Author : Jan Odelstad
Publisher : Springer Science & Business Media
ISBN 13 : 3642483887
Total Pages : 255 pages
Book Rating : 4.6/5 (424 download)
Book Synopsis Invariance and Structural Dependence by : Jan Odelstad
Download or read book Invariance and Structural Dependence written by Jan Odelstad and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.