Complementarity in Mathematics: A First Introduction to the Foundations of Mathematics and Its History: Mathematics and Its Applications, cartea 1
Autor W. Kuyken Limba Engleză Hardback – 30 sep 1977
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Specificații
ISBN-13: 9789027708144
ISBN-10: 9027708142
Pagini: 190
Ilustrații: XI, 175 p.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.45 kg
Ediția:1977
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and Its Applications
Locul publicării:Dordrecht, Netherlands
ISBN-10: 9027708142
Pagini: 190
Ilustrații: XI, 175 p.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.45 kg
Ediția:1977
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and Its Applications
Locul publicării:Dordrecht, Netherlands
Public țintă
ResearchCuprins
I. Semantical and Syntactical Aspects of Elementary Mathematical Theories.- I.1. Introduction to the Elementary Predicate Calculus without Equality.- I.2. Semantical Interpretation of the Propositional Calculus.- I.3. Semantical Interpretation of the Elementary Predicate Calculus.- I.4. Decision Procedure for the Elementary Predicate Calculus.- I.5. Predicate Calculus — the Theory Z.- I.6. Gödel’s Incompleteness Theorem.- I.7. The Incompleteness Theorems and Semantics.- I.8. Remarks on Non-Standard Mathematics.- II. Epistemological Aspects of Mathematics in Historical Perspective.- II. 1. Introduction.- II.2. The Philosophy of Mathematics in History.- II.3. Transition to the Present Century.- II.4. Directions in the 20th Century Philosophy of Mathematics.- II.4.1.1. Frege (1848–1925).- II.4.1.2. Russell (1872–1970).- II.4.2.1. Poincaré (1854–1912).- II.4.2.2. Brouwer (1881–1966).- II.4.2.3. The ‘Bourbaki’ Group.- III. An Outline of a Complementaristic Approach to Mathematics.- III.1. Facets and Methods of a Philosophy of Mathematics.- III.2. Two Kinds of Mathematical Existence.- III.3. Language, Set Theory and Mathematical Complementarity.- III.4. Complementarist Set Theory — an Outline.- III.5. The Unity of Mathematics: Algebra and Topology.- III.6. Bridging the Abyss Between the Discrete and the Continuous.- Selected Bibliography.- References for Further Study.- Index of Names.- Index of Subjects.