通俗と学術の間                                      

数理科学

数理科学

科学哲学序説-測定理論による諸科学の統一

 石川史郎 著 B5版 290ページ
  ダウンロード版   500円+税   グーグル
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  ISBN:9784907625207(ダウンロード)、9784907625214(POD)
  2015年2月20日刊

 これまで物理学のような体系的な哲学を持たなかった、工学を始めとする諸科学。構築のヒントは意外にも量子力学の測定理論。これに範をとって、実在的科学観に対比すべき言語的科学観が打ち立てられる。大学4年生のゼミの副読本をもとに、易しい例を多数取り入れて、高校程度の学力があれば全体像が把握できるよう新たに書き下ろした。

 詳しくはこちら


量子言語入門

 -量子力学の言語的解釈:大学院講義義ノート
  石川史郎, B5版 409頁

  ダウンロード版  1,100円+税   グーグル
  印刷版(POD)   2,800円+税   アマゾン

  ISBN:9784907625276(ダウンロード)、9784907625283(POD)
  2015年8月5日刊

量子力学の観測の理論にヒントを得て、「コペンハーゲン解釈」を言語化した「量子言語」が構築される。この量子言語の体系に基づき、量子力学の良く知られた諸問題 - ハイゼンベルクの不確定性原理、EPR-パラドックス、ベルの不等式、シュレディンガーの猫など - が新たな視点から考察される。量子言語は、量子系だけでなく、むしろ古典システムを記述する言語として威力を発揮する。フィッシャーの最尤法、信頼区間と仮説検定、分散分析、ベイズ統計、カルマンフィルターなど主に統計学のテーマが量子言語の観点から再構築される。本書は大学院の講義ノートをもとにしており、著者の手になる『科学哲学序説』をより体系的に学びたい方におすすめ。英語版の "Linguistic Interpretation of Quantum Mechanics" よりざっくばらんな講義風。

 詳しくはこちら

Linguistic Interpretation of Quantum Mechanics

- Towards World-Description in Quantum Language -

by Shiro ISHIKAWA, 409 pages (B5)

Paperback:5,092JPY + tax, to buy at amazon.co.jp

ebook (pdf):1,500 JPY + tax , to buy at google

  ISBN:9784907625252 (download) , 9784907625269(POD)
  published on July 20, 2015

Inspired by the Copenhagen interpretation of quantum mechanics, the author introduces two axioms, one for measurement and the other for causality, to establish a new paradigm or world-description called "linguistic interpretation" or "quantum language".

The paradigm casts a new light on the wellknown problems in quantum mechanics including Heisenberg's uncertainty principle, EPR-paradox, Bell's inequality, Schrödinger's cat (Wigner's friend), Wheeler's delayed choice experiment, and double-slit experiment.

He shows that the paradigm works not only in quantum systems but also in classical systems, referring to regression analysis and Kalman filter in statistics and so on.

He emphasizes the paradigm is a natural consequence in the history of philosophy, and shows how the famous problems in philosophy are solved such as Leibniz=Clarke correspondence "What is space-time ?", Zeno's paradox , and the principle of equal probability.

He thus leads us to a conclusion that quantum language is a core concept of science.

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量子論から見た西洋哲学史

  石川史郎著 A5版 208頁 

  ダウンロード版   100円+税   グーグル
  印刷版(POD)   1,700円+税   アマゾン

  ISBN:9784907625337(ダウンロード)、9784907625344(POD)
  2016年9月15日刊

著者は、量子論にヒントを得て、科学を包括的に記述する言語「量子言語」を体系化した。科学的・技術的問題は既に「量子言語入門」(紫峰出版 2015年)で論じられている。本書はその最終的な到達点から西洋哲学を俯瞰した。量子論を全く知らない文系の人も読み進めることができるように工夫されていて、「量子言語」の文芸部分を敷衍したものとなっている。具体的には、西洋哲学史における最大の二つの難問を解決している。「(i) 進歩問題: 西洋哲学は進歩・発展してきたのだろうか? または、「進歩・発展」の尺度は何か?」と「(ii) 心身問題:「心」と「身体」は如何に関連し合っているか?」 大学院講義ノートが基礎になっているが、堅苦しい部分はそっくり取り去られ、軽妙な語り口で過激に議論は展開する。著者の提示する西洋哲学史観に引きずりこまれるだろう。

 詳しくはこちら

History of Western Philosophy from a Perspective of Quantum Theory

- Introduction to the theory of Everyday Science -

by Shiro ISHIKAWA, 445 pages (B5)

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 ISBN:9784907625580(paperback), 9784907625573 (ebook) ,
 published on May 22, 2023

Recently I proposed Quantum Language (QL) as a language of (dualistic and idealistic) science, which is also characterized as a linguistic turn of quantum mechanics. QL has two subclasses, non-commutative QL and commutative QL. They are applicable to quantum systems and to classical systems, respectively.
QL is composed of Axiom 1 (measurement), Axiom 2 (causality), and the linguistic Copenhagen interpretation. This theory has a stronger descriptive power than (quantum) mechanics and statistics.

Axioms 1 and 2 are usual since they are operator algebraic generalizations of quantum mechanics. On the other hand, the part of “linguistic Copenhagen interpretation” is not usual. This is defined by “a rule for drawing a line between science and pseudoscience”.

For example, the Popper's falsifiability is one of the rules of the linguistic Copenhagen interpretation.
Other examples are:

1) “There exists only `one', and not `many'.” (due to Parmenides)  ->  “Measurement can only be done once”, “A state does not move.”

2)“There is no motion.”(due to Parmenides)  ->  “A state does not move.”

3) “There is only the present.” ( due to Augustinus)  ->  “There is no tense.”

4) “To be is to be perceived.” (due to Berkely)  ->  “Nothing can be said without measurement.”
...

It is surprising that philosophers who did not know quantum mechanics approached the Copenhagen interpretation as described above.
Thus, I consider that the Copenhagen Interpretation is not attached to quantum mechanics, but to quantum language.

I will show that QL is a scientific perfection of dualistic idealism in Western philosophy.
In fact, the following unsolved problems in Western philosophy can be solved only by QL,
not by statistics.

* Zeno paradoxes, the problem of universals, Descartes problem (=mind-body problem + subjectivity problem), the Leibniz-Clarke space-time correspondence, Hume's problem of induction, the Grue paradox, From Kantian synthesis to QL-synthesis, the brain in a vat, Hempel's flagpole problem, the black raven problem, Wittgenstein's problem “ Why does logic work in our world?”, etc.

The most fundamental theories in modern science are commonly said to be the three: theory of relativity, quantum mechanics, and statistics. However, as this book will show, commutative QL is more powerful and beautiful than statistics. Therefore, I would replace the above three by “ theory of relativity, quantum mechanics, and commutative QL”.

Linguistic Copenhagen Interpretation of Quantum Theory

- Why does statistics work in our world? -

by Shiro ISHIKAWA, 365 pages (B5)

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 Germany  France  Spain  Italy

ebook (pdf): sold at Google Play : Price $1.00
 Google

 ISBN:9784907625672(paperback), 9784907625665 (ebook) ,
 published on November 15, 2023

Various interpretations of quantum mechanics have been proposed such as the Copenhagen interpretation and the many-worlds interpretation. The linguistic Copenhagen interpretation in this book is a kind of the Copenhagen
interpretation derived from von Neumann's formulation of quantum mechanics on Hilbert spaces.

Von Neumann had the widest coverage of any mathematician of his time, integrating pure and applied sciences and making major contributions to many fields, including mathematics, physics, economics, computing, and statistics. He was not a genius who specialised only in mathematics and physics, but an all-round genius.

From this fact we are tempted to expect the following.

(#1) the quantum theory generated from the linguistic Copenhagen interpretation called Quantum Language(QL) is a very large theory that includes not only quantum mechanics of physics but also classical statistics.

More generally we may say

(#2) QL is the scientific realisation of the dualistic idealism of philosophy.

In this book I devote myself to proving (#1). QL consists of two axioms (measurement and causality) and the linguistic Copenhagen interpretation.
I first prove von Neumann-Lüders projection postulate in QL. This is a solutionin QL, and it is undecided whether it is a physical solution, but the theorem allows
QL to be discussed without being interfered by various paradoxes (e.g., Schrödinger's cat, etc.).

Also, recall that there are no axioms in statistics. This means that we do not yet have 'theoretical statistics'. However, if we consider that QL for classical systems = theoretical statistics, we can then introduce an elegant understanding into statistics. In most books of statistics, Fisher's maximum likelihood method is not given a due treatment. From the quantum linguistic point of view, the most basic arguments are Fisher's maximum likelihood method and regression analysis. They are strongly linked to the measurement and causality axioms, respectively.

As modern statistics continues to develop rapidly in the direction of application now, it is essential to take an overview of statistics as a whole under an umbrella of theoretical statistics.

For (#2), refer to my previous book (i.e., History of Western Philosophy from a perspective of quantum theory :Introduction to theory of everyday science, Shiho-Shuppan Publisher, 425p. (2023)).
Throughout this book as wall as the one above, I assert that von Neumann's formulation of quantum mechanics should not be confined in physics, but should be regarded as a fundamental theory of science.

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