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소개 책소개 보이기/감추기

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. 2. BOOK IV. THE TRILITERAL DIAGRAM. CHAPTER I. SYMBOLS AND CELLS. Change of Biliteral into Triliteral Diagram 39 The xy- Class subdivided into ‘the xym- Class’ and ‘the xym ′- Class’ 40 pg_xxiii The Inner and Outer Cells of the North- West Quarter assigned to these Classes 〃 The xy ′- Class, the x ′ y- Class, and the x ′ y ′- Class similarly subdivided 〃 The Inner and Outer Cells of the North- East, the South- West, and the South- East Quarter similarly assigned 〃 The Inner Square and the Outer Border have thus been assigned to ‘the m- Class’ and ‘the m ′- Class’ 〃 Rules for finding readily the Compartment, or Cell, assigned to any given Attribute or Attributes 〃 Table IV. Attributes of Classes, and Compartments, or Cells, assigned to them 42 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. The Proposition “ Some xm exist” 43 Seven other similar Propositions 〃 The Proposition “ No xm exist” 44 Seven other similar Propositions 〃 § 2. Representation of Propositions of Relation in terms of x and m, or of y and m. The Pair of Converse Propositions “ Some x are m” = “ Some m are x” 〃 Seven other similar Pairs 〃 The Pair of Converse Propositions “ No x are m” = “ No m are x” 〃 Seven other similar Pairs 〃 The Proposition “ All x are m” 45 Fifteen other similar Propositions 〃 Table V. Representations of Propositions in terms of x and m 46 Table VI. Representations of Propositions in terms of y and m 47 Table VII. Representations of Propositions in terms of x and m 48 Table VIII. Representations of Propositions in terms of y and m 49 pg_xxiv 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. The Digits “ I” and “ O” to be used instead of Red and Grey Counters 50 Rules 〃 Examples worked 〃 CHAPTER IV. INTERPRETATION, IN TERMS OF x AND y, OF TRILITERAL DIAGRAM, WHEN MARKED WITH COUNTERS OR DIGITS. Rules 53 Examples worked 54 BOOK V. SYLLOGISMS. CHAPTER I. INTRODUCTORY. ‘Syllogism’ 56 ‘Premisses’ 〃 ‘Conclusion’ 〃 ‘Eliminands’ 〃 ‘Retinends’ 〃 ‘Consequent’ 〃 The Symbol “ ∴” 〃 Specimen- Syllogisms 57 CHAPTER II. PROBLEMS IN SYLLOGISMS. § 1. Introductory. ‘Concrete’ and ‘Abstract’ Propositions 59 Method of translating a Proposition from concrete into abstract form 〃 Two forms of Problems 〃 § 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. Rules 60 Examples worked fully 〃 The same worked briefly, as models 64 § 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. Rules 66 Examples worked briefly, as models 〃

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목차 목차 보이기/감추기

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 “ No x exist” 〃 Three other similar Propositions 29 The Proposition “ Some xy exist” 〃 Three other similar Propositions 〃 The Proposition “ No xy exist” 〃 Three other similar Propositions 〃 The Proposition “ No x exist” is Double, and is equivalent to the two Propositions “ No xy exist” and “ No xy ′ exist” 30 pg_xxi § 3. Representation of Propositions of Relations. The Proposition “ Some x are y” 〃 Three other similar Propositions 〃 The Proposition “ Some y are x” 31 Three other similar Propositions 〃 Trio of equivalent Propositions, viz. “ Some xy exist” = “ Some x are y” = “ Some y are x” 〃 ‘Converse’ Propositions, and ‘Conversion’ 〃 Three other similar Trios 32 The Proposition “ No x are y” 〃 Three other similar Propositions 〃 The Proposition “ No y are x” 〃 Three other similar Propositions 〃 Trio of equivalent Propositions, viz. “ No xy exist” = “ No x are y” = “ No y are x” 33 Three other similar Trios 〃 The Proposition “ All x are y” is Double, and is equivalent to the two Propositions “ Some x are y” and “ No x are y ′” 〃 Seven other similar Propositions 34 Table II. Representation of Propositions of Existence 34 Table III. Representation of Propositions of Relation 35 CHAPTER IV. INTERPRETATION OF BILITERAL DIAGRAM, WHEN MARKED WITH COUNTERS. Interpretation of 36 And of three other similar arrangements 〃 pg_xxiiInterpretation of 〃 And of three other similar arrangements 〃 Interpretation of 37 And of three other similar arrangements 〃 Interpretation of 〃 And of three other similar arrangements 〃 Interpretation of 〃 And of three other similar arrangements 〃 Interpretation of 〃 And of seven other similar arrangements 38

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저자 소개 관련자료 보이기/감추기

기호 논리학.Symbolic Logic, by Lewis Carroll
이상한 나라의 엘리스를 쓴 영국의 작가.
3.
pg_xxvi
BOOK VI.

THE METHOD OF SUBSCRIPTS.

CHAPTER I.

INTRODUCTORY.

Meaning of x1, xy1, &c. 70
‘Entity’ 〃
Meaning of x0, xy0, &c. 〃
‘Nullity’ 〃
The Symbols “ †” and “ ¶” 〃
‘Like’ and ‘unlike’ Signs 〃
CHAPTER II.

REPRESENTATION OF PROPOSITIONS OF RELATION.

The Pair of Converse Propositions “ Some x are y” = “ Some y are x” 71
Three other similar Pairs 〃
The Pair of Converse Propositions “ No x are y” = “ No y are x” 〃
Three other similar Pairs 〃
The Proposition “ All x are y” 72
The Proposition “ All x are y” is Double, and is equivalent to the two
Propositions “ Some x exist” and “ No x and y
′” 〃
Seven other similar Propositions 〃
Rule for translating “ All x are y” from abstract into subscript form, and
vice versa 〃
pg_xxvii
CHAPTER III.

SYLLOGISMS.

§ 1.

Representation of Syllogisms.

Rules 73
§ 2.

Formulæ for Syllogisms.

Three Formulæ worked out:?

Fig. I. xm0 † ym
′
0 ¶ xy0 75
its two Variants (α) and (β) 〃
Fig. II. xm0 † ym1 ¶ x
′
y1 76
Fig. III. xm0 † ym0 † m1 ¶ x
′
y
′
1 77
Table IX. Formulæ and Rules 78
Examples worked briefly, as models 〃
§ 3.
Fallacies.

‘Fallacy’ 81
Method of finding Forms of Fallacies 82
Forms best stated in words 〃
Three Forms of Fallacies:?

(1) Fallacy of Like Eliminands not asserted to exist 〃
(2) Fallacy of Unlike Eliminands with an Entity- Premiss 83
(3) Fallacy of two Entity- Premisses 〃
§ 4.

Method of proceeding with a given Pair of Propositions.

Rules 84
pg_xxviii
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

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출판사 리뷰 출판사 리뷰 보이기/감추기

기호 논리학.Symbolic Logic, by Lewis Carroll 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 〃

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