TAKEUCHI Gaishi sent me the Road to Meaning through mathematics
My youth has been fond of mathematics since high school, but he has been frustrated over and over again, trying to keep him away, but because of his irresistible charm, he gets hurt again and loses his power. It was a day I kept feeling. However, it was the teacher's "What is a set?" Published by Kodansha as a book of Blue Bucks in 1976 that decisively overturned that setback.
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.
Tokyo Metropolitan Ome Higashi High School Former 3rd grade 4th group
BBQ party at Hinode-cho, Tokyo "Sakanaen"
Photograph backing September 11, 1999
Everyone turned 38 and it was a fun day for children to participate.
back to the topic.
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 Takeuti, 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 Gaisi Takeuti's "What is a set?" For me, after reading this book, mathematics decided to consider the language. Professor Gaisi Takeuti 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 Takeuti 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. That is. "
TANAKA Akio
4 March 2021
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