Skip to main content
SpringerLink
Log in

Invariance and Structural Dependence

  • Book
  • © 1992

Overview

Authors:
  1. Jan Odelstad

    1. Department of Philosophy, Uppsala University, Uppsala, Sweden

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

  • 344 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages I-XII
    Download chapter PDF

  2. Problem Area and Basic Formal Apparatus

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. The Concept of Dependence in Applied Mathematics; a First Account

      • Jan Odelstad
      Pages 3-39

    3. Basic Formal Concepts and Terminology

      • Jan Odelstad
      Pages 40-70

  3. An Informal Presentation of the Main Themes

    1. Front Matter

      Pages 71-71
      Download chapter PDF

    2. Relationals

      • Jan Odelstad
      Pages 73-95

    3. Subordination, Uncorrelation and Derivation

      • Jan Odelstad
      Pages 96-134

    4. An Example: Social Choice

      • Jan Odelstad
      Pages 135-151

    5. Conformity and Measures

      • Jan Odelstad
      Pages 152-172

  4. Formal Treatment of Basic Topics

    1. Front Matter

      Pages 173-173
      Download chapter PDF

    2. Transitions Between Systems of Relationals

      • Jan Odelstad
      Pages 175-200

    3. The Structure of Subordination

      • Jan Odelstad
      Pages 201-218

    4. Isomorphic Mappings and Invariance

      • Jan Odelstad
      Pages 219-234

  5. Back Matter

    Pages 235-248
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Department of Philosophy, Uppsala University, Uppsala, Sweden

    Jan Odelstad

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation