# Invariance and Structural Dependence

Book

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

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

1. Front Matter
Pages 1-1
Pages 3-39
Pages 40-70
3. ### An Informal Presentation of the Main Themes

1. Front Matter
Pages 71-71
Pages 73-95
Pages 96-134
Pages 135-151
Pages 152-172
4. ### Formal Treatment of Basic Topics

1. Front Matter
Pages 173-173
Pages 175-200
Pages 201-218
Pages 219-234
5. Back Matter
Pages 235-248

### 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

• 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
• 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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