Complete Works of Lewis Carroll (178 page)

42.
My writing-desk is full of live scorpions.

43.
No Mandarin ever reads Hogg’s poems.

44.
Shakespeare was clever.

45.
Rainbows are not worth writing odes to.

46.
These Sorites-examples are difficult.

47.
All my dreams come true.

48.
All the English pictures here are painted in oils.

49.
Donkeys are not easy to swallow.

50.
Opium-eaters never wear white kid gloves.

51.
A good husband always comes home for his tea.

52.
Bathing-machines are never made of mother-of-pearl.

53.
Rainy days are always cloudy.

54.
No heavy fish is unkind to children.

55.
No engine-driver lives on barley-sugar.

56.
All the animals in the yard gnaw bones.

57.
No badger can guess a conundrum.

58.
No cheque of yours, received by me, is payable to order.

59.
I cannot read any of Brown’s letters.

60.
I always avoid a kangaroo.

CHAPTER III.

SOLUTIONS.

§ 1.

Propositions of Relation reduced to normal form.

SL1
Solutions for § 1.

1.
The Univ.
is “persons.”
The Individual “I” may be regarded as a Class, of persons, whose peculiar Attribute is “represented by the Name ‘I’”, and may be called the Class of “I’s”.
It is evident that this Class cannot possibly contain more than one Member: hence the Sign of Quantity is “all”.
The verb “have been” may be replaced by the phrase “are persons who have been”.
The Proposition may be written thus:—

“All”

Sign of Quantity.

“I’s”

Subject.

“are”

Copula.

“persons who have been out for a walk”

Predicate.

or, more briefly,

“All | I’s | are | persons who have been out for a walk”.

2.
The Univ.
and the Subject are the same as in Ex.
1.
The Proposition may be written

“All | I’s | are | persons who feel better”.

3.
Univ.
is “persons”.
The Subject is evidently the Class of persons from which John is
excluded
;
i.e.
it is the Class containing all persons who are
not
“John”.

The Sign of Quantity is “no”.

The verb “has read” may be replaced by the phrase “are persons who have read”.

The Proposition may be written

“No | persons who are not ‘John’ | are | persons who have read the letter”.

4.
Univ.
is “persons”.
The Subject is evidently the Class of persons whose only two Members are “you and I”.

Hence the Sign of Quantity is “no”.

The Proposition may be written

“No | Members of the Class ‘you and I’ | are | old persons”.

5.
Univ.
is “creatures”.
The verb “run well” may be replaced by the phrase “are creatures that run well”.

The Proposition may be written

“No | fat creatures | are | creatures that run well”.

6.
Univ.
is “persons”.
The Subject is evidently the Class of persons who are
not
brave.

The verb “deserve” may be replaced by the phrase “are deserving of”.

The Proposition may be written

“No | not-brave persons | are | persons deserving of the fair”.

7.
Univ.
is “persons”.
The phrase “looks poetical” evidently belongs to the
Predicate
; and the
Subject
is the Class, of persons, whose peculiar Attribute is “
not
-pale”.

The Proposition may be written

“No | not-pale persons | are | persons who look poetical”.

8.
Univ.
is “persons”.

The Proposition may be written

“Some | judges | are | persons who lose their tempers”.

9.
Univ.
is “persons”.
The phrase “never neglect” is merely a stronger form of the phrase “am a person who does not neglect”.

The Proposition may be written

“All | ‘I’s’ | are | persons who do not neglect important business”.

10.
Univ.
is “things”.
The phrase “what is difficult” (
i.e.
“that which is difficult”) is equivalent to the phrase “all difficult things”.

The Proposition may be written

“All | difficult things | are | things that need attention”.

11.
Univ.
is “things”.
The phrase “what is unwholesome” may be interpreted as in Ex.
10.

The Proposition may be written

“All | unwholesome things | are | things that should be avoided”.

12.
Univ.
is “laws”.
The Predicate is evidently a Class whose peculiar Attribute is “relating to excise”.

The Proposition may be written

“All | laws passed last week | are | laws relating to excise”.

13.
Univ.
is “things”.
The Subject is evidently the Class, of studies, whose peculiar Attribute is “logical”; hence the Sign of Quantity is “all”.

The Proposition may be written

“All | logical studies | are | things that puzzle me”.

14.
Univ.
is “persons”.
The Subject is evidently “persons in the house”.

The Proposition may be written

“No | persons in the house | are | Jews”.

15.
Univ.
is “dishes”.
The phrase “if not well-cooked” is equivalent to the Attribute “not well-cooked”.

The Proposition may be written

“Some | not well-cooked dishes | are | unwholesome dishes”.

16.
Univ.
is “books”.
The phrase “make one drowsy” may be replaced by the phrase “are books that make one drowsy”.

The Sign of Quantity is evidently “all”.

The Proposition may be written

“All | unexciting books | are | books that make one drowsy”.

17.
Univ.
is “men”.
The Subject is evidently “a man who knows what he’s about”; and the word “when” shows that the Proposition is asserted of
every
such man,
i.e.
of
all
such men.
The verb “can” may be replaced by “are men who can”.

The Proposition may be written

“All | men who know what they’re about | are | men who can detect a sharper”.

18.
The Univ.
and the Subject are the same as in Ex.
4.

The Proposition may be written

“All | Members of the Class ‘you and I’ | are | persons who know what they’re about”.

19.
Univ.
is “persons”.
The verb “wear” may be replaced by the phrase “are accustomed to wear”.

The Proposition may be written

“Some | bald persons | are | persons accustomed to wear wigs”.

20.
Univ.
is “persons”.
The phrase “never talk” is merely a stronger form of “are persons who do not talk”.

The Proposition may be written

“All | fully occupied persons | are | persons who do not talk about their grievances”.

21.
Univ.
is “riddles”.
The phrase “if they can be solved” is equivalent to the Attribute “that can be solved”.

The Proposition may be written

“No | riddles that can be solved | are | riddles that interest me”.

§ 2.

Method of Diagrams.

SL4-A
Solutions for § 4, Nos.
1–12.

1. 

No
m
are
x
′
;

All
m
′
are
y
.

∴
No
x
′
are
y
′
.

2. 

No
m
′
are
x
;

Some
m
′
are
y
′
.

∴
Some
x
are
y
′
.

3. 

All
m
′
are
x
;

All
m
′
are
y
′
.