Summing up the arguments in Chap 1, we see:
Summary ( All of quantum language )
Quantum language (= measurement theory ) is formulated as follows.
\begin{align}
&
\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$3.1)
}}
{
\overset{
{}}{\fbox{Linguistic interpretation}}
}
}_{\mbox{ the manual on how to use spells}}
\label{eq1.2}
\end{align}
[Axioms] Here
[The linguistic interpretation] From the pure theoretical point of view, we do well without the interpretation. However,
The most important statement in the linguistic interpretation ($\S$3.1) is
Only one measurement is permitted
After all, I want to assert that
\begin{align}
\underset{\mbox{[dualistic idealism]}}{\mbox{Descartes philosophy}}\longrightarrow
\left\{\begin{array}{ll}
\color{blue}{\underset{\mbox{[Axioms]}}{\mbox{Continental Rationalism}}}
\\
\\
\color{red}{\underset{\mbox{[Linguistic interpretation]}}{\mbox{British empiricism}}}
\end{array}\right\}
\longrightarrow \underset{\mbox{[quantum language]}}{\mbox{Kant philosophy}}
\end{align}
[Axioms] Here
| (A): |
$ \underset{\mbox{(Kant philosophy)}}{\fbox{a priori synthetic judgment}} \quad \xrightarrow[\mbox{quantization}]{} \quad \underset{\mbox{(quantum language)}}{\fbox{Axioms 1 and 2}} $ which (i.e., ⑥$\rightarrow$⑧$\rightarrow$⑩ ) is realized in the right figure(i.e., the history of world-descriptions ). Therefore, what we should do is not "to understand" but "to use". After learning Axioms 1 and 2 by rote, we have to improve how to use them through trial and error. |
[The linguistic interpretation] From the pure theoretical point of view, we do well without the interpretation. However,
| (B): | it is better to know the linguistic interpretation of quantum mechanics (= the manual on how to use Axioms 1 and 2), if we would like to make progress quantum language early. |
That is, the spirit of quantum language is
