Articles liés à The Principles Of Mathematics
Synopsis
Book by Bertrand Russell
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Présentation de l'éditeur
Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which Principia Mathematica provided the detailed proof, and introduced the work of Frege to a wider audience.
In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics.
Biographie de l'auteur
Bertrand Russell (1872-1970). A celebrated mathematician and logician, Russell was and remains one of the most genuinely widely read and popular philosophers of modern times.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
- ÉditeurRoutledge
- Date d'édition1992
- ISBN 10 0415082994
- ISBN 13 9780415082990
- ReliureBroché
- Langueanglais
- Numéro d'édition3
- Nombre de pages576
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The Principles of Mathematics
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Routledge, 1992
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ISBN 13 : 9780415082990
Ancien ou d'occasion
paperback edition
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paperback edition. Etat : Sehr gut. 534 pgs. Very good and clean copy. - Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics to be written in English. It set forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. Russell proposed simply that what is commonly called mathematics is merely later deductions from logical premisses. He outlined the thesis for which Principia Mathematica provided the detailed proof, and introduced the work of Frege to a wider audience. In addition to the new introduction by John G. Slater of the University of Toronto, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. / TABLE OF CONTENTS -- INTRODUCTION TO THE SECOND EDITION -- PREFACE -- PAGE -- V -- XV -- PART I -- THE INDEFINABLES OF MATHEMATICS -- CHAPTER I -- DEFINITION OF PURE MATHEMATICS -- Definition of pure mathematics -- The principles of mathematics are no longer controversial -- Pure mathematics uses only a few notions, and these are logical constants -- -- All pure mathematics follows formally from twenty premisses -- Asserts formal implications -- And employs variables -- Which may have any value without exception -- Mathematics deals with types of relations -- Applied mathematics is defined by the occurrence of constants which are not logical -- Relation of mathematics to logic -- CHAPTER II -- SYMBOLIC LOGIC -- Definition and scope of symbolic logic -- The indefinables of symbolic logic -- -- Symbolic logic consists of three parts -- A The Propositional Calculus -- Definition -- -- Distinction between implication and formal implication -- Implication indefinable -- Two indefinables and ten primitive propositions in this calculus -- PAGE -- The ten primitive propositions -- Disjunction and negation defined -- B The Calculus of Classes -- Three new indefinables -- The relation of an individual to its class -- Propositional functions -- The notion of such that -- Two new primitive propositions -- Relation to propositional calculus -- Identity -- C The Calculus of Relations -- The logic of relations essential to mathematics -- New primitive propositions -- Relative products -- Relations with assigned domains -- D Peano's Symbolic Logic -- Mathematical and philosophical definitions -- Peano's indefinables -- -- Elementary definitions -- Peano's primitive propositions -- Negation and disjunction -- Existence and the null-class -- CHAPTER III -- IMPLICATION AND FORMAL IMPLICATION -- Meaning of implication -- Asserted and unasserted propositions -- Inference does not require two premisses -- Formal implication is to be interpreted extensionally -- The variable in a formal implication has an unrestricted field -- A formal implication is a single propositional function, not a relation of two -- Assertions -- Formal implication involved in rules of inference -- Conditions that a term in an implication may be varied -- CHAPTER IV -- PROPER NAMES, ADJECTIVES AND VERBS -- Proper names, adjectives and verbs distinguished -- Terms -- Things and concepts -- Concepts as such and as terms -- Conceptual diversity -- Meaning and the subject-predicate logic -- Table of Contents -- xxvii -- Verbs and truth -- All verbs, except perhaps is, express relations -- Relations per se and relating relations -- Relations are not particularized by their terms -- Definition of denoting -- CHAPTER V -- DENOTING -- Connection with subject-predicate propositions -- Denoting concepts obtained from predicates -- Extensional account of all, every, any, a and some -- PAGE -- Intensional account of the same -- Illustrations -- The difference between all, every, etc lies in the objects denoted, not in the -- way of denoting them -- The notion of the and definition -- The notion of the and identity -- Summary -- CHAPTER VI -- CLASSES -- Combination of intensional and extensional standpoints required -- Meaning of class -- Intensional and extensional genesis of class -- Distinctions overlooked by Peano -- The class as one and as many -- The notion of and -- All men is not analyzable into all and men -- There are null class-concepts, but there is no null class -- The class as one, except when it has one term, is distinct from the class as many -- Every, any, a and some each denote one object, but an ambiguous one -- The relation of a term to its class -- The relation of inclusion between classes -- The contradiction -- Summary -- CHAPTER VII -- PROPOSITIONAL FUNCTIONS -- Indefinability of such that -- Where a fixed relation to a fixed term is asserted, a propositional function can be analyzed into a variable subject and a constant assertion -- But this analysis is impossible in other cases -- Variation of the concept in a proposition -- Relation of propositional functions to classes -- A propositional function is in general not analyzable into a constant and a variable element -- CHAPTER VIII -- THE VARIABLE -- Nature of the variable -- Relation of the variable to any -- Formal and restricted variables -- Formal implication presupposes any -- Duality of any and some -- The class-concept propositional function is indefinable -- Other classes can be defined by means of such that -- Analysis of the variable -- CHAPTER IX -- RELATIONS -- PAC -- Characteristics of relations -- Relations of terms to themselves -- The domain and the converse domain of a relation -- Logical sum, logical product and relative product of relations -- A relation is not a class of couples -- Relations of a relation to its terms -- CHAPTER X -- THE CONTRADICTION -- Consequences of the contradiction -- Various statements of the contradiction -- An analogous generalized argument -- Variable propositional functions are in general inadmissible -- The contradiction arises from treating as one a class which is only many -- Other primâ facie possible solutions appear inadequat. 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Principles of Mathematics
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