Complete Works of Lewis Carroll
Page 112
Some fat people are not strong.
Univ. “persons”; m = healthy; x = fat; y = strong.
Some m are x;
No m′ are y.
Some x are y′.
There is no Conclusion.
§ 3.
Method of Subscripts.
SL4-BSolutions for § 4.
1. mx′0 † m′1y′0 ¶ x′y′0 [Fig. I.
i.e. “No x′ are y′.”
2. m′x0 † m′y′1 ¶ x′y′1 [Fig. II.
i.e. “Some x′ are y′.”
3. m′1x′0 † m′1y0 ¶ xy′1 [Fig. III.
i.e. “Some x are y′.”
4. x′m′0 † y′1m′0 ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]
5. mx′1 † ym0 ¶ x′y′1 [Fig. II.
i.e. “Some x′ are y′.”
6. x′m0 † my0 ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]
7. mx′0 † y′m1 ¶ xy′1 [Fig. II.
i.e. “Some x are y′.”
8. m′1x0 † m′y0 ¶ x′y′1 [Fig. III.
i.e. “Some x′ are y′.”
9. x′m′1 † my0 ¶ nothing.
[Fallacy of Unlike Eliminands with an Entity-Premiss.]
10. x1m′0 † y′1m0 ¶ x1y′0 † y′1x0 [Fig. I (β).
i.e. “All x are y, and all y′ are x′.”
11. mx0 † y′1m0 ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]
12. xm0 † y1m′0 ¶ y1x0 [Fig. I (α).
i.e. “All y are x′.”
13. m′1x′0 † ym0 ¶ x′y0 [Fig. I.
i.e. “No x′ are y.”
14. m1x′0 † m′1y′0 ¶ x′y′0 [Fig. I.
i.e. “No x′ are y′.”
15. xm0 † m′y0 ¶ xy0 [Fig. I.
i.e. “No x are y.”
16. x1m0 † y1m′0 ¶ (x1y0 † y1x0) [Fig. I (β).
i.e. “All x are y′ and all y are x′.”
17. xm0 † m′1y′0 ¶ xy′0 [Fig. I.
i.e. “No x are y′.”
18. xm′0 † my0 ¶ xy0 [Fig. I.
i.e. “No x are y.”
19. m1x′0 † m1y0 ¶ xy′1 [Fig. III.
i.e. “Some x are y′.”
20. mx0 † m′1y′0 ¶ xy′0 [Fig. I.
i.e. “No x are y′.”
21. x1m′0 † m′y1 ¶ x′y1 [Fig. II.
i.e. “Some x′ are y.”
22. xm1 † y1m′0 ¶ nothing.
[Fallacy of Unlike Eliminands with an Entity-Premiss.]
23. m1x′0 † ym1 ¶ xy1 [Fig. II.
i.e. “Some x are y.”
24. xm0 † y1m′0 ¶ y1x0 [Fig. I (α).
i.e. “All y are x′.”
25. mx′1 † my′0 ¶ x′y1 [Fig. II.
i.e. “Some x′ are y.”
26. mx′0 † y1m′0 ¶ y1x′0 [Fig. I (α).
i.e. “All y are x.”
27. x1m0 † y′1m′0 ¶ (x1y′0 † y′1x0) [Fig. I (β).
i.e. “All x are y, and all y′ are x′.”
28. m1x0 † my1 ¶ x′y1 [Fig. II.
i.e. “Some x′ are y.”
29. mx0 † y1m0 ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]
30. x1m0 † ym1 ¶ x′y1 [Fig. II.
i.e. “Some y are x′.”
31. x1m′0 † y1m′0 ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]
32. xm′0 † m1y′0 ¶ xy′0 [Fig. I.
i.e. “No x are y′.”
33. mx0 † my0 ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]
34. mx′0 † ym1 ¶ xy1 [Fig. II.
i.e. “Some x are y.”
35. mx0 † y1m′0 ¶ y1x0 [Fig. I (α).
i.e. “All y are x′.”
36. m1x0 † ym1 ¶ x′y1 [Fig. II.
i.e. “Some x′ are y.”
37. m1x′0 † ym0 ¶ xy′1 [Fig. III.
i.e. “Some x are y′.”
38. mx0 † m′y0 ¶ xy0 [Fig. I.
i.e. “No x are y.”
39. mx′1 † my0 ¶ x′y′1 [Fig. II.
i.e. “Some x′ are y′.”
40. x′m0 † y′1m′0 ¶ y′1x′0 [Fig. I (α).
i.e. “All y′ are x.”
41. x1m0 † ym′0 ¶ x1y0 [Fig. I (α).
i.e. “All x are y′.”
42. m′x0 † ym0 ¶ xy0 [Fig. I.
i.e. “No x are y.”
SL5-BSolutions for § 5, Nos. 13–24.
13. No Frenchmen like plumpudding;
All Englishmen like plumpudding.
Univ. “men”; m = liking plumpudding; x = French; y = English.
xm0 † y1m′0 ¶ y1x0 [Fig. I (α).
i.e. Englishmen are not Frenchmen.
14. No portrait of a lady, that makes her simper or scowl, is satisfactory;
No photograph of a lady ever fails to make her simper or scowl.
Univ. “portraits of ladies”; m = making the subject simper or scowl; x = satisfactory; y = photographic.
mx0 † ym′0 ¶ xy0 [Fig. I.
i.e. No photograph of a lady is satisfactory.
15. All pale people are phlegmatic;
No one looks poetical unless he is pale.
Univ. “people”; m = pale; x = phlegmatic; y = looking poetical.
m1x′0 † m′y0 ¶ x′y0 [Fig. I.
i.e. No one looks poetical unless he is phlegmatic.
16. No old misers are cheerful;
Some old misers are thin.
Univ. “persons”; m = old misers; x = cheerful; y = thin.
mx0 † my1 ¶ x′y1 [Fig. II.
i.e. Some thin persons are not cheerful.
17. No one, who exercises self-control, fails to keep his temper;
Some judges lose their tempers.
Univ. “persons”; m = keeping their tempers; x = exercising self-control; y = judges.
xm′0 † ym′1 ¶ x′y1 [Fig. II.
i.e. Some judges do not exercise self-control.
18. All pigs are fat;
Nothing that is fed on barley-water is fat.
Univ. is “things”; m = fat; x = pigs; y = fed on barley-water.
x1m′0 † ym0 ¶ x1y0 [Fig. I (α).
i.e. Pigs are not fed on barley-water.
19. All rabbits, that are not greedy, are black;
No old rabbits are free from greediness.
Univ. is “rabbits”; m = greedy; x = black; y = old.
m′1x′0 † ym′0 ¶ xy′1 [Fig. III.
i.e. Some black rabbits are not old.
20. Some pictures are not first attempts;
No first attempts are really good.
Univ. is “things”; m = first attempts; x = pictures; y = really good.
xm′1 † my0 ¶ nothing.
[Fallacy of Unlike Eliminands with an Entity-Premiss.]
21. I never neglect important business;
Your business is unimportant.
Univ. is “business”; m = important; x = neglected by me; y = your.
mx0 † y1m0 ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]
22. Some lessons are difficult;
What is difficult needs attention.
Univ. is “things”; m = difficult; x = lessons; y = needing attention.
xm1 † m1y′0 ¶ xy1 [Fig. II.
i.e. Some lessons need attention.
23. All clever people are popular;
All obliging people are popular.
Univ. is “people”; m = popular; x = clever; y = obliging.
x1m′0 † y1m′0 ¶ nothing.
[Fallacy of Like Eliminands not asserted to exist.]
24. Thoughtless people do mischief;
No thoughtful person forgets a promise.
Univ. is “persons”; m = thoughtful; x = mischievous; y = forgetful of promises.
m′1x′0 † my0 ¶ x′y0
>
i.e. No one, who forgets a promise, fails to do mischief.
SL6-BSolutions for § 6.
1. xm1 † my′0 ¶ xy1 [Fig. II.] Concl. right.
2. x1m′0 † ym′0 Fallacy of Like Eliminands not asserted to exist.
3. xm′1 † y′1m′0 ¶ xy1 [Fig. II.] Concl. right.
4. x1m′0 † ym0 ¶ x1y0 [Fig. I (α).] Concl. right.
5. m′x′1 † m′y0 ¶ x′y′1 [Fig. II.] Concl. right.
6. x′m0 † y1m0 Fallacy of Like Eliminands not asserted to exist.
7. m′x′1 † y′1m0 Fallacy of Unlike Eliminands with an Entity-Premiss.
8. m′x′0 † y′1m0 ¶ y′1x′0 [Fig. I (α).] Concl. right.
9. mx′1 † my0 ¶ x′y′1 [Fig. II.] Concl. right.
10. m′1x0 † m′1y′0 ¶ x′y1 [Fig. III.] Concl. right.
11. x1m0 † ym1 ¶ x′y1 [Fig. II.] Concl. right.
12. xm0 † m′y′0 ¶ xy′0 [Fig. I.] Concl. right.
13. xm0 † y′1m′0 ¶ y′1x0 [Fig. I (α).] Concl. right.
14. m′1x0 † m′1y′0 ¶ x′y1 [Fig. III.] Concl. right.
15. mx′1 † y1m0 ¶ x′y′1 [Fig. II.] Concl. right.
16. x′m0 † y′1m0 Fallacy of Like Eliminands not asserted to exist.
17. m′x0 † m′1y0 ¶ x′y′1 [Fig. III.] Concl. right.
18. x′m0 † my1 ¶ xy1 [Fig. II.] Concl. right.
19. mx′1 † m1y′0 ¶ x′y1 [Fig. II.] Concl. right.
20. x′m′0 † m′y′1 ¶ xy′1 [Fig. II.] Concl. right.
21. mx0 † m1y0 ¶ x′y′1 [Fig. III.] Concl. right.
22. x′1m′0 † ym′1 ¶ xy1 [Fig. II.] Concl. wrong: the right one is “Some x are y.”
23. m1x′0 † m′y′0 ¶ x′y′0 [Fig. I.] Concl. right.
24. x1m0 † m′1y′0 ¶ x1y′0 [Fig. I (α).] Concl. right.
25. xm′0 † m1y′0 ¶ xy′0 [Fig. I.] Concl. right.
26. m1x0 † y1m′0 ¶ y1x0 [Fig. I (α).] Concl. right.
27. x1m′0 † my′0 ¶ x1y′0 [Fig. I (α).] Concl. right.
28. x1m′0 † y′m′0 Fallacy of Like Eliminands not asserted to exist.
29. x′m0 † m′y′0 ¶ x′y′0 [Fig. I.] Concl. right.
30. x1m′0 † m1y0 ¶ x1y0 [Fig. I (α).] Concl. right.
31. x′1m0 † y′m′0 ¶ x′1y′0 [Fig. I (α).] Concl. right.
32. xm0 † y′m′0 ¶ xy′0 [Fig. I.] Concl. right.
33. m1x0 † y′1m′0 ¶ y′1x0 [Fig. I (α).] Concl. right.
34. x1m0 † ym′1 Fallacy of Unlike Eliminands with an Entity-Premiss.
35. xm1 † m1y′0 ¶ xy1 [Fig. II.] Concl. right.
36. m1x0 † y1m′0 ¶ y1x0 [Fig. I (α).] Concl. right.
37. mx′0 † m1y0 ¶ xy′1 [Fig. III.] Concl. right.
38. xm0 † my′0 Fallacy of Like Eliminands not asserted to exist.
39. mx0 † my′1 ¶ x′y′1 [Fig. II.] Concl. right.
40. mx′0 † ym1 ¶ xy1 [Fig. II.] Concl. right.
SL7-BSolutions for § 7.
1. No doctors are enthusiastic;
You are enthusiastic.
You are not a doctor.
Univ. “persons”; m = enthusiastic; x = doctors; y = you.
xm0 † y1m′0 ¶ y1x0 [Fig. I (α).
Conclusion right.
2. Dictionaries are useful;
Useful books are valuable.
Dictionaries are valuable.
Univ. “books”; m = useful; x = dictionaries; y = valuable.
x1m′0 † m1y′0 ¶ x1y′0 [Fig. I (α).
Conclusion right.
3. No misers are unselfish;
None but misers save egg-shells.
No unselfish people save egg-shells.
Univ. “people”; m = misers; x = selfish; y = people who save egg-shells.
mx′0 † m′y0 ¶ x′y0 [Fig. I.
Conclusion right.
4. Some epicures are ungenerous;
All my uncles are generous.
My uncles are not epicures.
Univ. “persons”; m = generous; x = epicures; y = my uncles.
xm′1 † y1m′0 ¶ xy′1 [Fig. II.
Conclusion wrong: right one is “Some epicures are not uncles of mine.”
5. Gold is heavy;
Nothing but gold will silence him.
Nothing light will silence him.
Univ. “things”; m = gold; x = heavy; y = able to silence him.
m1x′0 † m′y0 ¶ x′y0 [Fig. I.
Conclusion right.
6. Some healthy people are fat;
No unhealthy people are strong.
Some fat people are not strong.
Univ. “people”; m = healthy; x = fat; y = strong.
mx1 † m′y0
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
7. I saw it in a newspaper;
All newspapers tell lies.
It was a lie.
Univ. “publications”; m = newspapers; x = publications in which I saw it; y = telling lies.
x1m′0 † m1y′0 ¶ x1y′0 [Fig. I (α).
Conclusion wrong: right one is “The publication, in which I saw it, tells lies.”
8. Some cravats are not artistic;
I admire anything artistic.
There are some cravats that I do not admire.
Univ. “things”; m = artistic; x = cravats; y = things that I admire.
xm1 † m1y0
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
9. His songs never last an hour.
A song, that lasts an hour, is tedious.
His songs are never tedious.
Univ. “songs”; m = lasting an hour; x = his; y = tedious.
x1m0 † m1y′0 ¶ x′y1 [Fig. III.
Conclusion wrong: right one is “Some tedious songs are not his.”
10. Some candles give very little light;
Candles are meant to give light.
Some things, that are meant to give light, give very little.
Univ. “things”; m = candles; x = giving &c.; y = meant &c.
mx1 † m1y′0 ¶ xy1 [Fig. II.
Conclusion right.
11. All, who are anxious to learn, work hard.
Some of these boys work hard.
Some of these boys are anxious to learn.
Univ. “persons”; m = hard-working; x = anxious to learn; y = these boys.
x1m′0 † ym1
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
12. All lions are fierce;
Some lions do not drink coffee.
Some creatures that drink coffee are not fierce.
Univ. “creatures”; m = lions; x = fierce; y = creatures that drink coffee.
m1x′0 † my′1 ¶ xy′1 [Fig. II.
Conclusion wrong: right one is “Some fierce creatures do not drink coffee.”
13. No misers are generous;
Some old men are ungenerous.
Some old men are misers.
Univ. “persons”; m = generous; x = misers; y = old men.
xm0 † ym′1
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
14. No fossil can be crossed in love;
An oyster may be crossed in love.
Oysters are not fossils.
Univ. “things”; m = things that can be crossed in love; x = fossils; y = oysters.
xm0 † y1m′0 ¶ y1x0 [Fig. I (α).
Conclusion right.
15. All uneducated people are shallow;
Students are all educated.
No students are shallow.
Univ. “people”; m = educated; x = shallow; y = students.
m′1x′0 † y1m′0 ¶ xy′1 [Fig. III.
Conclusion wrong: right one is “Some shallow people are not students.”
16. All young lambs jump;
No young animals are healthy, unless they jump.
All young la
mbs are healthy.
Univ. “young animals”; m = young animals that jump; x = lambs; y = healthy.
x1m′0 † m′y0
No Conclusion. [Fallacy of Like Eliminands not asserted to exist.]
17. Ill-managed business is unprofitable;
Railways are never ill-managed.
All railways are profitable.
Univ. “business”; m = ill-managed; x = profitable; y = railways.
m1x0 † y1m0 ¶ x′y′1 [Fig. III.
Conclusion wrong: right one is “Some business, other than railways, is profitable.”
18. No Professors are ignorant;
All ignorant people are vain.
No Professors are vain.
Univ. “people”; m = ignorant; x = Professors; y = vain.
xm0 † m1y′0 ¶ x′y1 [Fig. III.
Conclusion wrong: right one is “Some vain persons are not Professors.”
19. A prudent man shuns hyænas.
No banker is imprudent.
No banker fails to shun hyænas.
Univ. “men”; m = prudent; x = shunning hyænas; y = bankers.
m1x′0 † ym′0 ¶ x′y0 [Fig. I.
Conclusion right.
20. All wasps are unfriendly;
No puppies are unfriendly.
No puppies are wasps.
Univ. “creatures”; m = friendly; x = wasps; y = puppies.
x1m0 † ym′0 ¶ x1y0 [Fig. I (α).
Conclusion incomplete: complete one is “Wasps are not puppies”.
21. No Jews are honest;
Some Gentiles are rich.
Some rich people are dishonest.
Univ. “persons”; m = Jews; x = honest; y = rich.
mx0 † m′y1
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
22. No idlers win fame;
Some painters are not idle.
Some painters win fame.
Univ. “persons”; m = idlers; x = persons who win fame; y = painters.
mx0 † ym′1
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
23. No monkeys are soldiers;
All monkeys are mischievous.
Some mischievous creatures are not soldiers.
Univ. “creatures”; m = monkeys; x = soldiers; y = mischievous.
mx0 † m1y′0 ¶ x′y1 [Fig. III.
Conclusion right.
24. All these bonbons are chocolate-creams;
All these bonbons are delicious.
Chocolate-creams are delicious.
Univ. “food”; m = these bonbons; x = chocolate-creams; y = delicious.
m1x′0 † m1y′0 ¶ xy1 [Fig. III.
Conclusion wrong, being in excess of the right one, which is “Some chocolate-creams are delicious.”
25. No muffins are wholesome;
All buns are unwholesome.
Buns are not muffins.