기호 논리학 Symbolic Logic, by Lewis Carroll

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기호 논리학 mathematical logic, 즉 , 심벌릭 로직 symbolic logic .
이책은 이상한 나라의 엘리스를 쓴 영국작가인 루이스 캐롤이 기술한 책.
수학적 연산을 할 수 있도록 논리 형식을 기호화하여 다루는 논리학을 지칭함. 수학적 이론 가운데 대수학代數學 에서처럼 언어 대신 기호를 활용하여 언어의 모호성이나 제약을 없애고 논리 체계의 순수성과 엄밀성에 치중하여 논리의 구조를 밝히려고 하는 형식 논리학이며 이는 19세기 후반에 러셀 등에 의하여 논리학의 주요 부분으로 시작해 발달.

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기호 논리학.Symbolic Logic, by Lewis Carroll

CONTENTS

BOOK I.

THINGS AND THEIR ATTRIBUTES.

CHAPTER I.

INTRODUCTORY.

PAGE
‘Things’ 1
‘Attributes’ 〃
‘Adjuncts’ 〃
CHAPTER II.

CLASSIFICATION.

‘Classification’ 1½
‘Class’ 〃
‘Peculiar’ Attributes 〃
‘Genus’ 〃
‘Species’ 〃
‘Differentia’ 〃
‘Real’ and ‘Unreal’, or ‘Imaginary’, Classes 2
‘Individual’ 〃
A Class regarded as a single Thing 2½
pg_xvi
CHAPTER III.

DIVISION.

§ 1.

Introductory.
‘Division’ 3
‘Codivisional’ Classes 〃
§ 2.

Dichotomy.

‘Dichotomy’ 3½
Arbitrary limits of Classes 〃
Subdivision of Classes 4
CHAPTER IV.

NAMES.

‘Name’ 4½
‘Real’ and ‘Unreal’ Names 〃
Three ways of expressing a Name 〃
Two senses in which a plural Name may be used 5
CHAPTER V.

DEFINITIONS.

‘Definition’ 6
Examples worked as models 〃
pg_xvii
BOOK II.

PROPOSITIONS.

CHAPTER I.

PROPOSITIONS GENERALLY.

§ 1.

Introductory.

Technical meaning of “ some” 8
‘Proposition’ 〃
‘Normal form’ of a Proposition 〃
‘Subject’, ‘Predicate’, and ‘Terms’ 9
§ 2.

Normal form of a Proposition.

Its four parts:―

(1) ‘Sign of Quantity’ 〃
(2) Name of Subject 〃
(3) ‘Copula’ 〃
(4) Name of Predicate 〃
§ 3.

Various kinds of Propositions.

Three kinds of Propositions:―

(1) Begins with “ Some” . Called a ‘Particular’ Proposition: also a
Proposition ‘in I’ 10
(2) Begins with “ No” . Called a ‘Universal Negative’ Proposition: also
a Proposition ‘in E’ 〃
(3) Begins with “ All” . Called a ‘Universal Affirmative’ Proposition:
also a Proposition ‘in A’ 〃
pg_xviii
A Proposition, whose Subject is an Individual, is to be regarded as
Universal 〃
Two kinds of Propositions, ‘Propositions of Existence’, and ‘Propositions
of Relation’ 〃
CHAPTER II.

PROPOSITIONS OF EXISTENCE.

‘Proposition of Existence ’ 11
CHAPTER III.

PROPOSITIONS OF RELATION.

§ 1.

Introductory.

‘Proposition of Relation’ 12
‘Universe of Discourse,’ or ‘Univ.’ 〃
§ 2.

Reduction of a Proposition of Relation to Normal form.

Rules 13
Examples worked 〃
§ 3.

A Proposition of Relation, beginning with “All”, is a Double Proposition.

Its equivalence to two Propositions 17
pg_xix
§ 4.

What is implied, in a Proposition of Relation, as to the Reality of its
Terms?

Propositions beginning with “ Some” 19
Propositions beginning with “ No” 〃
Propositions beginning with “ All” 〃
§ 5.

Translation of a Proposition of Relation into one or more Propositions of
Existence.

Rules 20
Examples worked 〃
BOOK III.

THE BILITERAL DIAGRAM.

CHAPTER I.

SYMBOLS AND CELLS.

The Diagram assigned to a certain Set of Things, viz. our Univ. 22
Univ. divided into ‘the x- Class’ and ‘the x
′- Class’ 23
The North and South Halves assigned to these two Classes 〃
The x- Class subdivided into ‘the xy- Class’ and ‘the xy
′- Class’ 〃
The North- West and North- East Cells assigned to these two Classes 〃
The x
′- Class similarly divided 〃
The South- West and South- East Cells similarly assigned 〃
The West and East Halves have thus been assigned to ‘the y- Class’ and
‘the y
′- Class’ 〃
Table I. Attributes of Classes, and Compartments, or Cells, assigned to
them 25
pg_xx
CHAPTER II.

COUNTERS.

Meaning of a Red Counter placed in a Cell 26
Meaning of a Red Counter placed on a Partition 〃
American phrase “ sitting on the fence” 〃
Meaning of a Grey Counter placed in a Cell 〃

CHAPTER III.

REPRESENTATION OF PROPOSITIONS.

§ 1.

Introductory.

The word “ Things” to be henceforwards omitted 27
‘Uniliteral’ Proposition 〃
‘Biliteral’ do. 〃
Proposition ‘in terms of’ certain Letters 〃
§ 2.

Representation of Propositions of Existence.

The Proposition “ Some x exist” 28
Three other similar Propositions 〃
The Proposition

작가정보

저자(글) Lewis Carroll

4.
BOOK VII.

SORITESES.

CHAPTER I.

INTRODUCTORY.

‘Sorites’ 85
‘Premisses’ 〃
‘Partial Conclusion’ 〃
‘Complete Conclusion’ (or ‘Conclusion’) 〃
‘Eliminands’ 〃
‘Retinends’ 〃
‘consequent’ 〃
The Symbol “ ∴” 〃
Specimen- Soriteses 86
CHAPTER II.

PROBLEMS IN SORITESES.

§ 1.

Introductory.

Form of Problem 87
Two Methods of Solution 〃
§ 2.

Solution by Method of Separate Syllogisms.

Rules 88
Example worked 〃
pg_xxix
§ 3.

Solution by Method of Underscoring.

‘Underscoring’ 91
Subscripts to be omitted 〃
Example worked fully 92
Example worked briefly, as model 93
Seventeen Examination- Papers 94

BOOK VIII.

EXAMPLES, WITH ANSWERS AND SOLUTIONS.

CHAPTER I.

EXAMPLES.

§ 1.

Propositions of Relation, to be reduced to normal form 97
§ 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 98
§ 3.

Marked Triliteral Diagrams, to be interpreted in terms of x and y 99
§ 4.

Pairs of Abstract Propositions, proposed as Premisses: Conclusions to
be found 100
pg_xxx
§ 5.
Pairs of Concrete Propositions, proposed as Premisses: Conclusions to
be found 101
§ 6.

Trios of Abstract Propositions, proposed as Syllogisms: to be examined 106
§ 7.

Trios of Concrete Propositions, proposed as Syllogisms: to be examined 107
§ 8.

Sets of Abstract Propositions, proposed as Premisses for Soriteses:
Conclusions to be found 110
§ 9.

Sets of Concrete Propositions, proposed as Premisses for Soriteses:
Conclusions to be found 112
CHAPTER II.

ANSWERS.

Answers to

§ 1 125
§ 2 126
§ 3 127
§ 4 〃
§ 5 128
§ 6 130
§ 7 131
§ 8 132
§ 9 〃
pg_xxxi
CHAPTER III.

SOLUTIONS.

§ 1.

Propositions of Relation reduced to normal form.


Solutions for § 1 134
§ 2.

Method of Diagrams.

Solutions for

§ 4 Nos. 1 to 12 136
§ 5 〃 1 to 12 138
§ 6 〃 1 to 10 141
§ 7 〃 1 to 6 144
§ 3.

Method of Subscripts.

Solutions for

§ 4 146
§ 5 Nos. 13 to 24 147
§ 6 148
§ 7 150
§ 8 155
§ 9 157
NOTES 164
APPENDIX, ADDRESSED TO TEACHERS 165
NOTES TO APPENDIX 195
INDEX.

§ 1. Tables 197
§ 2. Words &c. explained 〃