Complementarity in Mathematics: A First Introduction to the Foundations of Mathematics and Its History / Edition 1

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Product Details

  • ISBN-13: 9789048183487
  • Publisher: Springer Netherlands
  • Publication date: 12/22/2010
  • Series: Mathematics and Its Applications (closed) Series , #1
  • Edition description: Softcover reprint of hardcover 1st ed. 1977
  • Edition number: 1
  • Pages: 175
  • Product dimensions: 9.00 (w) x 6.00 (h) x 0.40 (d)

Table of Contents

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.2.1 Greek Mathematics.- II.2.2. From Hellenistic Philosophy to Modern Rationalism.- II.2.3. The Period in Early Modern Philosophy.- II.2.3.1. Descartes (1596–1650).- II.2.3.2. Newton (1642–1727).- II.2.3.3. Leibniz (1646–1716).- II.2.3.4. Kant (1724–1804).- II.3. Transition to the Present Century.- II.4. Directions in the 20th Century Philosophy of Mathematics.- II.4.1. Logicism.- II.4.1.1. Frege (1848–1925).- II.4.1.2. Russell (1872–1970).- II.4.2. Intuitionism.- II.4.2.1. Poincaré (1854–1912).- II.4.2.2. Brouwer (1881–1966).- II.4.2.3. The ‘Bourbaki’ Group.- II.4.3. Formalism.- 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.

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