버트런드 러셀의 수리 수학적 철학의 기초적 서론.The Book of Introduction to Mathematical Philosophy,

Bertrand Russell 지음

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버트런드 러셀의 수리 수학적 철학의 기초적 서론.The Book of Introduction to Mathematical Philosophy, byBertrand Russell
목차에서 보듯이, 자연수 ,수의 정의,수학적 귀납법 및 연역법,극한, 집합, 논리 등등의 여러 분야의 수학적인 책.
영국의 논리학자, 철학자, 수학자, 사회 반전운동가인 버트런드 러셀의 대표 저서. 이 책은 1918년 러셀이 동맹군을 비방한 글을 투고로 6개월간 투옥되었을 때 감옥에서 쓴 책. 이전에 화이트헤드와 함께 썼던 난해한 Principia Mathematica을 보다 쉽게 풀어 쓴 책.
이 책은 수학의 기초론에 대한 철학적 사상에 결정적인 역할. 여기 기초가 되는 사상은 논리주의, 직관주의, 형식주의, 이 중 논리주의를 주도한 러셀은 수학 기초론의 초기 형성에 기여.
버트런드 러셀 Bertrand Arthur William Russell 1872. 1970. 영국의 철학자, 수학자. 케임브리지 트리니티 칼리지에서 수학과 철학을 배웠다. 50년에 노벨문학상을 받았다.

목차

버트런드 러셀의 수리 수학적 철학의 기초적 서론.The Book of Introduction to Mathematical Philosophy, byBertrand Russell
CONTENTS
CHAP. PAGE
PREFACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
EDITOR’S NOTE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
1. THE SERIES OF NATURAL NUMBERS. . . . . . . . . . . . . . . . . . . . 1
2. DEFINITION OF NUMBER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3. FINITUDE AND MATHEMATICAL INDUCTION . . . . . . . . . . 24
4. THE DEFINITION OF ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5. KINDS OF RELATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6. SIMILARITY OF RELATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7. RATIONAL, REAL, AND COMPLEX NUMBERS. . . . . . . . . . . 77
8. INFINITE CARDINAL NUMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . 95
9. INFINITE SERIES AND ORDINALS . . . . . . . . . . . . . . . . . . . . . . . . 110
10. LIMITS AND CONTINUITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
11. LIMITS AND CONTINUITY OF FUNCTIONS. . . . . . . . . . . . . . 132
12. SELECTIONS AND THE MULTIPLICATIVE AXIOM . . . . . . 145
13. THE AXIOM OF INFINITY AND LOGICAL TYPES . . . . . . . 163
14. INCOMPATIBILITY AND THE THEORY OF DEDUCTION 179
15. PROPOSITIONAL FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
16. DESCRIPTIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
17. CLASSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
18. MATHEMATICS AND LOGIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

책 속으로

버트런드 러셀의 수리 수학적 철학의 기초적 서론.The Book of Introduction to Mathematical Philosophy, byBertrand Russell
목차에서 보듯이, 자연수 ,수의 정의,수학적 귀납법 및 연역법,극한, 집합, 논리 등등의 여러 분야의 수학적인 책.
영국의 논리학자, 철학자, 수학자, 사회 반전운동가인 버트런드 러셀의 대표 저서. 이 책은 1918년 러셀이 동맹군을 비방한 글을 투고로 6개월간 투옥되었을 때 감옥에서 쓴 책. 이전에 화이트헤드와 함께 썼던 난해한 Principia Mathematica을 보다 쉽게 풀어 쓴 책.
이 책은 수학의 기초론에 대한 철학적 사상에 결정적인 역할. 여기 기초가 되는 사상은 논리주의, 직관주의, 형식주의, 이 중 논리주의를 주도한 러셀은 수학 기초론의 초기 형성에 기여.
버트런드 러셀 Bertrand Arthur William Russell 1872. 1970. 영국의 철학자, 수학자. 케임브리지 트리니티 칼리지에서 수학과 철학을 배웠다. 50년에 노벨문학상을 받았다.

출판사 서평

PREFACE
This book is intended essentially as an “Introduction,” and
does not aim at giving an exhaustive discussion of the problems
with which it deals. It seemed desirable to set forth certain
results, hitherto only available to those who have mastered logical symbolism, in a form offering the minimum of difficulty to
the beginner. The utmost endeavour has been made to avoid
dogmatism on such questions as are still open to serious doubt,
and this endeavour has to some extent dominated the choice
of topics considered. The beginnings of mathematical logic are
less definitely known than its later portions, but are of at least
equal philosophical interest. Much of what is set forth in the
following chapters is not properly to be called “philosophy,”
though the matters concerned were included in philosophy so
long as no satisfactory science of them existed. The nature of
infinity and continuity, for example, belonged in former days
to philosophy, but belongs now to mathematics. Mathematical philosophy, in the strict sense, cannot, perhaps, be held to
include such definite scientific results as have been obtained in
this region; the philosophy of mathematics will naturally be
expected to deal with questions on the frontier of knowledge, as
to which comparative certainty is not yet attained. But speculation on such questions is hardly likely to be fruitful unless
the more scientific parts of the principles of mathematics are
known. A book dealing with those parts may, therefore, claim
to be an introduction to mathematical philosophy, though it
can hardly claim, except where it steps outside its province,
to be actually dealing with a part of philosophy. It does deal,
however, with a body of knowledge which, to those who accept it, appears to invalidate much traditional philosophy, and
even a good deal of what is current in the present day. In
this way, as well as by its bearing on still unsolved problems,
mathematical logic is relevant to philosophy. For this reason,
as well as on account of the intrinsic importance of the subject, some purpose may be served by a succinct account of the
main results of mathematical logic in a form requiring neither
a knowledge of mathematics nor an aptitude for mathematical
symbolism. Here, however, as elsewhere, the method is more
important than the results, from the point of view of further
research; and the method cannot well be explained within the
framework of such a book as the following. It is to be hoped
that some readers may be sufficiently interested to advance to
a study of the method by which mathematical logic can be
made helpful in investigating the traditional problems of philosophy. But that is a topic with which the following pages
have not attempted to deal.
BERTRAND RUSSELL

작가정보

저자(글) Bertrand Russell

버트런드 러셀의 수리 수학적 철학의 기초적 서론.The Book of Introduction to Mathematical Philosophy, byBertrand Russell
버트런드 러셀 Bertrand Arthur William Russell 1872. 1970. 영국의 철학자, 수학자. 케임브리지 트리니티 칼리지에서 수학과 철학을 배웠다. 50년에 노벨문학상을 받았다.