SRFL Memory

Wednesday, 25 March 2026

Paper 2003-2007 1-192

Tokyo
19 August 2020
Sekinan Geometry Early

TAKEUCHI Gaishi sent me the Road to Meaning through mathematics. Translated by Google 2021

TAKEUCHI Gaishi sent me the Road to Meaning through mathematics. Translated by Google

TAKEUCHI Gaishi Mathematician of Japan 1926-2017

TAKEUCHI Gaishi sent me the Road to Meaning through mathematics

My youth has been fond of mathematics since high school, but I have been frustrated over and over again, trying to keep him away, but because of the irresistible charm, I got hurt again and loses the power. It was a day I kept new feeling. It was come from TAKEUCHI's “What is a set?” published by Kodansha as a book of Blue Bucks in 1976.

This book explains the most basic concept of set in mathematics from Cantor, which was the starting point, to the latest in modern set theory in a very easy-to-understand manner. However, it may be necessary to annotate the expression that it is easy to understand .

As a second high school language teacher, I spent three years from 1976 to 1978 at Tokyo Metropolitan Ome Higashi High School in Ome City, Tokyo, where I met a young math teacher. He taught mathematics as a lecturer at Tokyo University of Science after completing a master’s course, but felt the limits of his abilities and chose to start again as a high school teacher and was assigned to Ome Higashi High School. He was thinking of taking a PhD at Kyoto University if he had the ability, but he told me that he hadn’t had the ability to do so. In such a story, when I told him about Gaisi Takeuti’s book, it seemed interesting, so he asked me to study together, so in my spare time after school, the blackboard In a room, he became a teacher and I became a student, and from the beginning of the book, the two of us examined the potential problems one by one.

One of the hearts of this book was to describe how the numbers 1-9 are generated by set theory. I couldn’t understand some of them by myself, so I asked him, a teacher with a blackboard on his back. After thinking for a while, he tried to write the solution on the blackboard, but he ran around and replied, “I don’t know this.” I couldn’t have understood that he was a university lecturer. He said it was “difficult” and the study of the day was over, which was the final study session of this set theory.

Since then, I have talked with him on various topics. He was always polite because I was a little older. He didn’t break his stance when I told him to speak more normally. In March 1979, I changed from the same school to a part-time job at Tokyo Metropolitan Agricultural High School in Fuchu City, and from April I became a major student in Wako during the daytime. He was soon transferred to Tokyo Metropolitan High School, one of the leading colleges in Hachioji, and one night he met him by train for the first time in a while. He asked me about the situation in the language department of the national university and told him what I knew. He certainly thought I would continue to study the language.

.....................................................................................................

The generation of numbers from 1 to 9 by set theory certainly contained something that I could not understand at the time. Even though he majored in mathematics, in the situation of set theory at the end of the 1970s, it seemed to be quite difficult to understand unless he was a specialist. Long after 2008, I wrote a Paper called Generative Theorem to answer this long-standing homework. I needed von Neumann Algebra von Neumann algebra at this time. This Paper is a little long, so I will show the Link destination below. I haven’t seen him who studied with him for a long time, but what are you doing?

GENERATION THEOREM

There is another memory in this generation from 1 to 9. I’ve written it several times, but to repeat it, it’s a conversation with Professor Eiichi Chino, who was studying structural linguistics when he was a research student at Wako. After the lecture one day, I suddenly had a conversation with the teacher near the entrance. The teacher asked me what I was studying now. When I replied that I was thinking about Professor Gaisi Takeuchi, who was devoted to it, and briefly thought about the internal structure of meaning, for example, how 1 to 9 are generated. Seriously, “Stop that, it’s not what we think, it’s what Wittgenstein and others think,” he said in an angry manner. I was surprised at the teacher’s reaction for a moment, but responded “I understand” on the spot.

The Prague Linguistic Circle of Prague was formed in Prague in the 1920s, where Sergej Karcevskij wrote “Asymmetric Duplexity of Linguistic Symbols”, which made predictions about the global structure of meaning in language, but then language. The pursuit of the semantic structure in was not finally made. Despite being one of the most important things in language, it was so difficult to find out what it meant.

After World War II, Roman Jakobson was building a conceptual anthropology in the United States, and he met Claude Levi-Strauss, who envisioned a new structural linguistics and blossomed there. Since it was difficult to pursue, we proceeded in the phonetic direction such as phonology or phonemes. Later in 1973, Jakobson wrote the Japanese translation of ESSAY DE LINGUISTIQUE GENERALE, Misuzu Shobo, 1973, in which he proposed the concept of semantic minimum, the central description of which is 137 pages in Japanese. From page 140, but on page 139, Jakobson states:

“If the study of word structure was limited to a list of grammatical meanings on the one hand and to phonemes and their underlying discriminatory special catalogues on the other hand, then a review of the sound aspects of a given language. In order to do so, the meaning itself should be correct, even if it does not matter, as long as the meanings are clearly distinguished from each other, and also in the study of conceptual aspects. , The expression of meaning itself would be correct to say that it does not matter as long as the meanings are distinguished from each other, but these two extremes never exhaust the linguistic material. . “

After that, we will move on to the theory of phonemes, which is the combination of phonemes. His perception at this time did not go into the internal structure of the meaning itself. It is probably difficult to hope for further progress in the usual way.

In summary, I think it is probably impossible to describe the structure of the meaning of natural language in natural language. Throughout the 20th century, the internal structure of meaning itself could not be pursued as a clear collection of logic. My conclusion is that if it could be pursued, it would have to rely on the super language of foundations of mathematics or the mathematics itself. Therefore, I chose the mathematical direction. Super language is now a field of logic, and I think its roots must still depend on mathematics.

But I have always paid close respect to Jakobson’s achievements. His book “General Linguistics” Misuzu Shobo, 1973 and “Language Sound Form Theory” Iwanami Shoten 1986 have been on my desk for quite some time. And the greatest benefit from him was strongly influenced by his semantic minimum meaning minimal body, and in 2008 I dedicated a piece of his Paper, From Cell to Manifold, to him.

CELL THEORY FROM CELL TO MANIFOLD FOR LEIBNIZ AND JAKOBSON

Let’s return to TAKEUCHI Gaishi.

It is “What is a set?”. For me, after reading this book, mathematics decided to consider the language. Professor Gaisi Takeuchi has shown to me the importance of continuing mathematics no matter how difficult it may be, and aiming for the difficult peak of meaning. I wrote his Paper called Growth of Word in 2006 and put the name of Professor Takeuchi in the title.

GROWTH OF WORD DEDICATED TO TAKEUCHI GAISHI

“Mathematics Seminar” February 2018 Special Feature Gaisi Takeuchi and Foundations of Mathematics Nihon Hyoronsha 2018, Professor Takeuchi’s idea “Similar to the sunset …” still keeps my heart strike. If I hadn’t met my teacher’s book, What is a Set, in 1976, my return to mathematics might have been delayed. I would like to quote a part of that essay below.

“When I try to remember my encounter with mathematics now, most of the things that come to my mind are not something that has been completed, and I couldn’t do it well no matter how hard I tried, or I missed it while thinking about doing it. It may be that my encounter with mathematics did not mean that I did not meet mathematics. “

” The wonderfulness of encountering mathematics does not diminish its appeal no matter how many times I meet it. “

TANAKA Akio
4 March 2021

Sekinan Library

For WITTGENSTEIN Ludwig Revised　2005-2014

For WITTGENSTEIN Ludwig Revised Position of Language 2005-2014

Position of Language

TANAKA Akio

1  Quantization 1  is a cliff for consideration of language.
2 Mathematical interpretation of quantized language is now a first step to the theoretical ascent.
3 If there is not mathematics, next conjectures are impossible.
(i) Difference between word and sentence--- Commutative and noncommutative ring
(ii) Continuation from word to sentence--- Tomita’s fundamental theorem
(iii) Word’s finiteness and sentence’s infinity--- Property infinite  and  purely infinite
(iv) Cyclic  structure of word’s meaning--- Infinite cyclic group
4  Meaning minimum 2 ,  mirror language 3  and  mirror symmetry 4  are inevitable approach to the study of language especially for  language universals 5 .
5 Symplectic Language Theory, Floer Homology Language and Arithmetic Geometry Language are adopted as the model theory   for natural language in the recent.
6 Hereinafter the model theory will be entered to the new concept .  The Model s  of Language Universals 6   will be shown by the description of mathematics .

[References]
1 . Quantized Language
Quantization of Language /Floer Homology Language
2 . Meaning minimum
Structure of Meaning / Symplectic Language Theory
3 . Mirror language
Mirror Symmetry on Rational Curve / Symplectic Language Theory
4 . Mirror symmetry
Homology Mirror Symmetry Conjecture by KONTSEVICH / Symplectic Language Theory
5 . Language universals
Generating Function / Symplectic Language Theory
6. Models of Language Universals
Language Universal Models

Tokyo December 10, 2005
Tokyo November 27, 2008 Revised
Tokyo March 24, 2009 Revised
Tokyo June 27, 2009 Revised
Tokyo February 28, 2011 Revised
Tokyo August 3, 2012 Revised
Tokyo December 8, 2014 Reprinted
SIL

The Time of Language Ode to The Early Bourbaki To Grothendieck　2012-2014　

The Time of Language Ode to The Early Bourbaki To Grothendieck 2012-2014

TANAKA Akio

In early 1970s, I had think of language from the side of mathematics, that level of mine is very low and primitive, moreover I never had any talent to mathematics.
But my eager to trying the approach was going to overcome hard barriers before me. So the route had really fascinated my mind for long time.

At that time I had read Chinese classics almost every day. WANG Guowei*, DUAN Yucai and WANG Yingzhi. They were giants on Chinese language historically and modernly.
On the other hand I had thought of language generally, not defined by Chinese.
But in front of the vast world of language, I had stood still lonely, not taking any method for approaching.
Mathematics was the only gleam of hope in the wasteland.

I never took the route of ordinary linguistics.
I really dreamt a dream that time.
There exists set theory before me.
Probably there was the influence of Bourbaki**, that several translations to Japanese, shared from Tokyo Tosho Publisher, were on the desk of mine.
My talent and endeavour were so low, so I had not any results at that time.
My desire was deep but my hand was so shallow.
The time passed by.

In 1979 the meeting again with CHINO Eiichi*** made me the chance to learn on language, the object was clear and direct.
Language universals by mathematics became the never-ending goal of the study hereafter.
Sergej Karcevskij**** gave me the courage to the research.
All the way to investigation were taught from CHINO, who was the genuine teacher on language.
In mathematics I took the route from geometry, especially by projection.
Now I stand at algebraic geometry.
Grothendieck is in the northernmost at the end of Bourbaki.

SAITO Takeshi said at the essay on Grothendieck***** that the object of mathematics for Bourbaki was the set of being attached by construction and the object of mathematics for Grothendieck was the object of category representing the presentable functor.
The time has come for describing****** on language by mathematics despite my poor ability.
Sincere thanks for the pioneers letting us make the fascinating route of modern mathematics.

1. *WANG Guowei
Encounter in life / A Letter /2005
Influenced paper / On Time Property Inherent in Characters / 2003 , Quantum Theory for Language / 2004
2. **Bourbaki
SAITO Takeshi. Bourbaki, Mathematics Seminar, vol..41 no..4 487. Nihonhyoronsha, Tokyo, 2002.
3.***CHINO Eiicji
First met in 1969, again in 1979. Fortuitous Meeting
4. ****Sergej Karcevskij
Note on Karcevskij's theme. Note for KARCEVSKIJ Sergej's "Dudualisme asymetrique du signe linguistique"
5. *****Grothendieck
SAITO Takeshi. Grothendieck, Mathematics Seminar, vol..49 no..5 584. Nihonhyoronsha, Tokyo, 2010.
6. ******describing
Note on Grothendieck's theorem. Vector Bundle Model

Tokyo
January 10, 2012
Sekinan Research Field of Language

[Note, 28 October 2014]
When I first learnt French in 1964, I was the second grade of high school. My aim to learning was to get the lowest readable situation for modern poems of French Symbolism represented by Arthur Rimbaud and Paul Verlaine. Afterwards in 1969 I knew the importance of Martinet's work at the linguistic class of university. Probably in the early 1970s, I bought Bourbaki's books at the old-book-shop at Kanda, Tokyo, when Bourbaki's fame reached to the poor-talented linguistic student like me. I was enchanted Bourbaki's works and I somehow would like to adopt their results to my linguistic study. But my mathematical level was too low to get near Bourbaki's world. From those days my wandering around mathematics and linguistics kept long long way like the Beatles song, The long and winding road. What I again met mathematics, especially algebraic algebra was already over the twentieth century. From 2003 I began to write papers being assisted with CHINO Eiichi's advice and Sergej Karcevskij's work. At that times Chinese Qing dynasty's vast linguistic works topically represented by WANG Guowei was also assisting my study. At the result my first satisfied paper,"On Time Property Inherent in Characters"1 was completed. The theme in my life, model making of language universals was begun further later in 2008 at Zoho site 2 sekinanlogos 3. At Complex Manifold Deformation Theory 4 I started writing more clearer descriptive papers by mathematics especially according to algebraic geometry. And now I step up one more and entered in arithmetic geometry 5 for solving more difficult themes such as dimension, synthesis and fusion of meaning in word.

Refer to the next.

On Time Property Inherent in Characters
Zoho site
sekinanlogos
Complex Manifold Deformation Theory
Arithmetic geometry

Wednesday, 25 March 2026

Paper 2003-2007 1-192

Paper 2003-2007 1-192

TAKEUCHI Gaishi sent me the Road to Meaning through mathematics. Translated by Google 2021

For WITTGENSTEIN Ludwig Revised 2005-2014

For WITTGENSTEIN Ludwig Revised Position of Language 2005-2014

The Time of Language Ode to The Early Bourbaki To Grothendieck 2012-2014

The Time of Language Ode to The Early Bourbaki To Grothendieck 2012-2014

For WITTGENSTEIN Ludwig Revised　2005-2014

The Time of Language Ode to The Early Bourbaki To Grothendieck　2012-2014　