar-plums of mine are cigars;
(3) The whole of my property, that is not in this box, consists of cigars.
Univ. “things of mine”; a = cigars; b = in this box; c = pencils; d = sugar-plums.
8.
(1) No experienced person is incompetent;
(2) Jenkins is always blundering;
(3) No competent person is always blundering.
Univ. “persons”; a = always blundering; b = competent; c = experienced; d = Jenkins.
9.
(1) No terriers wander among the signs of the zodiac;
(2) Nothing, that does not wander among the signs of the zodiac, is a comet;
(3) Nothing but a terrier has a curly tail.
Univ. “things”; a = comets; b = curly-tailed; c = terriers; d = wandering among the signs of the zodiac.
10.
(1) No one takes in the Times, unless he is well-educated;
(2) No hedge-hogs can read;
(3) Those who cannot read are not well-educated.
Univ. “creatures”; a = able to read; b = hedge-hogs; c = taking in the Times; d = well-educated.
11.
(1) All puddings are nice;
(2) This dish is a pudding;
(3) No nice things are wholesome.
Univ. “things”; a = nice; b = puddings; c = this dish; d = wholesome.
12.
(1) My gardener is well worth listening to on military subjects;
(2) No one can remember the battle of Waterloo, unless he is very old;
(3) Nobody is really worth listening to on military subjects, unless he can remember the battle of Waterloo.
Univ. “persons”; a = able to remember the battle of Waterloo; b = my gardener; c = well worth listening to on military subjects; d = very old.
13.
(1) All humming-birds are richly coloured;
(2) No large birds live on honey;
(3) Birds that do not live on honey are dull in colour.
Univ. “birds”; a = humming-birds; b = large; c = living on honey; d = richly coloured.
14.
(1) No Gentiles have hooked noses;
(2) A man who is a good hand at a bargain always makes money;
(3) No Jew is ever a bad hand at a bargain.
Univ. “persons”; a = good hands at a bargain; b = hook-nosed; c = Jews; d = making money.
15.
(1) All ducks in this village, that are branded ‘B,’ belong to Mrs. Bond;
(2) Ducks in this village never wear lace collars, unless they are branded ‘B’;
(3) Mrs. Bond has no gray ducks in this village.
Univ. “ducks in this village”; a = belonging to Mrs. Bond; b = branded ‘B’; c = gray; d = wearing lace-collars.
16.
(1) All the old articles in this cupboard are cracked;
(2) No jug in this cupboard is new;
(3) Nothing in this cupboard, that is cracked, will hold water.
Univ. “things in this cupboard”; a = able to hold water; b = cracked; c = jugs; d = old.
17.
(1) All unripe fruit is unwholesome;
(2) All these apples are wholesome;
(3) No fruit, grown in the shade, is ripe.
Univ. “fruit”; a = grown in the shade; b = ripe; c = these apples; d = wholesome.
18.
(1) Puppies, that will not lie still, are always grateful for the loan of a skipping-rope;
(2) A lame puppy would not say “thank you” if you offered to lend it a skipping-rope.
(3) None but lame puppies ever care to do worsted-work.
Univ. “puppies”; a = caring to do worsted-work; b = grateful for the loan of a skipping-rope; c = lame; d = willing to lie still.
19.
(1) No name in this list is unsuitable for the hero of a romance;
(2) Names beginning with a vowel are always melodious;
(3) No name is suitable for the hero of a romance, if it begins with a consonant.
Univ. “names”; a = beginning with a vowel; b = in this list; c = melodious; d = suitable for the hero of a romance.
20.
(1) All members of the House of Commons have perfect self-command;
(2) No M.P., who wears a coronet, should ride in a donkey-race;
(3) All members of the House of Lords wear coronets.
Univ. “M.P.’s”; a = belonging to the House of Commons; b = having perfect self-command; c = one who may ride in a donkey-race; d = wearing a coronet.
21.
(1) No goods in this shop, that have been bought and paid for, are still on sale;
(2) None of the goods may be carried away, unless labeled “sold”;
(3) None of the goods are labeled “sold,” unless they have been bought and paid for.
Univ. “goods in this shop”; a = allowed to be carried away; b = bought and paid for; c = labeled “sold”; d = on sale.
22.
(1) No acrobatic feats, that are not announced in the bills of a circus, are ever attempted there;
(2) No acrobatic feat is possibl
e, if it involves turning a quadruple somersault;
(3) No impossible acrobatic feat is ever announced in a circus bill.
Univ. “acrobatic feats”; a = announced in the bills of a circus; b = attempted in a circus; c = involving the turning of a quadruple somersault; d = possible.
23.
(1) Nobody, who really appreciates Beethoven, fails to keep silence while the Moonlight-Sonata is being played;
(2) Guinea-pigs are hopelessly ignorant of music;
(3) No one, who is hopelessly ignorant of music, ever keeps silence while the Moonlight-Sonata is being played.
Univ. “creatures”; a = guinea-pigs; b = hopelessly ignorant of music; c = keeping silence while the Moonlight-Sonata is being played; d = really appreciating Beethoven.
24.
(1) Coloured flowers are always scented;
(2) I dislike flowers that are not grown in the open air;
(3) No flowers grown in the open air are colourless.
Univ. “flowers”; a = coloured; b = grown in the open air; c = liked by me; d = scented.
25.
(1) Showy talkers think too much of themselves;
(2) No really well-informed people are bad company;
(3) People who think too much of themselves are not good company.
Univ. “persons”; a = good company; b = really well-informed; c = showy talkers; d = thinking too much of one’s self.
26.
(1) No boys under 12 are admitted to this school as boarders;
(2) All the industrious boys have red hair;
(3) None of the day-boys learn Greek;
(4) None but those under 12 are idle.
Univ. “boys in this school”; a = boarders; b = industrious; c = learning Greek; d = red-haired; e = under 12.
27.
(1) The only articles of food, that my doctor allows me, are such as are not very rich;
(2) Nothing that agrees with me is unsuitable for supper;
(3) Wedding-cake is always very rich;
(4) My doctor allows me all articles of food that are suitable for supper.
Univ. “articles of food”; a = agreeing with me; b = allowed by my doctor; c = suitable for supper; d = very rich; e = wedding-cake.
28.
(1) No discussions in our Debating-Club are likely to rouse the British Lion, so long as they are checked when they become too noisy;
(2) Discussions, unwisely conducted, endanger the peacefulness of our Debating-Club;
(3) Discussions, that go on while Tomkins is in the Chair, are likely to rouse the British Lion;
(4) Discussions in our Debating-Club, when wisely conducted, are always checked when they become too noisy.
Univ. “discussions in our Debating-Club”; a = checked when too noisy; b = dangerous to the peacefulness of our Debating-Club; c = going on while Tomkins is in the chair; d = likely to rouse the British Lion; e = wisely conducted.
29.
(1) All my sons are slim;
(2) No child of mine is healthy who takes no exercise;
(3) All gluttons, who are children of mine, are fat;
(4) No daughter of mine takes any exercise.