기호 논리학 (Symbolic Logic, by Lewis Carroll)
Lewis Carroll
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 〃
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 〃
주제 분류
