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 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.]

  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.