Complete Works of Lewis Carroll (187 page)

    i.e.
“No
x
are
y
.”

39.
mx
′
1
†
my
0
    ¶
x
′y′
1
    [Fig.
II.

    i.e.
“Some
x
′
are
y
′
.”

40.
x
′m
0
†
y
′
1
m
′
0
    ¶
y
′
1
x
′
0
    [Fig.
I (α).

    i.e.
“All
y
′
are
x
.”

41.
x
1
m
0
†
ym
′
0
    ¶
x
1
y
0
    [Fig.
I (α).

    i.e.
“All
x
are
y
′
.”

42.
m
′x
0
†
ym
0
    ¶
xy
0
    [Fig.
I.

    i.e.
“No
x
are
y
.”

SL5-B
Solutions for § 5, Nos.
13
–24.

13.
No Frenchmen like plumpudding;

All Englishmen like plumpudding.

Univ.
“men”;
m
 = liking plumpudding;
x
 = French;
y
 = English.

xm
0
†
y
1
m
′
0
    ¶
y
1
x
0
        [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.

mx
0
†
ym
′
0
    ¶
xy
0
        [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.

m
1
x
′
0
†
m
′y
0
    ¶
x
′y
0
        [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.

mx
0
†
my
1
    ¶
x
′y
1
        [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
′y
1
        [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.

x
1
m
′
0
†
ym
0
    ¶
x
1
y
0
        [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
′
1
x
′
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
†
my
0
    ¶ 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.

mx
0
†
y
1
m
0
    ¶ 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.

xm
1
†
m
1
y
′
0
    ¶
xy
1
        [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.

x
1
m
′
0
†
y
1
m
′
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
′
1
x
′
0
†
my
0
    ¶
x
′y
0

i.e.
No one, who forgets a promise, fails to do mischief.

SL6-B
Solutions for § 6.

  1.
xm
1
†
my
′
0
    ¶
xy
1
        [Fig.
II.]         Concl.
right.

  2.
x
1
m
′
0
†
ym
′
0
        Fallacy of Like Eliminands not asserted to exist.

  3.
xm
′
1
†
y
′
1
m
′
0
    ¶
xy
1
        [Fig.
II.]         Concl.
right.

  4.
x
1
m
′
0
†
ym
0
    ¶
x
1
y
0
        [Fig.
I (α).]         Concl.
right.

  5.
m
′x′
1
†
m
′y
0
    ¶
x
′y′
1
        [Fig.
II.]         Concl.
right.

  6.
x
′m
0
†
y
1
m
0
        Fallacy of Like Eliminands not asserted to exist.

  7.
m
′x′
1
†
y
′
1
m
0
        Fallacy of Unlike Eliminands with an Entity-Premiss.

  8.
m
′x′
0
†
y
′
1
m
0
    ¶
y
′
1
x
′
0
        [Fig.
I (α).]         Concl.
right.

  9.
mx
′
1
†
my
0
    ¶
x
′y′
1
        [Fig.
II.]         Concl.
right.

10.
m
′
1
x
0
†
m
′
1
y
′
0
    ¶
x
′y
1
        [Fig.
III.]         Concl.
right.

11.
x
1
m
0
†
ym
1
    ¶
x
′y
1
        [Fig.
II.]         Concl.
right.

12.
xm
0
†
m
′y′
0
    ¶
xy
′
0
        [Fig.
I.]         Concl.
right.

13.
xm
0
†
y
′
1
m
′
0
    ¶
y
′
1
x
0
        [Fig.
I (α).]         Concl.
right.

14.
m
′
1
x
0
†
m
′
1
y
′
0
    ¶
x
′y
1
        [Fig.
III.]         Concl.
right.

15.
mx
′
1
†
y
1
m
0
    ¶
x
′y′
1
        [Fig.
II.]         Concl.
right.

16.
x
′m
0
†
y
′
1
m
0
        Fallacy of Like Eliminands not asserted to exist.

17.
m
′x
0
†
m
′
1
y
0
    ¶
x
′y′
1
        [Fig.
III.]         Concl.
right.

18.
x
′m
0
†
my
1
    ¶
xy
1
        [Fig.
II.]         Concl.
right.

19.
mx
′
1
†
m
1
y
′
0
    ¶
x
′y
1
        [Fig.
II.]         Concl.
right.

20.
x
′m′
0
†
m
′y′
1
    ¶
xy
′
1
        [Fig.
II.]         Concl.
right.

21.
mx
0
†
m
1
y
0
    ¶
x
′y′
1
        [Fig.
III.]         Concl.
right.

22.
x
′
1
m
′
0
†
ym
′
1
    ¶
xy
1
        [Fig.
II.]         Concl.
wrong: the right one is “Some
x
are
y
.”

23.
m
1
x
′
0
†
m
′y′
0
    ¶
x
′y′
0
        [Fig.
I.]         Concl.
right.

24.
x
1
m
0
†
m
′
1
y
′
0
    ¶
x
1
y
′
0
        [Fig.
I (α).]         Concl.
right.

25.
xm
′
0
†
m
1
y
′
0
    ¶
xy
′
0
        [Fig.
I.]         Concl.
right.

26.
m
1
x
0
†
y
1
m
′
0
    ¶
y
1
x
0
        [Fig.
I (α).]         Concl.
right.

27.
x
1
m
′
0
†
my
′
0
    ¶
x
1
y
′
0
        [Fig.
I (α).]         Concl.
right.

28.
x
1
m
′
0
†
y
′m′
0
        Fallacy of Like Eliminands not asserted to exist.

29.
x
′m
0
†
m
′y′
0
    ¶
x
′y′
0
        [Fig.
I.]         Concl.
right.

30.
x
1
m
′
0
†
m
1
y
0
    ¶
x
1
y
0
        [Fig.
I (α).]         Concl.
right.

31.
x
′
1
m
0
†
y
′m′
0
    ¶
x
′
1
y
′
0
        [Fig.
I (α).]         Concl.
right.

32.
xm
0
†
y
′m′
0
    ¶
xy
′
0
        [Fig.
I.]         Concl.
right.

33.
m
1
x
0
†
y
′
1
m
′
0
    ¶
y
′
1
x
0
        [Fig.
I (α).]         Concl.
right.

34.
x
1
m
0
†
ym
′
1
        Fallacy of Unlike Eliminands with an Entity-Premiss.

35.
xm
1
†
m
1
y
′
0
    ¶
xy
1
        [Fig.
II.]         Concl.
right.