Abstract of Chap. 2
Quantum language (= measurement theory ) is formulated as follows. $\underset{\mbox{ (=quantum language)}}{\fbox{pure measurement theory (A)}} := \underbrace{ \underset{\mbox{ ($\S$2.7)}}{ \overset{ [\mbox{ (pure) Axiom 1}] }{\fbox{pure measurement}} } + \underset{\mbox{ ( $\S$10.3)}}{ \overset{ [{\mbox{ Axiom 2}}] }{\fbox{Causality}} } }_{\mbox{ a kind of incantation (a priori judgment)}} + \underbrace{ \underset{\mbox{ ($\S$3.1) }} { \overset{ {}}{\fbox{Linguistic interpretation}} } }_{\mbox{ the manual on how to use spells}}$ That is, "measurement" and "causality" are closely related in quantum language:

It should be compared to Newtonian mechanics: \begin{align} \underset{\mbox{ (physics)}}{\fbox{Newtonian mechanics}} = \overset{\mbox{ }}{\fbox{Nothing}} + \overset{\mbox{ (Newtonian equation)}}{\fbox{Causality}} \end{align}
Measurement theory asserts that
 (A): Describe every phenomenon modeled on Axioms 1 and 2 (by a hint of the linguistic interpretation)!
In this chapter 2, we introduce Axiom 1 (measurement). Axiom 2 concerning causality will be explained in Chapter 10.
Some may have a question that
Why does Newtonian mechanics have "measurement"?

This will be answered throughout this book. However, I add a brief answer below:
Recall Einstein's words:
The moon is there whether one looks at it or not.
which implies that physics exists without measurement. That is, Newton as well as Einstein found out the essence:

"measurement" is not the concept in physics

The The Hilbert space formulation of quantum mechanics is due to von Neumann (1903-1957). I cannot emphasize too much the importance of his work. We think that

von Neumann's quantum mechanics $\doteqdot$ quantu mechanics

The above "$\doteqdot$" cannot be replaced by "$=$" since von Neumann believed in that quantum mechanis is physics.

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: $$\left\{\begin{array}{ll} \mbox{ ⑦ :the standard interpretation of quantum mechanics} \\ \mbox{ \qquad (i.e., the true colors of the Copenhagen interpretation) } \\ \\ \mbox{ ⑧ : the final goal of the dualistic idealism (Descartes=Kant philosophy) } \\ \\ \mbox{ ⑨ : theoretical statistics of the future } \end{array}\right.$$