TAKEUCHI Gaishi sent me the Road to Meaning through mathematics. 4 March 2021
From Author;
This automatic translation has indistinct expressions.
I humbly beg your pardon.
Original text is written by Japanese.
5.
TAKEUCHI Gaishi
5.
TAKEUCHI Gaishi
History of Takeuchi
“Mathematics Seminar” February 2018 issue
Special feature: History of Takeuchi and basic theory of mathematics
Nippon Hyoronsha 2018
TAKEUCHI Gaishi sent me the Road to Meaning through mathematics
In my youth, I loved mathematics the most since high school, but I repeatedly failed.the law of nature
Even though I wanted to return it and never come near it again, I felt its irresistible charm.force
Because of this, I was hurt by approaching her again, and there were days when I continued to feel powerless.。
However, in 1976 Kodansha's Bluebacks finally overcame this setback. of
The teacher's book ``What is a gathering?'' was published as a single book.
This book starts with the most basic concept in mathematics, which is sets.Wow
It is a truly enlightening book that covers everything from Cantor's teachings to the most recent modern set theory.mosquito
This is a simple explanation. However, add annotation to expressions that are easy to understand.must
It may be necessary。
As a second high school Japanese language teacher, I spent three years from 1976 to 1978 in Tokyo.green
He spent time at Tokyo Metropolitan Ome Higashi High School in Ume City, where he met a young mathematics teacher.out
met. He completed his master's program at Tokyo University of Science and is teaching mathematics as a lecturer at the University of Science.Ta
However, feeling the limits of his abilities, he decided to start over as a high school teacher and went to Ome Higashi.high
I have been assigned to a school. He told me that if he had the ability, he should take the doctoral program at Kyoto University.cormorant
He told me that he thought he didn't have that power, and that's why he came to this point.Ku
It was. During these conversations, when I told them about Takeuchi's book, they thought it was interesting.reactor
That's why she asked me if we would like to study together, so I went to the school after school.two
During other people's free time, we would sit in a room with a blackboard, and he would be the teacher and I would be the student, and we would read the best books.first time
From there, the two of us went over each point that seemed to be a problem.
One of the central points of this book is how the numbers 1 to 9 are generated using set theory.hand
I was about to say something. I just can't understand some of it myself.Na
There was something wrong with me, so I asked him, the teacher with his back to the blackboard, about it. He is Shibaand others
After thinking about it, I tried to write the solution on the blackboard, but hesitated and said, ``This doesn't work for me.''circle
I don't know.'' As a university lecturer, I know something that he doesn't understand.teeth
It couldn't have been. He ended his study for the day by saying, ``It's difficult.''of
This was the last study session on set theory.
Since then, I have had many conversations with him about various topics. I was a little olderof
And he was always polite. Even when I told him to talk more normally, he didn't.of
I didn't lose my stance. In March 1979, I transferred from the same school to Tokyo Metropolitan Agricultural High School in Fuchu City.of
Instead of working part-time, he became a major student at Wako during the day from April. he will sooneight
I was transferred to a metropolitan high school that was one of the leading preparatory schools in Oji City, and one night, I met him for a long time.Bu
I met Ri on the train. He asked me about the status of linguistics departments at national universities, and Icircle
I told him about the range. He said that I have continued to study languages since then.oh
I was sure that I had it.
Tokyo Metropolitan Ome Higashi High School Former Class 3/4 Barbecue at “Sakanaen” in Hinode-cho, Tokyoー
meeting
Photo Endorsement September 11, 1999
Everyone is now 38 years old, and it was a fun day with the children also participating.
back to the topic.Generation of numbers 1 to 9 using set theory certainly didn't make sense to me at the time.untie
It contained the impossible. Even though he majors in mathematics, he still has a collection of books from the late 1970s.combine
In the discussion situation, it seemed quite difficult to understand unless one was an expert in that area.I
Much later, in 2008, he wrote a paper called Generative Theorem.、
I answered this long-standing challenge. At this time, I was thinking of von Neumann Algebra.of
Iman algebra, required. This paper is a bit long, so the link is below.vinegar
That's it. studied togetherI haven't seen him for a long time, why?Ru
I wonder.
There is another memory in this generation of numbers 1 to 9. I've written it several times, but I'm repeating it.vinegar
and a conversation with Professor Eiichi Chino, who taught structural linguistics when he was a research student at Wako.in
be. One day, after the lecture, I happened to have a conversation with the teacher near the entrance. destinationborn
asked me what I was studying now. I immediately fell in love with Takeuchi.outside
Thinking of Mr. Shi, I would like to briefly explain the internal structure of the meaning, for example, from 1 to 9.of
When I replied that I was wondering if it would be generated like that, the teacher said seriously,child
Don't say that, that's not what we think, that's what Wittgenstein and others think.picture
That's it," he said angrily. I was momentarily surprised by the teacher's reaction, but then...field
``Okay,'' I replied.
The Linguistic Circle of Prague was formed in Prague in the 1920s.become
Sergej Karcevskij wrote ``Asymmetric Duality of Linguistic Signs'' andword
showed predictions about the global structure of meaning inmeaning
The pursuit of flavor structure was not pursued in the end. One of the most important things in languageRu
Nevertheless, it has been very difficult to explore what meaning is.
After World War II, Roman Jakobson established conceptual anthropology in the United States.One
He met Claude Levi-Strauss of France, who was in Tokyo, and created a new structural linguistics.think
However, since the pursuit of meaning itself is difficult, phonology andteeth
He moved in the direction of phonetics, such as phonemes. Later, in 1973, Jakobson became ESSAY
DE LINGUISTIQUE GENERALE Japanese translation “General Linguistics” Misuzu Shobo1973著
In that process, I proposed the concept of semantic minimum field, andmiddle
The mental description is on pages 137 to 140 in the Japanese translation, but on page 139, Jakobsonby
It is stated below.
``If the study of word structure is, on the one hand, an inventory of grammatical meanings, and on the other hand, phonemes and theirroot
The sonic aspects of a given language, if limited to the underlying differential inventory.of
For purposes of consideration, it is correct to say that meaning itself does not matter.Ru
As it should be, the meanings only need to be clearly distinguished from each other.mosquito
Furthermore, in the study of conceptual aspects, the expression form of meaning itself isstomach
It would be correct to say that there is no problem as long as it is expressed separately.。
However, these two extremes by no means exhaust linguistic material.Na
stomach. ”
After this, we will move on to phoneme theory, which is the combination of phonemes.child
Jakobson's understanding at the time was that he did not go into the internal structure of meaning itself.Na
stomach. It is probably difficult to hope for any further progress using conventional methods.
In summary, it is probably impossible to describe the meaning structure of natural language in natural language.reactor
I think so. Throughout the 20th century, the internal structure of meaning itself was defined by a clear logic.set
I was unable to pursue this as a product. If it could be pursued, it would be in the basic theory of mathematics.overtake
My conclusion is that it must depend on language or mathematics itself. followhand
I chose the math direction. Hyperlanguage is now a branch of logic.stomach
This is because I believe that the basis of this lies in mathematics.
But I've always had deep respect for Jakobson's work. He wrote “one
``General Linguistics'' Misuzu Shobo, 1973 and ``Language Sound Form'' Iwanami Shoten 1986 are quite長
It was on my desk for a while. And the biggest benefit from him is his semantic
minimum meaning Strongly influenced by the minimum body, in 2008 I wrote a paper、
From Cell to Manifold、 I put them together and dedicated them to him.
Let's return to Fumi Takeuchi's ``What is a gathering?'' For me after reading this book、
The direction was decided to examine language through mathematics. Mr. Fumi Takeuchi,I
However, from then on, he realized the importance of continuing mathematics no matter how difficult it was.attack
He decisively showed me that I should aim for the top of the mountain. I in 2006
Growth of Word Paper called , and wrote Takeuchi Sensei's name in the title.
"Mathematics Seminar" February 2018 issue Special feature History of Takeuchi and basic theory of mathematics Nippon Hyoronsha
In 2018, Professor Takeuchi's essay ``Similar to a sunset...'' was published in .Na
It touches my heart. I did not come across your book ``What is a set?'' in 1976.Na
Otherwise, my return to mathematics may have been much delayed. Some of his thoughts are below.to
I want to quote it.
``When I try to remember my encounter with mathematics now, what comes to mind is、
Most of the time, it's not something that's finished, and no matter how hard I try, I can't make it work.Ta
There are many things that I wanted to do but failed to do. When I tried it,I
's encounter with mathematics may mean that he did not encounter mathematics at all. ”
“The great thing about encountering mathematics is that no matter how many times you encounter it, its charm never fades."
TANAKA Akio
4 March 2021
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