Abstract of Chap. 8

The term "practical logic" means the logic in measurement theory. It is certain that pure logic (=mathematical logic) is merely a kind of rule in mathematics (or meta-mathematics). If it is so, the mathematical logic is not guaranteed to be applicable to our world. For instance, mathematical syllogism ( "$A \Rightarrow B$" and "$B \Rightarrow C$" imply "$A \Rightarrow C$" ) does not assure the following famous statement:

 $(\sharp_1):$ Since Socrates is a man and all men are mortal, it follows that Socrates is mortal.
That is, we think that
 $(\sharp_2):$ the above ($\sharp_1$) is not clarified yet.
In this chapter, we prove the $(\sharp_1)$ in classical systems. Also, we point out that syllogism does not hold in quantum systems This chapter is mostly extracted from the following:
 [1]: S. Ishikawa, "Mathematical Foundations of Measurement Theory,"Keio University Press Inc. 2006. ( download free) [2]: S. Ishikawa, "Fuzzy Inferences by Algebraic Method," Fuzzy Sets and Systems, Vol. 87, No. 2, 1997, pp.181-200.doi: 10.1016/S0165-0114(96)00035-8 ( download free)

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