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. |

$(\sharp_2):$ | the above ($\sharp_1 $) is not clarified yet. |

[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**