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INTRODUCTION TO THE SECOND EDITION THE Principles of Mathematics " was published in 1903, and most of it was written in 1900. In the subsequent years the subjects of which it treats have been widely discussed, and the technique of mathematical logic has been greatly improved ; while some new problems have arisen, some old ones have been solved, and others, though, they remain in a controversial condition, have taken on completely new forms. In these circumstances, it seemed useless to attempt to amend this or that, in the book, which no longer expresses my present views. Such interest as the book now possesses is historical, and consists in the fact that it represents a certain stage in the development of its subject. I have therefore altered nothing, but shall endeavour, in this Introduction, to say in what respects 1 adhere to the opinions which it expresses, and in what other respects subsequent research seems to me to have shown them to be erroneous. The fundamental thesis of th
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Principles of Mathematics
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Principles of mathematics
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W. W. Norton & Co.,, 1964
ISBN 10: 0393002497
ISBN 13: 9780393002492
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Principles of Mathematics
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Norton & Company, Incorporated, W. W., 1964
ISBN 10: 0393002497
ISBN 13: 9780393002492
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The principles of mathematics.[Definition of pure mathematics -- The ten primitive propositions -- The Calculus o f Classes -- Three new indefinables -- The relation of an individual to its class -- The notion of such that -- Relation to propositional calculus -- The Calculus of Relations -- The logic of relations essential to mathematics -- Definition of distance -- Measurement of distances -- Infinity and continuity -- The supposed contradictions of infinity have been resolved -- Correlation of series -- Independent series and series by correlation -- New primitive propositions -- Mathematical and philosophical definitions -- Peano's indefinables -- Elementary definitions -- Peano's primitive propositions -- Negation and disjunction]
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New York : W.W. Norton, 1980, 1938., 1980
ISBN 10: 0393002497
ISBN 13: 9780393002492
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Soft cover. Condizione: Very Good. xxxix, 534 p. : ill. ; 19 cm. ; LC: QA9; Dewey: 510.1 ; ISBN: 0393002497 (pbk.) :; 9780393002492 (pbk.) ; OCLC: 11741484 ; pictorial stiff paper wrappers ; Contents: Definition of pure mathematics -- The ten primitive propositions -- The Calculus o f Classes -- Three new indefinables -- The relation of an individual to its class -- The notion of such that -- Relation to propositional calculus -- The Calculus of Relations -- The logic of relations essential to mathematics -- Definition of distance -- Measurement of distances -- Infinity and continuity -- The supposed contradictions of infinity have been resolved -- Correlation of series -- Independent series and series by correlation -- New primitive propositions -- Mathematical and philosophical definitions -- Peano's indefinables -- Elementary definitions -- Peano's primitive propositions -- Negation and disjunction -- Existence and the nullclass -- Asserted and unasserted propositions -- Inference does not require two premisses - - Formal implication is to be interpreted extensionally -- A formal implication is a single propositional function not a relation of two -- Assertions -- Formal implication involved in rules of inference -- Terms -- Things and concepts -- Concepts a s such and as terms -- Conceptual diversity -- All verbs except perhaps is express relations -- Relations per se and relating relations -- Relations are not particularized by their terms -- Connection with subjectpredicate propositions -- Denoting concepts obtained from predicates -- Extensional account of all every any a and some -- Intensional account of the same -- 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 -- Meaning of class -- Intensional and extensional genesis of classes -- 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 and some each denote one object but an ambiguous one -- The relation of inclusion between classes -- The contradiction -- Prepositional -- The variable -- Relations - - The contradiction -- Number -- Definition of cardinal numbers -- Addition and multiplication -- Finite and infinite -- Theory of finite numbers -- Addition of terms and addition of classes -- Whole and part -- Infinite wholes -- Ratios and fractions -- The meaning of magnitude -- The range of quantity -- Numbers as expressing magnitudes: measurement -- Zero -- Infinity, the infintesimal and continuity -- The genesis of series -- The meaning of order -- Asymmetrical relations -- Difference of sense and difference of sign -- On the difference between open and closed series -- Progressions and ordinal numbers -- Dedekind's theory of number -- Distance -- The correlation of series -- Real numbers -- Limits and irrational numbers -- Cantor' s first definition of continuity -- Ordinal continuity -- Transfinite cardinals -- Transfinite ordinals -- The infinitesimal calculus -- The inifinitesimal and the improper infinite -- Philosophical arguments concerning the infinitesimal -- The philosophy of the continuum -- The philosophy of the infinite -- Dimensions and complex numbers -- Projective geometry -- Descriptive geometry -- Metrical geometry -- Relation of metrical to projective and descriptive geometry -- Definitions of various spaces -- The continuity of space -- Logical arguments against points -- Kant's theory of space -- Matter -- Motion -- Causality -- Definition of a dynamical world -- Newton's laws of motion -- Absolute and relative motion -- Hertz' dynamics -- The logical and arithmetical doctrines of Frege -- The doctrine of types. ; store stamps ; clipped corner on front ep ; VG. Book. Codice articolo 5467
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The Principles of Mathematics
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Principles of mathematics
Editore:
W.W. Norton & Company, inc, 1938
ISBN 10: 0393002497
ISBN 13: 9780393002492
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Hardcover. Condizione: Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority! Codice articolo S_372384088
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