Abstract ( 19.0: how to describe "brief")

Recall the spirit of quantum language ( i.e., the spirit of the quantum mechanical world view), that is,

$(\sharp):$ every phenomenon should be described by quantum language ( knowing it is somewhat unreasonable )!
Thus, we consider that even the "belief" should be described in terms of quantum language. For this, it suffices to consider the identification: $$ \mbox{ "belief" $=$ "odds by bookmaker" } $$
This approach has a great merit such that {the principle of equal weight holds}. This chapter is extracted from Chapter 8 in
$(\sharp):$ S. Ishikawa, Mathematical Foundations of Measurement Theory, Keio University Press Inc. 2006.

Again recall that, as mentioned in $\S$1.1, the main purpose of this book is to assert the following figure 1.1:
Fig.1.1: the location of "quantum language" in the world-views
This(particularly, ⑦--⑨) implies that quantum language has the following three aspects: $$ \left\{\begin{array}{ll} \mbox{ ⑦ :the standard interpretation of quantum mechanics} \\ \mbox{ $\qquad$ (i.e., the true colors of the Copenhagen interpretation) } \\ \\ \mbox{ ⑧ : the final goal of the dualistic idealism (Descartes=Kant philosophy) } \\ \\ \mbox{ ⑨ : theoretical statistics of the future } \end{array}\right. $$