INFLUENTIAL
Book
1.
Blaise Pascal
1.
Blaise Pascal
PASCAL, Blaise
『Pansees』 A. J. Krailsheimer PENGUIN BOOKS
1966年
Macro Time and Micro Time
TANAKA Akio
24 July 2013
1.
Through natural language, in human being, occurred the electrical signal
by eye or ear. These complex situations are beyond this paper's limits.
2.
Language is a physical object as signal and its transmission. At this
circumstances, language must be recognised to be the existence that has
finite time.
3.
An apple on the desk gradually becomes rotten by passing the time very
after the crop in the orchard. #0
4.
Like an apple, language has passing physical time in oneself.
5.
Language is metamorphosed by the time progressing. #1
6.
Language includes the outer world from human being to universe. At this
declaration, I recall Blaise Pascal's Pensées. XXXIII. PROOFS OF JESUS
CHRIST 308 The infinite distance between body and mind symbolizes the
infinitely more infinite distance between mind and charity, for charity is
supernatural. (Translated by A.J. Krailsheimer, 1966) #2
7.
Language's time goes freely from the present to the future or the present
to the past. #3
8.
Language symbolises the time from finiteness to infinity. #4
9.
Human being recognises this vast language world perfectly. #5
References
#0
August 3, 2012 / Sekinan Research Field of Language
#1
/ sekinanlogos
#2
PASCAL PENSÉES. Translated with an introduction by A.J. Krailsheimer.
PENGUIN BOOKS 1966.
#3
Escalator Language Theory / December 16, 2006 / Sekinan Research
Field of Language
#4
February 1, 2009 / sekinanlogos
#5
/January 9, 2009 / sekinanlogos
Read more: ![]()
https://srfl-paper.webnode.com/news/macro-time-and-
micro-time/
2.
Ludwig Wittgenstein
2.
Ludwig Wittgenstein
WITTGENSTEIN, Ludwig
『Tractatus Logico-Philosophicus』 C. K. Ogden Translated DOVER
1999年
For WITTGENSTEIN Ludwig Revised
Position of Language
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 Universals6 will be shown by the description of
mathematics.
[References]
1 . Quantized Language
2 . Meaning minimum
3 . Mirror language
4 . Mirror symmetry
Language Theory
5 . Language universals
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
Read more: ![]()
https://geometrization-
language.webnode.com/products/for-wittgenstein-revised-position-
of-language/
Citation from Ludwig Wittgenstein
TRACTATUS LOGICO-PHILOSOPHICUS Translated by C. K. Ogden
Dover edition
Text is lined up according to the order of citation at the essay, ![]()
The Time
of Wittgenstein
6.521
The solution of the problem of life is seen in the vanishing of this problem.
(Is not this the reason why men to whom after long doubting the sense of
life became clear, could not then say wherein this sense consisted?)
6.432
How the world is, is completely indifferent for what is higher. God does
not reveal himself in the world.
6.35
Although the spots in our picture are geometrical figures, geometry can
evidently nothing about their actual form and position. But the network is
purely geometrical, and all its properties can be given a priori.
Laws, like the law of causation, etc., treat of the network and not of what
the network describes.
6.54
My propositions are elucidatory in this way: he who understands me
finally recognizes them as senseless, when he has climbed out through
them, on them, over them. (He must so to speak throw away the ladder,
after he has climbed up on it.)
He must surmount these propositions; then he sees the world rightly.
PUBLISHER'S NOTE by DOVER PUBLICATIONS. INC.
This translation of the German work that originally appeared in Ostwald's
Amalen der Natur-philosophie, final number (1921), was carefully revised
by the author himself. In addition, the philosopher and mathematician
Frank P. Ramsay assisted C. K. Ogden with the translation.
Tokyo
February 7, 2012
The Time of Wittgenstein
There surely exists the time of ![]()
Wittgenstein for me.
That time about in my age 30s, in the middle of 1970s.
One may aware of the kernel of the problem after almost all the hardships
were gone and the problem is going under pursuing in the daily work for
oneself, as Wittgenstein wrote at ![]()
6.521 in TRACTATUS LOGICO-
PHILOSOPHICUS.
Wittgenstein wrote on language immanently at least in TRACTATUS.
He also said in TRACTATUS ![]()
6.432 that how world exists does not care from
the higher dimensions.
I also wanted to write on language from the immanent side in language.
But I had not any pursuing method for writing on language at that time,
only remaining set theory typically presented by ![]()
Bourbaki that some
translations were surely on my desk.
Set theory was enough fascinating at the time, but it did not give me any
relative and constructive situations on language or widely on the world. It
was isolated and non-relative for writing on language. I wanted the bond
of the world.
Now I have geometry for which the world can be bonded enough tightly.
In 1970s I was never aware of the existence of geometry by myself,
probably not being influenced from Wittgenstein's ![]()
6.35 in TRACTATUS,
Geometry absolutely tell nothing on how the figure is and where the figure
situated.
So I had remain silently in the days not being able to write on the theme,
the basic essence of language. Then I never knew the object on language,
language universals that was taught from ![]()
CHINO Eiichi later in 1980s.
CHINO showed me the paper of Sergej Karcevskij, ![]()
Du dualisme
asymétrique du singe linguistique. The theme determined my remain life
hereafter. CHINO was the true teacher of my study.
Wittgenstein wrote at the last ![]()
6.54 of TRACTATUS that his some
propositions must be abandoned. I began to go through the wood of hard
theme of language universals by mathematics especially using geometry.
About what can be told to, I never must be silent.
Reference
Tokyo
January 20, 2012
3.
William Shakespeare
3.
William Shakespeare
SHAKESPEARE, William
『WILLIAM SHAKESPEARE COMPLETE WORKS COMPACT EDITION』
Oxford University Press
1988年
Henry the Fourth, For SAEKI Shizuto and Shakespeare
In my mid-20s, I had worked at a high school in Tachikawa, Tokyo. One
day, after teaching class, I waited the colleague at the physics study room,
who was two year older than me and the best friend at the school. At the
room he was absent and I waited sitting the chair and began to read the
bringing book for the time if he was absent.
The book was the compact-sized complete works of Shakespeare. In those
days, I had time to time to time read Shakespeare for researching what
was poetry or verse's essence. I had strongly wanted what was verse or
how verse differs from prose . But never I had grasped the tail of it.
Several papers and books were already read at that time. Some poets' and
researchers' writings were also looked through. But I had perfectly never
made sense of it on verse. It was the very precious theme for me on the
way studying language. For example, what is the rhyme of verse or what
difference occurs between verse and prose? So I decided to read
Shakespeare which seemed the most typical verse work in the world.
When I was reading Shakespeare on the laboratory-work desk in my
friend study room, I suddenly understood perfectly the essence of verse
by the beginning of the play, King Henry the Fourth's saying. It became
one of the biggest pivotal points of my life.
The complete works was bought at old book store at Kanda, Tokyo. Its
jacket was dark red and very light in weight. Probably the book were so old
and enough dried up. I liked its classical binding.
On the colleague returning the room, my mind was swaying for a while
with my happy finding. The friend's name was SAEKI Shizuto who always
taught me the many wisdom related with life and study by his sensitive
talent to nature and universe. He was teaching geology in the high school.
Tokyo
14 December 2012
20 July 2015 Revised
Read more: ![]()
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for-saeki-shizuto-and-shakespeare/
4.
Nicolas Bourbaki
4.
Nocolas Bourbaki
ニコラス・ブルバキ
『ブルバキ 数学原論 集合論 要約』 前原昭二訳 東京図書
1968年
The Time of Language
Ode to The Early Bourbaki To Grothendieck
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,
both historical and modern.
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 Eiichi
First met in 1969, again in 1979. ![]()
Fortuitous Meeting
4. ****Sergej Karcevskij
Note on Karcevskij's theme. ![]()
Note for KARCEVSKIJ Sergej's "Du dualisme
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
[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 and
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.
1.![]()
On Time Property Inherent in Characters
2.![]()
Zoho site
3.![]()
sekinanlogos
4.![]()
Complex Manifold Deformation Theory
5.![]()
Arithmetic geometry
[Note 2 2 May 2019]
5 years passed from I wrote Note at October 2014.
The situation for the research changed rather largely.
I and wife became older and I become 72 years old this summer while the
both have illness.
We often go to the hospital for the treatment for what I often think that all
the illness are probably on the nerves which make persistent flows in our
body, which inevitably need energy for fluidity.
At these circumstances I began to write a new paper titled What is signal?
The existence that generates language, Original title, What is signal? A
mathematical model of nerve.
The text is the next.
21-november-2018-23-april-2019/
So far I have thought of language at the point from language universals
which are the most fantastic theme for me. But illness and its base nerve
showed me the new site of language that is the real base of language. It
was the signal which has energy and flows and hatch language in the
human being.
Now I stand back at the manuscript written in 2003 at Hakuba, Nagano,
Japan titled Manuscript of Quantum Theory for Language. The text is the
next.
theory-for-language-with-preface-note-and-note-2-2003-2018/
Quantum is the real kernel of my research, by which signal and language
may be unified being constructed for human being.
Tokyo
2 May 2019
Sekinan Library
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note-2-added/
5.
TAKEUCHI Gaishi
5.
TAKEUCHI Gaishi
竹内外史
『数学セミナー』2018年2月号
特集 竹内外史と数学基礎論
日本評論社 2018年
TAKEUCHI Gaishi sent me the Road to Meaning through mathematics
私の青春は、高校時代から数学がもっとも好きであったが幾度となく挫折を繰り
返し、もう二度と近づかないようにしようとおもいながら、その抗いがたい魅力
のゆえにふたたび近づいて傷つき、みずからの非力を感じ続けた日々であった。
しかしその挫折を決定的に覆したのが、1976年に講談社からブルーバックス の
一冊として刊行された先生の『集合とはなにか』であった。
この本は、集合という数学においてもっとも基礎となる概念を、その起点となっ
たカントールから説き起こし、現代集合論の直近に至るまでを、ほんとうにわか
りやすく述べたものである。しかしわかりやすいという表現には注釈をつける必
要があるかもしれない。
私は二校目の高校国語科教師として、1976年から1978年までの3年間を東京都青
梅市に所在した都立青梅東高校で過ごしたが、そこで一人の若き数学教師と出
会った。彼は東京理科大で修士課程を経て理科大の講師として数学を教えていた
が、みずからの能力の限界を感じ、高校教員として再出発する道を選び青梅東高
校に赴任してきた。彼は私に、もし能力があれば京大の博士課程を受けてみよう
かと考えていたが、その力はないとおもったので現在に至ったと、私に語ってく
れた。そうした話の中で、私が竹内外史の本のことを伝えると、それはおもしろ
そうだから二人で勉強してみないかと、私に持ちかけてくれたので、放課後の二
人の空き時間に黒板のある部屋で、彼が先生となり私が学生となって、本の最初
から、問題となりそうなところを二人で逐一検討していった。
この本の中心の一つは、数字の１から9が集合論によってどのように生成されて
いくかを述べるところにあった。私はその一部に自身ではどうしても理解できな
いところがあり、それを黒板を背にした先生である彼に問い尋ねた。彼はしばら
く考えてから、その解決方法を黒板に書こうとしたが逡巡し、「これは私にはわ
からない」と答えた。大学の講師であった彼がわからないことが、私にわかるは
ずはなかった。彼は「難しい」と言ってこの日の勉強は終わり、結局それがこの
集合論の最後の勉強会となった。
彼とはそれからも、いろいろな話題で話が弾んだ。私の方が少し年上であったの
で、彼は常に礼儀正しかった。もっと普通に話してよ、と私が伝えても彼はその
姿勢を崩さなかった。1979年3月で、私は同校から府中市にある都立農業高校の
定時制勤務に替わり、4月から昼間は和光の専攻科生となった。彼もまもなく八
王子市にある有数の進学校であった都立高校に転勤し、ある日の夜、彼と久しぶ
りに電車で出会った。彼は私に国立大学の言語学科の状況について尋ね、私はわ
かる範囲のことを彼に伝えた。彼は、私がその後も言語の勉強を続けているとお
もっていたことは確かだった。
東京都立青梅東高校 旧3年4組 東京都日の出町「さかな園」でのバーベキュー
会
写真の裏書 1999年9月11日
みな38歳になり子どもたちも参加してたのしい一日となった
話を戻そう。集合論による数字の1から9までの生成は、確かに当時の私では理解
不可能なところを含んでいた。数学が専攻の彼であっても、1970年代末の集合
論の状況では、そこが専門でない限り理解はかなり難しかったとおもわれた。私
ははるか後年の2008年になって、Generative Theorem というPaper を書き、
この長年の宿題に応えた。私はこのとき、von Neumann Algebra フォン・ノ
イマン代数、を必要とした。この Paper は少し長いので、以下にLink 先を示す
こととする。一緒に勉強した彼とはすでに久しく会っていないが、どうしている
だろうか。
この1から9までの生成には、別の憶い出がある。幾度か書いてきたが繰り返す
と、和光での研究生時代、構造言語学を講じていらした千野栄一先生との会話で
ある。ある日の講義終了後、入口付近でふと先生と会話することがあった。先生
は私に、今何を勉強しているかと尋ねられた。私は咄嗟に、傾倒していた竹内外
史先生のことをおもい、簡潔に、意味の内部構造を、例えば１から９までがどの
ように生成されるかなどと考えていますと答えると、先生は真剣に、「そんなこ
とはやめろ、おれたちが考えることではない、それは Wittgenstein などが考え
ることだ」と、怒るようにして言った。私は一瞬先生の反応に驚いたが、その場
では「わかりました」とお応えした。
1920年代のプラハでプラハ言語学サークル Linguistic Circle of Prague が結成
され、そこでSergej Karcevskij が「言語記号の非対称的二重性」を書き、言語
における意味の大局的な構造に対する予想を示したが、その後、言語における意
味構造の追求は遂になされなかった。言語において最も重要なことの一つである
にもかかわらず、意味とは何かを追究することはそれほど困難なことであった。
第二次大戦後、アメリカにおいて Roman Jakobson が、構想人類学を構築しつ
つあったフランスの Claude Levi-Strauss と出会い、新しい構造言語学を構想
し花開くこととなるが、そこでも意味そのものの追求は困難なゆえに音韻または
音素等の音声学的な方向へと進んでいった。後年の1973年、Jakobson はESSAY
DE LINGUISTIQUE GENERALE 邦訳『一般言語学』みすず書房・1973年を著
わし、その中で semantic minimum 意味最小体という概念を打ち出し、その中
心的な記述は邦訳で137頁から140頁であるが、139頁において、Jakobson は以
下のように述べている。
「もし語の構造の研究が一方では文法的意味の一覧表に、他方では音素とその根
底にある弁別特製の目録に限られていたとすれば、ある所与の言語の音の側面の
検討のためには、意味それ自体は、問題にならないと言っても正しいことになる
はずである、ー 意味は互いにはっきり区別されてさえいればいいのいであるか
ら、また、概念の側面の研究においても、意味の表現形そのものは、意味を互い
に区別して表わすかぎり、問題にならないと言って正しいことになるであろう。
しかし、これらの両最極端が、言語学的素材を究め尽すわけではけっしてな
い。」
と述べ、このあとでは、音素の結合という、音素論へとふたたび移ってゆく。こ
のときの Jakobson の認識では、意味そのものの内部構造には踏み込んでいな
い。通常の方法ではこれ以上の進展を望むのは多分困難であろう。
要約すれば自然言語の意味の構造を、自然言語で述べることは多分不可能であろ
うと私は考える。20世紀を通して、意味そのものの内部構造は、明確な論理の集
積としては追究できなかった。もし追究できるとしたら、それは数学基礎論の超
言語か数学そのものに依るしかないであろうというのが私の結論である。従って
私は数学による方向を選んだ。超言語は現在では、論理学の一分野となってい
て、私はその根底はやはり数学に依るしかないとおもうからである。
しかし私は、常にJakobson の業績に深い敬意を払ってきた。彼が著わした『一
般言語学』みすず書房・1973年と『言語音形論』岩波書店 1986年は、かなり長
い間、私の机辺にあった。そして彼からの最も大きな恩恵は、彼の semantic
minimum 意味最小体に強い影響を受けて、2008年に私は一篇の Paper、
From Cell to Manifold、 をまとめて、彼にささげた。
ふたたび竹内外史の『集合とはなにか』に戻ろう。私にとってはこの本の読後、
数学によって言語を検討しようという方向が決定された。竹内外史先生は、私
が、以後どんなに困難であっても数学を続けることの大切さを、意味という難攻
の山頂を目指すことを、私に決定的に示してくださった。私は2006年に
Growth of Word という Paper を書き、表題に竹内先生のお名前を記した。
『数学セミナー』2018年2月号 特集 竹内外史と数学基礎論 日本評論社
2018年、 に収載された竹内先生の随想「夕焼けにも似て・・・・・」は今もな
お私の胸を打つ。1976年に先生の著『集合とはなにか』と出会わなっかったな
らば、私の数学への復帰はずっと遅れたかもしれない。その随想の一部を以下に
引用したい。
「いま数学との出会いについて思い出そうとすると、思い出に出てくるものは、
たいていは何か出来上がったものではなくて、どう頑張っても旨くできなかった
ことや、やりたいと思いながらやりそびれたことばかりである。してみると、私
の数学との出会いは、数学と出会わなかったということになるかも知れない。」
「数学との出会いのすばらしさは、何度出会ってもその魅力が薄れないことであ
る。」
TANAKA Akio
4 March 2021
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