Complete Works of Lewis Carroll (187 page)
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Authors: Lewis Carroll
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.