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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."
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