1. I have been out for a walk;
I am feeling better.
Univ. is “persons”; m = the Class of I’s; x = persons who have been out for a walk; y = persons who are feeling better.
All m are x; All m are y. | Diagram representing all m are x and all m are y | Diagram representing x y exists ∴ Some x are y. |
i.e. Somebody, who has been out for a walk, is feeling better.
pg139 2. No one has read the letter but John;
No one, who has not read it, knows what it is about.
Univ. is “persons”; m = persons who have read the letter; x = the Class of Johns; y = persons who know what the letter is about.
No x′ are m; No m′ are y. | Diagram representing x prime m and y m prime do not exist | Diagram representing x prime y does not exist ∴ No x′ are y. |
i.e. No one, but John, knows what the letter is about.
3. Those who are not old like walking;
You and I are young.
Univ. is “persons”; m = old; x = persons who like walking; y = you and I.
All m′ are x; All y are m′. | Diagram representing all m prime are x and all y are m prime | Diagram representing all y are x ∴ All y are x. |
i.e. You and I like walking.
4. Your course is always honest;
Your course is always the best policy.
Univ. is “courses”; m = your; x = honest; y = courses which are the best policy.
All m are x; All m are y. | Diagram representing all m are x and all m are y | Diagram representing x y exists ∴ Some x are y. |
i.e. Honesty is sometimes the best policy.
5. No fat creatures run well;
Some greyhounds run well.
Univ. is “creatures”; m = creatures that run well; x = fat; y = greyhounds.
No x are m; Some y are m. | Diagram representing x m does not exist and y m exists | Diagram representing x prime y exists ∴ Some y are x′. |
i.e. Some greyhounds are not fat.
pg140 6. Some, who deserve the fair, get their deserts;
None but the brave deserve the fair.
Univ. is “persons”; m = persons who deserve the fair; x = persons who get their deserts; y = brave.
Some m are x; No y′ are m. | Diagram representing x m exists and y prime m does not exist | Diagram representing x y exists ∴ Some y are x. |
i.e. Some brave persons get their deserts.
7. Some Jews are rich;
All Esquimaux are Gentiles.
Univ. is “persons”; m = Jews; x = rich; y = Esquimaux.
Some m are x; All y are m′. | Diagram representing x m exists all y are m | Diagram representing x y prime exists ∴ Some x are y′. |
i.e. Some rich persons are not Esquimaux.
8. Sugar-plums are sweet;
Some sweet things are liked by children.
Univ. is “things”; m = sweet; x = sugar-plums; y = things that are liked by children.
All x are m; Some m are y. | Diagram representing all x are m and y m exists |
There is no Conclusion.
9. John is in the house;
Everybody in the house is ill.
Univ. is “persons”; m = persons in the house; x = the Class of Johns; y = ill.
All x are m; All m are y. | Diagram representing all x are m and all m are y | Diagram representing all x are y ∴ All x are y. |
i.e. John is ill.
pg14110. Umbrellas are useful on a journey;
What is useless on a journey should be left behind.
Univ. is “things”; m = useful on a journey; x = umbrellas; y = things that should be left behind.
All x are m; All m′ are y. | Diagram representing all x are m and all m prime are y | Diagram representing x prime y exists ∴ Some x′ are y. |
i.e. Some things, that are not umbrellas, should be left behind on a journey.
11. Audible music causes vibration in the air;
Inaudible music is not worth paying for.
Univ. is “music”; m = audible; x = music that causes vibration in the air; y = worth paying for.
All m are x; All m′ are y′. | Diagram representing all m are x and all m prime are y prime | Diagram representing x prime y does not exist ∴ No x′ are y. |
i.e. No music is worth paying for, unless it causes vibration in the air.
12. Some holidays are rainy;
Rainy days are tiresome.
Univ. is “days”; m = rainy; x = holidays; y = tiresome.
Some x are m; All m are y. | Diagram representing x m exists and all m are y | Diagram representing x y exists ∴ Some x are y. |
i.e. Some holidays are tiresome.
Some x are m; No m are y′. Some x are y.
| Diagram representing x m and y prime m does not exist | Diagram representing x y exists Hence proposed Conclusion is right. |
All x are m; No y are m′. No y are x′.
| Diagram representing all x are m and y m prime does not exist | There is no Conclusion. |
Some x are m′; All y′ are m. Some x are y.
| Diagram representing x m prime exists and all y prime are m | Diagram representing x y exists Hence proposed Conclusion is right. |
All x are m; No y are m. All x are y′.
| Diagram representing all x are m and y m does not exist | Diagram representing all x are y prime Hence proposed Conclusion is right. |
Some m′ are x′; No m′ are y. Some x′ are y′.
| Diagram representing x prime m prime exists and y m prime does not exist | Diagram representing x prime y prime exists Hence proposed Conclusion is right. |
No x′ are m; All y are m′. All y are x.
| Diagram representing x prime m does not exist and all y are m prime | There is no Conclusion. |
Some m′ are x′; All y′ are m′. Some x′ are y′.
| Diagram representing x prime m prime exists and all y prime are m prime | There is no Conclusion. |
No m′ are x′; All y′ are m′. All y′ are x.
| Diagram representing x prime m prime does not exist and all y prime are m prime | Diagram representing all y prime are x Hence proposed Conclusion is right. |
Some m are x′; No m are y. Some x′ are y′.
| Diagram representing x prime m exists and y m does not exist | Diagram representing x prime y prime exists Hence proposed Conclusion is right. |
All m′ are x′; All m are y. Some y are x′.
| Diagram representing all m prime are x prime and all m are y | Diagram representing x prime y exists Hence proposed Conclusion is right. |
No doctors are enthusiastic;
You are enthusiastic.
You are not a doctor.
Univ. “persons”; m = enthusiastic; x = doctors; y = you.
No x are m; All y are m. All y are x′. | Diagram representing x m does not exist and all y are m | Diagram representing all y are x prime ∴ All y are x′. |
Hence proposed Conclusion is right.
All dictionaries are useful;
Useful books are valuable.
Dictionaries are valuable.
Univ. “books”; m = useful; x = dictionaries; y = valuable.
All x are m; All m are y. All x are y. | Diagram representing all x are m and all m are y | Diagram representing all x are y ∴ All x are y. |
Hence proposed Conclusion is right.
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.
No m are x′; No m′ are y. No x′ are y. | Diagram representing x prime m and y m prime do not exist | Diagram representing x prime y does not exist ∴ No x′ are y. |
Hence proposed Conclusion is right.
Some epicures are ungenerous;
All my uncles are generous.
My uncles are not epicures.
Univ. “persons”; m = generous; x = epicures; y = my uncles.
Some x are m′. All y are m. All y are x′. | Diagram representing x m prime exists and all y are m | Diagram representing x y prime exists ∴ Some x are y′. |
Hence proposed Conclusion is wrong, the right one being “Some epicures are not uncles of mine.”
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.
All m are x; No m′ are y. No x′ are y. | Diagram representing all m are x and y m prime does not exist | Diagram representing x prime y does not exist ∴ No x′ are y. |
Hence proposed Conclusion is right.
Some healthy people are fat;
No unhealthy people are strong.
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′. | Diagram representing x m exists and y m prime does not exist | There is no Conclusion. |
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.]
pg14732. 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.”
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.
pg14818. 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.
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.
pg149 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.
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.”
pg151 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.
pg15215. 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 lambs 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.]
pg15322. 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.
Univ. “food”; m = wholesome; x = muffins; y = buns.
xm0 † y1m0
No Conclusion. [Fallacy of Like Eliminands not asserted to exist.]
26. Some unauthorised reports are false;
All authorised reports are trustworthy.
Some false reports are not trustworthy.
Univ. “reports”; m = authorised; x = true; y = trustworthy.
m′x′1 † m1y′0
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
27. Some pillows are soft;
No pokers are soft.
Some pokers are not pillows.
Univ. “things”; m = soft; x = pillows; y = pokers.
xm1 † ym0 ¶ xy′1 [Fig. II.
Conclusion wrong: right one is “Some pillows are not pokers.”
28. Improbable stories are not easily believed;
None of his stories are probable.
None of his stories are easily believed.
Univ. “stories”; m = probable; x = easily believed; y = his.
m′1x0 † ym0 ¶ xy0 [Fig. I.
Conclusion right.
pg15429. No thieves are honest;
Some dishonest people are found out.
Some thieves are found out.
Univ. “people”; m = honest; x = thieves; y = found out.
xm0 † m′y1
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
30. No muffins are wholesome;
All puffy food is unwholesome.
All muffins are puffy.
Univ. is “food”; m = wholesome; x = muffins; y = puffy.
xm0 † y1m0
No Conclusion. [Fallacy of Like Eliminands not asserted to exist.]
31. No birds, except peacocks, are proud of their tails;
Some birds, that are proud of their tails, cannot sing.
Some peacocks cannot sing.
Univ. “birds”; m = proud of their tails; x = peacocks; y = birds that cannot sing.
x′m0 † my′1 ¶ xy′1 [Fig. II.
Conclusion right.
32. Warmth relieves pain;
Nothing, that does not relieve pain, is useful in toothache.
Warmth is useful in toothache.
Univ. “applications”; m = relieving pain; x = warmth; y = useful in toothache.
x1m′0 † m′y0
No Conclusion. [Fallacy of Like Eliminands not asserted to exist.]
33. No bankrupts are rich;
Some merchants are not bankrupts.
Some merchants are rich.
Univ. “persons”; m = bankrupts; x = rich; y = merchants.
mx0 † ym′1
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
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.
Univ. “persons”; m = bores; x = dreaded; y = begged to prolong their visits.
m1x′0 † my0 ¶ xy′1 [Fig. III.
Conclusion wrong: the right one is “Some dreaded persons are not begged to prolong their visits.”
35. All wise men walk on their feet;
All unwise men walk on their hands.
No man walks on both.
Univ. “men”; m = wise; x = walking on their feet; y = walking on their hands.
m1x′0 † m′1y′0 ¶ x′y′0 [Fig. I.
Conclusion wrong: right one is “No man walks on neither.”
pg15536. No wheelbarrows are comfortable;
No uncomfortable vehicles are popular.
No wheelbarrows are popular.
Univ. “vehicles”; m = comfortable; x = wheelbarrows; y = popular.
xm0 † m′x0 ¶ xy0 [Fig. I.
Conclusion right.
37. No frogs are poetical;
Some ducks are unpoetical.
Some ducks are not frogs.
Univ. “creatures”; m = poetical; x = frogs; y = ducks.
xm0 † ym′1
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
38. No emperors are dentists;
All dentists are dreaded by children.
No emperors are dreaded by children.
Univ. “persons”; m = dentists; x = emperors; y = dreaded by children.
xm0 † m1y′0 ¶ x′y1 [Fig. III.
Conclusion wrong: right one is “Some persons, dreaded by children, are not emperors.”
39. Sugar is sweet;
Salt is not sweet.
Salt is not sugar.
Univ. “things”; m = sweet; x = sugar; y = salt.
x1m′0 † y1m0 ¶ (x1y0 † y1x0) [Fig. I (β).
Conclusion incomplete: omitted portion is “Sugar is not salt.”
40. Every eagle can fly;
Some pigs cannot fly.
Some pigs are not eagles.
Univ. “creatures”; m = creatures that can fly; x = eagles; y = pigs.
x1m′0 † ym′1 ¶ x′y1 [Fig. II.
Conclusion right.
1.
1
i.e. ¶ a1b0 † b1a0
2.
1
3.
1
4.
1