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Selected Papers in Logic and Foundations, Didactics, Economics

  • Book
  • © 1979

Overview

Authors:
  1. Karl Menger
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Part of the book series: Vienna Circle Collection (VICC, volume 10)

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Table of contents (29 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    1. Introduction

      • Karl Menger
      Pages 1-7

  3. Paper Introducing Logical Tolerance

    1. Front Matter

      Pages 9-9
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    2. Logical Tolerance in the Vienna Circle

      • Karl Menger
      Pages 11-16

    3. The New Logic

      • Karl Menger
      Pages 17-45

    4. On Intuitionism

      • Karl Menger
      Pages 46-58

  4. Opuscula Logica

    1. Front Matter

      Pages 59-59
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    2. Meaningfulness and Structure

      • Karl Menger
      Pages 61-67

    3. A New Point of View on the Logical Connectives

      • Karl Menger
      Pages 68-78

    4. An Intuitionistic-Formalistic Dictionary of Set Theory

      • Karl Menger
      Pages 79-87

    5. Ultrasets and the Paradoxes of Set Theory

      • Karl Menger
      Pages 88-90

    6. A Logic of the Doubtful on Optative and Imperative Logic

      • Karl Menger
      Pages 91-102

  5. Fundamental Concepts in Pure and Applied Mathematics

    1. Front Matter

      Pages 103-103
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    2. A Counterpart of Occam’s Razor

      • Karl Menger
      Pages 105-135

    3. A Theory of the Application of the Function Concept to Science

      • Karl Menger
      Pages 136-143

    4. Variables, Constants, Fluents

      • Karl Menger
      Pages 144-152

    5. Wittgenstein on Formulae and Variables

      • Karl Menger
      Pages 153-158

  6. Didactics of Mathematics

    1. Front Matter

      Pages 159-159
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    2. Introduction

      • Karl Menger
      Pages 161-162

    3. A New Approach to Teaching Intermediate Mathematics

      • Karl Menger
      Pages 163-173
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Keywords

About this book

This volume brings together those papers of mine which may be of interest not only to various specialists but also to philosophers. Many of my writings in mathematics were motivated by epistemological considerations; some papers originated in the critique of certain views that at one time dominated the discussions of the Vienna Cirele; others grew out of problems in teaching fundamental ideas of mathematics; sti II others were occasioned by personal relations with economists. Hence a wide range of subjects will be discussed: epistemology, logic, basic concepts of pure and applied mathematics, philosophical ideas resulting from geometric studies, mathematical didactics and, finally, economics. The papers also span a period of more than fifty years. What unifies the various parts of the book is the spirit of searching for the elarification of basic concepts and methods and of articulating hidden ideas and tacit procedures. Part 1 ineludes papers published about 1930 which expound an idea that Carnap, after a short period of opposition in the Cirele, fully adopted ; and, under the name "Princip/e of To/erance", he eloquently formulated it in great generality in his book, Logica/ Syntax of Language (1934), through which it was widely disseminated. "The New Logic" in Chapter 1 furthermore ineludes the first report (I932) to a larger public of Godel's epochal discovery presented among the great logic results of ali time. Chapter 2 is a translation of an often quoted 1930 paper presenting a detailed exposition and critique of intuitionism.

Bibliographic Information

  • Book Title: Selected Papers in Logic and Foundations, Didactics, Economics

  • Authors: Karl Menger

  • Series Title: Vienna Circle Collection

  • DOI: https://doi.org/10.1007/978-94-009-9347-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1979

  • Hardcover ISBN: 978-90-277-0320-0Published: 31 March 1979

  • Softcover ISBN: 978-90-277-0321-7Published: 31 March 1979

  • eBook ISBN: 978-94-009-9347-1Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XII, 344

  • Topics: Logic, Category Theory, Homological Algebra, Epistemology

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