From Author
This translation has some ambiguity by auto translation.
Original Japanese text is shown below.
https://stonesouth.blogspot.com/2022/08/takeuchi-gaishi-and-generation-theorem.html
TAKEUCHI Gaishi and Generation Theorem
5.
TAKEUCHI Gaishi sent me the Road to Meaning through mathematics
Takeuchi Gaishi
The history of bamboo inside and outside
Mathematics Seminar, February 2018 issue
Special Feature Gaishi Takeuchi and Foundations of Mathematics
Nippon Hyoronsha 2018
When I was young, I liked mathematics the most since high school, but I failed many times.the law of nature
The irresistible attraction, even as I tried to return it and never come near it again.force
For that reason, I was hurt by approaching again, and it was days when I continued to feel my own powerlessness.。
However, it was Bluebacks from Kodansha in 1976 that overturned that setback decisively. of
It was the teacher's "What is a set?" published as a single volume.
This book takes as its starting point the most fundamental concept in mathematics, the set.Tsu
From the early Cantor to the most recent of modern set theory,mosquito
It is described in an easy-to-understand manner. However, annotate expressions that are easy to understandmust
may need。
From 1976 to 1978, I spent three years as a Japanese language teacher at a second high school in Tokyo.green
I spent my time at O High School in Umeichi, where I met a young mathematics teacher.out
met. He has been teaching mathematics as a lecturer at the Tokyo University of Science after his master's degree.rice field
However, feeling the limits of his abilities, he chose to start over as a high school teacher.high
I have been assigned to school. He said to me, if you have the ability, take a doctoral course at Kyoto University.cormorant
He told me that he had thought about it, but he thought he didn't have the power to do so, so he came to the present.nine
was In the midst of such conversations, when I mentioned Gaishi Takeuchi's book, it was funny.reactor
That's why he suggested to me if we should study together, so after schooltwo
In his spare time, in a room with a blackboard, he became a teacher and I became a student.first time
From then on, the two of us went over every possible problem.
One of the central points of this book is how the numbers 1 through 9 are generated by set theory.hand
I was about to say a few things. I can't quite understand some of them myself.na
I asked him, the teacher with the blackboard behind him, about it. he is shibaand others
After thinking about it for a long time, I tried to write the solution on the blackboard.circle
No,” he replied. I know what he doesn't know who was a university lecturerteeth
It wasn't supposed to be. He said "it's hard" and ended his studies for the day, and that was it.of
It was the last study session of set theory.
Since then, I have had many conversations with him. I was a little olderof
And he was always polite. Even when I told him to speak more normally, heof
I didn't lose my composure. In March 1979, I moved from the same school to N High School in Fuchu City.of
Instead of working part-time, I became a university advanced course student from April. he will soonEight
I was transferred to H High School in Oji City, and one night I met him for a long time.bu
We met on the train. He asked me about the state of the linguistics department at the national university, and Icircle
I told him about the range. He said that I continued to study languages after that.oh
I was sure I had it.
O High School Former 3rd grade 4th class Barbecue at Hinodecho, Tokyo "Sakanaen"meeting
Photo endorsement September 11, 1999
Everyone turned 38 this year, and it was a fun day with children participating.
back to the topic.The generation of the numbers 1 to 9 by set theory certainly did not make sense to me at the time.untie
It contained the impossible. Even though he majored in mathematics, the late 1970scombine
In the situation of the argument, it seemed that it was quite difficult to understand unless you were a specialist.Me
much later, in 2008, wrote a paper called Generation Theorem.、
I answered this longstanding homework. At this time, Iof
required the Iman algebra. This paper is a bit long, so here's the linkvinegar
It is assumed that studied togetherI haven't seen him in a long time.Ru
I wonder.
There is another memory in this generation of 1 to 9. I have written several times, but I repeatvinegar
A conversation with Professor C, who taught structural linguistics when I was a research student at Wako.and
be. One day, after a lecture, I happened to have a conversation with the teacher near the entrance. Destinationpregnancy
asked me what I was studying. Takeuchi who was devoted at onceoutside
Thinking of Mr. Shi, briefly explain the internal structure of meaning, for example, howof
When I answered that I was thinking about generating such achild
No, it's not what we think, it's what Wittgenstein and others think.e
That's right," he said angrily. I was surprised by the teacher's reaction for a moment, but thatfield
I replied, "Okay."
The Linguistic Circle of Prague was founded in Prague in the 1920s.to make
where Sergej Karcevskij wrote ``Asymmetric duality of linguistic signs'',word
He showed his expectations for the global structure of meaning inmeaning
Pursuit of taste structure was not made at last. one of the most important things in languageRu
Nevertheless, it was so difficult to pursue what the meaning was.
After World War II, Roman Jakobson constructed a conceptual anthropology in America.one
He met Claude Levi-Strauss, a Frenchthink
However, since it is difficult to pursue the meaning itself, phonology andteeth
It progressed in the direction of phonetics such as phonemes. Years later, in 1973, Jakobson announced the ESSAY
DE LINGUISTIQUE GENERALE Japanese translation "General Linguistics" Misuzu Shobo /1973writing
In it, I set out the concept of semantic minimum, andmiddle
The mental description is translated into Japanese on pages 137-140. On page 139, Jakobson writesby
It states as below.
``If the study of word structure leads to a list of grammatical semantics on the one hand, and phonemes and theirroot
Sound aspects of a given language, if confined to the special inventory at the bottomof
For the sake of discussion, it is correct to say that the meaning per se does not matter.Ru
It should be, as long as the meanings are distinct from each othermosquito
, and also in the study of the conceptual aspect, the expression of meaning itselfstomach
It would be correct to say that there is no problem as long as。
But these two extremes by no means exhaust the linguistic material.na
stomach. ”
After this, we move again to the theory of phonemes, the combination of phonemes.child
Jakobson's perception of thena
stomach. It would probably be difficult to hope for further progress in the usual way.
In short, it is probably impossible to describe the semantic structure of natural language in natural language.reactor
I think Throughout the twentieth century, the internal structure of meaning itselfset
I could not pursue it as a product. If it can be pursued, it is the foundation of mathematicsovertake
My conclusion is that we will have to rely on language or mathematics itself. obeyhand
I chose the direction by mathematics. Hyperlinguistics is now a branch of logic.stomach
Because I think that the basis of it must depend on mathematics.
But I have always had a deep respect for Jakobson's work. He wrote "one
General Linguistics, Misuzu Shobo, 1973, and Linguistic Phonetology, Iwanami Shoten, 1986.long
It was on my desk for a while. And the greatest benefit from him is his semantic
minimum meaning In 2008, I wrote a paper、
From Cell to Manifold、 and gave it to him.
Let's go back to Gaishi Takeuchi's "What is a Gathering?" After reading this book for me、
Mathematics determined the direction to consider language. Mr. Gaishi TakeuchiMe
However, the importance of continuing mathematics no matter how difficult it isattack
He showed me conclusively that I should aim for the summit of Mt. In 2006 I
Growth of Word Paper called and wrote Takeuchi-sensei's name in the title.
"Mathematics Seminar" February 2018 issue "Feature: Gaishi Takeuchi and the Foundations of Mathematics" Nippon Hyoronsha
In 2018, Dr. Takeuchi's essay "Yuyake ni imi ni …", which was published inna
hit my chest In 1976, I didn't come across your book "What is a set?"na
If not, my return to mathematics may have been much delayed. Below are some of the thoughtsTo
I want to quote
“When I try to recall my encounter with mathematics now, what comes to mind is、
Most of the time it's not a finished product, and no matter how hard I try, it just doesn't turn out well.rice field
It's all about things and things I wanted to do but failed to do. When I tryMe
The first encounter with mathematics may be the result of not having encountered mathematics. ”
“The wonderful thing about encountering mathematics is that it never fades no matter how many times you encounter it.a
be. ”
Akio TANAKA
4 March 2021
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