Complete Works of Lewis Carroll (163 page)

The Reader, who has successfully grappled with all the Examples hitherto set, and who thirsts, like Alexander the Great, for “more worlds to conquer,” may employ his spare energies on the following 17 Examination-Papers.
He is recommended not to attempt more than
one
Paper on any one day.
The answers to the questions about words and phrases may be found by referring to the Index at p.
197.

     I.
§
4
, 31 (p.
100); §
5
, 31–34 (p.
102); §
6
, 16, 17 (p.
106); §
7
, 16 (p.
108); §
8
, 5, 6 (p.
110); §
9
, 5, 22, 42 (pp.
112, 115, 119).
What is ‘Classification’?
And what is a ‘Class’?

    II.
§
4
, 32 (p.
100); §
5
, 35–38 (pp.
102, 103); §
6
, 18 (p.
107); §
7
, 17, 18 (p.
108); §
8
, 7, 8 (p.
110); §
9
, 6, 23, 43 (pp.
112, 115, 119).
What are ‘Genus’, ‘Species’, and ‘Differentia’?

   III.
§
4
, 33 (p.
100); §
5
, 39–42 (p.
103); §
6
, 19, 20 (p.
107); §
7
, 19 (p.
109); §
8
, 9, 10 (p.
111); §
9
, 7, 24, 44 (pp.
113, 116, 120).
What are ‘Real’ and ‘Imaginary’ Classes?

   IV.
§
4
, 34 (p.
100); §
5
, 43–46 (p.
103); §
6
, 21 (p.
107); §
7
, 20, 21 (p.
109); §
8
, 11, 12 (p.
111); §
9
, 8, 25, 45 (pp.
113, 116, 120).
What is ‘Division’?
When are Classes said to be ‘Codivisional’?

    V.
§
4
, 35 (p.
100); §
5
, 47–50 (p.
103); §
6
, 22, 23 (p.
107); §
7
, 22 (p.
109); §
8
, 15, 16 (p.
111); §
9
, 9, 28, 46 (pp.
113, 116, 120).
What is ‘Dichotomy’?
What arbitrary rule does it sometimes require?

   VI.
§
4
, 36 (p.
100); §
5
, 51–54 (p.
103); §
6
, 24 (p.
107); §
7
, 23, 24 (p.
109); §
8
, 17 (p.
111); §
9
, 10, 29, 47 (pp.
113, 117, 120).
What is a ‘Definition’?

  VII.
§
4
, 37 (p.
100); §
5
, 55–58 (pp.
103, 104); §
6
, 25, 26 (p.
107); §
7
, 25 (p.
109); §
8
, 18 (p.
111); §
9
, 11, 30, 49 (pp.
113, 117, 121).
What are the ‘Subject’ and the ‘Predicate’ of a Proposition?
What is its ‘Normal’ form?

 VIII.
§
4
, 38 (p.
100); §
5
, 59–62 (p.
104); §
6
, 27 (p.
107); §
7
, 26, 27 (p.
109); §
8
, 20 (p.
111); §
9
, 12, 31, 50 (pp.
113, 117, 121).
What is a Proposition ‘in
I
’?
‘In
E
’?
And ‘in
A
’?

   IX.
§
4
, 39 (p.
100); §
5
, 63–66 (p.
104); §
6
, 28, 29 (p.
107); §
7
, 28 (p.
109); §
8
, 21 (p.
111); §
9
, 13, 32, 51 (pp.
114, 117, 121).
What is the ‘Normal’ form of a Proposition of Existence?

    X.
§
4
, 40 (p.
100); §
5
, 67–70 (p.
104); §
6
, 30 (p.
107); §
7
, 29, 30 (p.
109); §
8
, 22 (p.
111); §
9
, 14, 33, 52 (pp.
114, 117, 122).
What is the ‘Universe of Discourse’?

   XI.
§
4
, 41 (p.
100); §
5
, 71–74 (p.
104); §
6
, 31, 32 (p.
107); §
7
, 31 (p.
109); §
8
, 23 (p.
111); §
9
, 15, 34, 53 (pp.
114, 118, 122).
What is implied, in a Proposition of Relation, as to the Reality of its Terms?

  XII.
§
4
, 42 (p.
100); §
5
, 75–78 (p.
105); §
6
, 33 (p.
107); §
7
, 32, 33 (pp.
109, 110); §
8
, 25 (p.
111); §
9
, 16, 35, 54 (pp.
114, 118, 122).
Explain the phrase “sitting on the fence”.

 XIII.
§
5
, 79–83 (p.
105); §
6
, 34, 35 (p.
107); §
7
, 34 (p.
110); §
8
, 26 (p.
111); §
9
, 17, 36, 55 (pp.
114, 118, 122).
What are ‘Converse’ Propositions?

 XIV.
§
5
, 84–88 (p.
105); §
6
, 36 (p.
107); §
7
, 35, 36 (p.
110); §
8
, 27 (p.
111); §
9
, 18, 37, 56 (pp.
114, 118, 123).
What are ‘Concrete’ and ‘Abstract’ Propositions?

  XV.
§
5
, 89–93 (p.
105); §
6
, 37, 38 (p.
107); §
7
, 37 (p.
110); §
8
, 28 (p.
111); §
9
, 19, 38, 57 (pp.
115, 118, 123).
What is a ‘Syllogism’?
And what are its ‘Premisses’ and its ‘Conclusion’?

 XVI.
§
5
, 94–97 (p.
106); §
6
, 39 (p.
107); §
7
, 38, 39 (p.
110); §
8
, 29 (p.
111); §
9
, 20, 39, 58 (pp.
115, 119, 123).
What is a ‘Sorites’?
And what are its ‘Premisses’, its ‘Partial Conclusions’, and its ‘Complete Conclusion’?

XVII.
§
5
, 98–101 (p.
106); §
6
, 40 (p.
107); §
7
, 40 (p.
110); §
8
, 30 (p.
111); §
9
, 21, 41, 59, 60 (pp.
115, 119, 124).
What are the ‘Universe of Discourse’, the ‘Eliminands’, and the ‘Retinends’, of a Syllogism?
And of a Sorites?

BOOK VIII.

EXAMPLES, ANSWERS, AND SOLUTIONS.

[N.B.
Reference tags for Examples, Answers & Solutions will be found in the right margin.]

CHAPTER I.

EXAMPLES.

EX1§ 1.

Propositions of Relation, to be reduced to normal form.

  1.
I have been out for a walk.

  2.
I am feeling better.

  3.
No one has read the letter but John.

  4.
Neither you nor I are old.

  5.
No fat creatures run well.

  6.
None but the brave deserve the fair.

  7.
No one looks poetical unless he is pale.

  8.
Some judges lose their tempers.

  9.
I never neglect important business.

10.
What is difficult needs attention.

11.
What is unwholesome should be avoided.

12.
All the laws passed last week relate to excise.

13.
Logic puzzles me.

14.
There are no Jews in the house.

15.
Some dishes are unwholesome if not well-cooked.

16.
Unexciting books make one drowsy.

17.
When a man knows what he’s about, he can detect a sharper.

18.
You and I know what we’re about.

19.
Some bald people wear wigs.

20.
Those who are fully occupied never talk about their grievances.

21.
No riddles interest me if they can be solved.

EX2§ 2.

Pairs of Abstract Propositions, one in terms of x and m, and the other in terms of y and m, to be represented on the same Triliteral Diagram.

  1.
No
x
are
m
;

No
m
′
are
y
.

  2.
No
x
′
are
m
′
;

All
m
′
are
y
.

  3.
Some
x
′
are
m
;

No
m
are
y
.

  4.
All
m
are
x
;

All
m
′
are
y
′
.

  5.
All
m
′
are
x
;

All
m
′
are
y
′
.

  6.
All
x
′
are
m
′
;

No
y
′
are
m
.

  7.
All
x
are
m
;

All
y
′
are
m
′
.

  8.
Some
m
′
are
x
′
;

No
m
are
y
.

  9.
All
m
are
x
′
;

No
m
are
y
.

10.
No
m
are
x
′
;

No
y
are
m
′
.

11.
No
x
′
are
m
′
;

No
m
are
y
.

12.
Some
x
are
m
;

All
y
′
are
m
.

13.
All
x
′
are
m
;

No
m
are
y
.

14.
Some
x
are
m
′
;

All
m
are
y
.

15.
No
m
′
are
x
′
;

All
y
are
m
.

16.
All
x
are
m
′
;

No
y
are
m
.

17.
Some
m
′
are
x
;

No
m
′
are
y
′
.

18.
All
x
are
m
′
;

Some
m
′
are
y
′
.

19.
All
m
are
x
;

Some
m
are
y
′
.

20.
No
x
′
are
m
;

Some
y
are
m
.

21.
Some
x
′
are
m
′
;

All
y
′
are
m
.

22.
No
m
are
x
;

Some
m
are
y
.

23.
No
m
′
are
x
;

All
y
are
m
′
.

24.
All
m
are
x
;

No
y
′
are
m
′
.

25.
Some
m
are
x
;

No
y
′
are
m
.

26.
All
m
′
are
x
′
;

Some y are
m
′
.

27.
Some
m
are
x
′
;

No
y
′
are
m
′
.

28.
No
x
are
m
′
;

All
m
are
y
′
.

29.
No
x
′
are
m
;

No
m
are
y
′
.

30.
No
x
are
m
;

Some
y
′
are
m
′
.

31.
Some
m
′
are
x
;

All
y
′
are
m
;

32.
All
x
are
m
′
;

All
y
are
m
.

EX3§ 3.

Marked Triliteral Diagrams, to be interpreted in terms of x and y.

1

2

3

4