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Lewis Carroll. Selected Mathematical Works: Symbolic Logic + The Game of Logic + Feeding the Mind: by Charles Lutwidge Dodgson, alias Lewis Carroll
Selected Mathematical Works: Symbolic Logic + The Game of Logic + Feeding the Mind
Table of Contents
SYMBOLIC LOGIC
A Syllogism worked out
PART I. ELEMENTARY
PREFACE TO THE FOURTH EDITION
INTRODUCTION
TO LEARNERS
BOOK I. THINGS AND THEIR ATTRIBUTES
CHAPTER I. INTRODUCTORY
CHAPTER II. CLASSIFICATION
CHAPTER III. DIVISION
§ 1. Introductory
§ 2. Dichotomy
CHAPTER IV. NAMES
CHAPTER V. DEFINITIONS
BOOK II. PROPOSITIONS
CHAPTER I. PROPOSITIONS GENERALLY
§ 1. Introductory
§ 2. Normal form of a Proposition
§ 3. Various kinds of Propositions
CHAPTER II. PROPOSITIONS OF EXISTENCE
CHAPTER III. PROPOSITIONS OF RELATION
§ 1. Introductory
§ 2. Reduction of a Proposition of Relation to Normal form
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
§ 3. A Proposition of Relation, beginning with “All”, is a Double Proposition
§ 4. What is implied, in a Proposition of Relation, as to the Reality of its Terms?
§ 5. Translation of a Proposition of Relation into one or more Propositions of Existence
(1)
(2)
(3)
(4)
(5)
(6)
BOOK III. THE BILITERAL DIAGRAM
CHAPTER I. SYMBOLS AND CELLS
CHAPTER II. COUNTERS
CHAPTER III. REPRESENTATION OF PROPOSITIONS
§ 1. Introductory
§ 2. Representation of Propositions of Existence
§ 3. Representation of Propositions of Relation
CHAPTER IV. INTERPRETATION OF BILITERAL DIAGRAM WHEN MARKED WITH COUNTERS
BOOK IV. THE TRILITERAL DIAGRAM
CHAPTER I. SYMBOLS AND CELLS
CHAPTER II. REPRESENTATION OF PROPOSITIONS IN TERMS OF x AND m, OR OF y AND m
§ 1. Representation of Propositions of Existence in terms of x and m, or of y and m
§ 2. Representation of Propositions of Relation in terms of x and m, or of y and m
CHAPTER III. REPRESENTATION OF TWO PROPOSITIONS OF RELATION, ONE IN TERMS OF x AND m, AND THE OTHER IN TERMS OF y AND m, ON THE SAME DIAGRAM
(1)
(2)
(3)
(4)
CHAPTER IV. INTERPRETATION, IN TERMS OF x AND y, OF TRILITERAL DIAGRAM, WHEN MARKED WITH COUNTERS OR DIGITS
BOOK V. SYLLOGISMS. CHAPTER I. INTRODUCTORY
CHAPTER II. PROBLEMS IN SYLLOGISMS
§ 1. Introductory
§ 2. Given a Pair of Propositions of Relation, which contain between them a pair of codivisional Classes, and which are proposed as Premisses: to ascertain what Conclusion, if any, is consequent from them
(1)
(2)
(3)
(4)
(1) [see p. 60]
(2) [see p. 61]
(3) [see p. 62]
(4) [see p. 63]
§ 3. Given a Trio of Propositions of Relation, of which every two contain a Pair of codivisional Classes, and which are proposed as a Syllogism; to ascertain whether the proposed Conclusion is consequent from the proposed Premisses, and, if so, whether it is complete
(1)
(2)
(3)
(4)
(5)
(6)
BOOK VI. THE METHOD OF SUBSCRIPTS. CHAPTER I. INTRODUCTORY
CHAPTER II. REPRESENTATION OF PROPOSITIONS OF RELATION
CHAPTER III. SYLLOGISMS
§ 1. Representation of Syllogisms
§ 2. Formulæ for solving Problems in Syllogisms
Fig. I
Fig. II
Fig. III
(1) [see p. 64]
(2) [see p. 64]
(3) [see p. 64]
(4) [see p. 66]
(5) [see p. 67]
(6) [see p. 67]
(7) [see p. 69]
§ 3. Fallacies
(1) Fallacy of Like Eliminands not asserted to exist
(2) Fallacy of Unlike Eliminands with an Entity-Premiss
(3) Fallacy of two Entity-Premisses
§ 4. Method of proceeding with a given Pair of Propositions
BOOK VII. SORITESES. CHAPTER I. INTRODUCTORY
CHAPTER II. PROBLEMS IN SORITESES
§ 1. Introductory
§ 2. Solution by Method of Separate Syllogisms
§ 3. Solution by Method of Underscoring
BOOK VIII. EXAMPLES, ANSWERS, AND SOLUTIONS
CHAPTER I. EXAMPLES
EX1§ 1. Propositions of Relation, to be reduced to normal form
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
EX3§ 3. Marked Triliteral Diagrams, to be interpreted in terms of x and y
EX4§ 4. Pairs of Abstract Propositions, proposed as Premisses: Conclusions to be found
EX5§ 5. Pairs of Concrete Propositions, proposed as Premisses: Conclusions to be found
EX6§ 6. Trios of Abstract Propositions, proposed as Syllogisms: to be examined
EX7§ 7. Trios of Concrete Propositions, proposed as Syllogisms: to be examined
EX8§ 8. Sets of Abstract Propositions, proposed as Premisses for Soriteses: Conclusions to be found
EX9§ 9
Sets of Concrete Propositions, proposed as Premisses for Soriteses: Conclusions to be found. 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
CHAPTER II. ANSWERS
AN1Answers to § 1
AN2Answers to § 2
AN3Answers to § 3
AN4Answers to § 4
AN5Answers to § 5
AN6Answers to § 6
AN7Answers to § 7
AN8Answers to § 8
AN9Answers to § 9
CHAPTER III. SOLUTIONS
§ 1. Propositions of Relation reduced to normal form. SL1Solutions for § 1
§ 2. Method of Diagrams. SL4-ASolutions for § 4, Nos. 1–12
SL5-ASolutions for § 5, Nos. 1–12
SL6-ASolutions for § 6, Nos. 1–10. 1
2
3
4
5
6
7
8
9
10
SL7-ASolutions for § 7, Nos. 1–6. 1
2
3
4
5
6
§ 3. Method of Subscripts. SL4-BSolutions for § 4
SL5-BSolutions for § 5, Nos. 13–24
SL6-BSolutions for § 6
SL7-BSolutions for § 7
SL8Solutions for § 8
SL9Solutions for § 9
NOTES
(A) [See p. 80]
APPENDIX, ADDRESSED TO TEACHERS
§ 1. Introductory
§ 2. The “Existential Import” of Propositions
§ 3. The use of “is-not” (or “are-not”) as a Copula
§ 4. The theory that “two Negative Premisses prove nothing”
§ 5. Euler’s Method of Diagrams
§ 6. Venn’s Method of Diagrams
§ 7. My Method of Diagrams
§ 8. Solution of a Syllogism by various Methods
§ 9. My Method of treating Syllogisms and Sorites
§ 10. Some account of Parts II, III
1
2
3
4
5
6
7
8
9
NOTES TO APPENDIX (A) [See p. 167, line 6.]
(B) [See p. 171, at end of Section 2.]
(C) [See p. 173, § 4.]
THE GAME OF LOGIC. By Lewis Carroll
PREFACE
CHAPTER I. NEW LAMPS FOR OLD
1. Propositions
2. Syllogisms
3. Fallacies
CHAPTER II. CROSS QUESTIONS
1. Elementary
2. Half of Smaller Diagram
3. Half of Smaller Diagram
4. Smaller Diagram
5. Smaller Diagram
6. Larger Diagram
7. Both Diagrams to be employed
CHAPTER III. CROOKED ANSWERS
1. Elementary
2. Half of Smaller Diagram
3. Half of Smaller Diagram
4. Smaller Diagram
5. Smaller Diagram
6. Larger Diagram
CHAPTER IV. HIT OR MISS
FEEDING THE MIND
NOTE
