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Invariance and Structural Dependence

  • Jan Odelstad

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 380)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Problem Area and Basic Formal Apparatus

    1. Front Matter
      Pages 1-1
    2. Jan Odelstad
      Pages 40-70
  3. An Informal Presentation of the Main Themes

    1. Front Matter
      Pages 71-71
    2. Jan Odelstad
      Pages 73-95
    3. Jan Odelstad
      Pages 135-151
    4. Jan Odelstad
      Pages 152-172
  4. Formal Treatment of Basic Topics

    1. Front Matter
      Pages 173-173
    2. Jan Odelstad
      Pages 175-200
    3. Jan Odelstad
      Pages 201-218
    4. Jan Odelstad
      Pages 219-234
  5. Back Matter
    Pages 235-248

About this book

Introduction

This is a revised version of a doctoral thesis, submitted in mimeographed fonn to the Faculty of Arts, Uppsala University, 1988. It deals with the notions of struc­ tural dependence and independence, which are used in many applications of mathe­ matics to science. For instance, a physical law states that one physical aspect is structurally dependent on one or more other aspects. Structural dependence is closely related to the mathematical idea of functional dependence. However, struc­ tural dependence is primarily thought of as a relation holding between aspects rather than between their measures. In this book, the traditional way of treating aspects within measurement theory is modified. An aspect is not viewed as a set-theoretical structure but as a function which has sets as arguments and set-theoretical structures as values. This way of regarding aspects is illustrated with an application to social choice and group deci­ sion theory. Structural dependence is connected with the idea of concomitant variations and the mathematical notion of invariance. This implies that the study of this notion has roots going back to Mill's inductive logic, to Klein's Erlangen Program for geome­ try and to Padoa's method for proving the independence of symbols in formal logic.

Keywords

Entscheidungstheorie Invarianz Measurement Theory Messtheorie decision theory invariance mathematics regionalization science and technology sets social choice stability transition value-at-risk

Authors and affiliations

  • Jan Odelstad
    • 1
  1. 1.Department of PhilosophyUppsala UniversityUppsalaSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-48388-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55260-4
  • Online ISBN 978-3-642-48388-2
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site
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