Complete Works of Lewis Carroll (168 page)

All
x
are
y
.

28.

All
x
are
m
;

No
y
′
are
m
′
.

All
x
are
y
.

29.

No
x
′
are
m
;

No
m
′
are
y
′
.

No
x
′
are
y
′
.

30.

All
x
are
m
;

All
m
are
y
′
.

All
x
are
y
′
.

31.

All
x
′
are
m
′
;

No
y
′
are
m
′
.

All
x
′
are
y
.

32.

No
x
are
m
;

No
y
′
are
m
′
.

No
x
are
y
′
.

33.

All
m
are
x
′
;

All
y
′
are
m
.

All
y
′
are
x
′
.

34.

All
x
are
m
′
;

Some
y
are
m
′
.

Some
y
are
x
.

35.

Some
x
are
m
;

All
m
are
y
.

Some
x
are
y
.

36.

All
m
are
x
′
;

All
y
are
m
.

All
y
are
x
′
.

37.

No
m
are
x
′
;

All
m
are
y
′
.

Some
x
are
y
′
.

38.

No
x
are
m
;

No
m
are
y
′
.

No
x
are
y
′
.

39.

No
m
are
x
;

Some
m
are
y
′
.

Some
x
′
are
y
′
.

40.

No
m
are
x
′
;

Some
y
are
m
.

Some
x
are
y
.

EX7§ 7.

Trios of Concrete Propositions, proposed as Syllogisms: to be examined.

  1.
No doctors are enthusiastic;

You are enthusiastic.

    You are not a doctor.

  2.
Dictionaries are useful;

Useful books are valuable.

    Dictionaries are valuable.

  3.
No misers are unselfish;

None but misers save egg-shells.

    No unselfish people save egg-shells.

  4.
Some epicures are ungenerous;

All my uncles are generous.

    My uncles are not epicures.

  5.
Gold is heavy;

Nothing but gold will silence him.

    Nothing light will silence him.

  6.
Some healthy people are fat;

No unhealthy people are strong.

    Some fat people are not strong.

  7.
“I saw it in a newspaper.”

“All newspapers tell lies.”

    It was a lie.

  8.
Some cravats are not artistic;

I admire anything artistic.

    There are some cravats that I do not admire.

  9.
His songs never last an hour;

A song, that lasts an hour, is tedious.

    His songs are never tedious.

10.
Some candles give very little light;

Candles are
meant
to give light.

    Some things, that are meant to give light, give very little.

11.
All, who are anxious to learn, work hard;

Some of these boys work hard.

    Some of these boys are anxious to learn.

12.
All lions are fierce;

Some lions do not drink coffee.

    Some creatures that drink coffee are not fierce.

13.
No misers are generous;

Some old men are ungenerous.

    Some old men are misers.

14.
No fossil can be crossed in love;

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
′
.