The Principles of Mathematics

Beschreibung

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 extension. Bestandsnummer des Verkäufers 1253810

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