Complete Works of Lewis Carroll (190 page)

m
1
x
′
0
†
my
0
    ¶
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.

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

Conclusion wrong: right one is “No man walks on neither.”

36.
No wheelbarrows are comfortable;

No uncomfortable vehicles are popular.

No wheelbarrows are popular.

Univ.
“vehicles”;
m
 = comfortable;
x
 = wheelbarrows;
y
 = popular.

xm
0
†
m
′x
0
    ¶
xy
0
        [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.

xm
0
†
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.

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

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

x
1
m
′
0
†
ym
′
1
    ¶
x
′y
1
        [Fig.
II.

Conclusion right.

SL8
Solutions for § 8.

  1.
1
cd
0
† 2
a
1
d
′
0
† 3
b
1
c
′
0
;         1
cd
† 2
ad
′
† 3
bc
′
    ¶
ab
0
†
a
1
†
b
1

i.e.
¶
a
1
b
0
†
b
1
a
0

  2.
1
d
1
b
′
0
† 2
ac
′
0
† 3
bc
0
;         1
db
′
† 3
bc
† 2
ac
′
    ¶
da
0
†
d
1
    i.e.
¶
d
1
a
0

  3.
1
ba
0
† 2
cd
′
0
† 3
d
1
b
′
0
;         1
ba
† 3
db
′
† 2
cd
′
    ¶
ac
0

  4.
1
bc
0
† 2
a
1
b
′
0
† 3
c
′d
0
;         1
bc
† 2
ab
′
† 3
c
′d
    ¶
ad
0
†
a
1
    i.e.
¶
a
1
d
0

   5.
1
b
′
1
a
0
† 2
bc
0
† 3
a
′d
0
;         1
b
′a
† 2
bc
† 3
a
′d
    ¶
cd
0

  6.
1
a
1
b
0
† 2
b
′c
0
† 3
d
1
a
′
0
;         1
ab
† 2
b
′c
† 3
da
′
    ¶
cd
0
†
d
1
    i.e.
¶
d
1
c
0

  7.
1
db
′
0
† 2
b
1
a
′
0
† 3
cd
′
0
;         1
db
′
† 2
ba
′
† 3
cd
′
    ¶
a
′c
0

  8.
1
b
′d
0
† 2
a
′b
0
† 3
c
1
d
′
0
;         1
b
′d
† 2
a
′b
† 3
cd
′
    ¶
a
′c
0
†
c
1
    i.e.
¶
c
1
a
′
0

  9.
1
b
′
1
a
′
0
† 2
ad
0
† 3
b
1
c
′
0
;         1
b
′a′
† 2
ad
† 3
bc
′
    ¶
dc
′
0

10.
1
cd
0
† 2
b
1
c
′
0
† 3
ad
′
0
;         1
cd
† 2
bc
′
† 3
ad
′
    ¶
ba
0
†
b
1
    i.e.
¶
b
1
a
0

11.
1
bc
0
† 2
d
1
a
′
0
† 3
c
′
1
a
0
;         1
bc
† 3
c
′a
† 2
da
′
    ¶
bd
0
†
d
1
    i.e.
¶
d
1
b
0