科学史と書物
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1 科学史と書物 知識 情報註釈 観測 慶應義塾大学 西脇与作 1
2 要旨 < 科学史の中での書物の変化 > 知識を探求する学問がギリシャの哲学から始ま り 科学革命によって経験科学が台頭し それ が 20 世紀に花開き 現在に至っている この科 学の歴史の中で 知識 情報 データを扱う書 物のもつ役割も変わってきた どのような役割 の変化があったのかを哲学的に眺めてみたい 2
3 基本語彙 語彙 世界 Event, Fact( 出来事 事象 事実 事態 ) State( 状態 ) Data( データ ) * 出来事は対象の組み合わせであり 対象は状態をもち 出来事や対象の状態の断片がデータである 言語 Proposition, Statement, Sentence( 命題 言明 文 ) Term, Noun( 名辞 名詞 ) * 命題の内容は出来事であり それを表現したのが言明で 文法上は文と分類される 命題は名辞の組み合わせからなり 対応する文は名詞の組み合わせである 認識 Knowledge, Information *Know Inform: 知る わかる 知らせる 伝える 3
4 知識と情報の類似構造 入力処理出力 刺激処理反応 問題処理解答? 知識の追求知る わかる A(sender) 情報の伝達 B(receiver) 4
5 知る ( わかる ) と知らせる ( 伝える ) 知る a priori X を知る A が X を知る 知ること = 知識 知らせること = 情報 X: 知識や情報の内容 データ 知らせる a posteriori X を知らせる A が X を B に知らせる B が X を知る B が X を A に知らせる A が X を知る Knowledge=statics of knowing Information=dynamics of knowing 5
6 知識と情報アプリオリな知識 アポステリオリな情報? ギリシャの哲学 中世の神学 科学革命と経験科学 科学の理論 科学的な情報 説明や予測 観測や実験によるデータ 日常生活で使う知識や情報 * 知報 6
7 経験の役割 経験の重視知識の相対化 自然化 操作化知識の記号化 形式化 数学化 表象 表現 表示 そして伝達情報伝達の仕組み 装置情報の生成 保存と変形 消去 7
8 Euclid's Elements ユークリッドの 原論 13 巻からなるギリシャ数学の集大成で紀元前 300 年頃の完成 テキストの内容は演繹的な構成に特徴があり 定義 公理 公準 定理からなっている A page from the first of more than a thousand editions of Euclid's Elements (Venice, 1482). Printing revolutionized the study of mathematics since it could mass-produce accurate calculations and diagrams. 8
9 原論 の構成 定義 公理 公準 定理 : 演繹的な証明 数学テキストの標準 知識の典型としての幾何学 ギリシャ数学の根幹となる幾何学 9
10 Definitions, Axioms, and Postulates Euclid s Definitions A point is that which has no parts. A line is that which has length without breadth. The limits of a line are points. A straight line is that which lies equally to the points on it. A surface is that which has only length and breadth. The limits of a surface are lines. Euclid s Axioms Things which are equal to the same thing are also equal to one another. If equals be added to equals, the wholes are equal. If equals be subtracted from equals, the remainders are equal. Things which coincide with one another are equal to one another. The whole is greater than the part. Euclid s Postulates A straight line can be drawn between any two points. A finite line can be extended infinitely in both directions. A circle can be drawn with any centre and any radius. All right angles are equal to each other. Given a line and a point not on the line, only one line can be drawn through the point parallel to the line. 10
11 点と線について次の問に答えなさい 点には部分がなく サイズがない サイズがない点はどうして存在できるのか 点が集まると線になるが 点をどのように集めると線になるのか また 線をどのように集めると面ができるのか 太さのない線でつくられる三角形は存在できるのか 11
12 解答 [ 解答 1] 点には部分がなく それゆえサイズがない サイズのない点をいくら集めてもサイズが生まれるはずがない サイズの生まれる原因や理由がどこにもないゆえ 延長のないものから延長は生じない 何ものも理由なしに存在しない といった形而上学の原理に従い 答えは No である [ 解答 2] 区間 [0,1] が0と1の間にある個々の点 (= 実数 ) からできているように 実数の集合は個々の実数を要素に含んでいる 点から線ができ 線は点に分解できる 線は点の集合であり 点は線の要素である 面や空間についても同様で それゆえ 答えはYesである 12
13 幾何学と原子論 点 (point) 線 (line) 面 図形 原子 (atom) 軌跡 (trajectory) 表面 物体 サイズのない点でサイズのある原子を表現し 運動の軌跡を太さのない線で表現する 幾何学的な世界が物理世界と異なると定義しながら 物理世界の表現に幾何学を使う 13
14 命題の種類についての復習 言語表現 認識の仕方 存在のあり方 分析的な文 トートロジーと定義だけからいつでも真になる文 総合的な文 分析的でない文 アプリオリな知識 経験を必要とせずにその真偽がわかる文の内容 アポステリオリな知識 真偽に経験を必要とする文の内容 必然的な出来事 偶然的な出来事 14
15 ゼノンのパラドクス 仮定 : 運動がある 運動は限りなく分割可能である アキレスはカメに追いつけない だが アキレスはカメを追い抜く これは矛盾である それゆえ 運動は存在しない というパラドクスの一般的な理解とは違って 運動を捉える分割障害を直すために 仮定 : 運動は限りなく分割可能である 運動がある アキレスはカメに追いつけない だが アキレスはカメを追い抜く これは矛盾である それゆえ 運動は限りなく分割できない と考えてみよう この論証の結論部分 運動は限りなく分割できない はどのように解釈できるのか 三角形の内角の和は180 度である の否定が 三角形の内角の和は 180 度より小さい と 三角形の内角の和は180 度より大きい の二通りに分けられるよ 15 うに 二通りの解釈が出てくる
16 < 論証の解釈 : 古典版 > < ゼノンの論証の解釈 > 仮定 : 運動は限りなく分割可能である 運動がある アキレスはカメに追いつけない だが アキレスはカメを追い抜く これは矛盾である それゆえ 運動は非可算個 (uncountable) 分割可能である < 論証の解釈 : 非古典版 > 仮定 : 運動は限りなく分割可能である 運動がある アキレスはカメに追いつけない だが アキレスはカメを追い抜く これは矛盾である それゆえ 運動は有限個 (finite) 分割可能である 16
17 形而上学と物理学の違いゼノンのパラドクスから 形而上学 ( ゼノンの解決 ) 古典物理学 否定される命題内容 運動それ自体 否定される命題内容 運動の加算分割 運動変化を否定する大胆な形而上学と 大胆な形而上学と 運動変化を研究対象にする物理学の物理学の運動を扱う扱い方の否定運動を扱う扱い方の否定とを比較すれば 両者の違いが明瞭になる 17
18 アリストテレスの形而上学 三つの特徴 註釈 commentary 論証 argument 説明 explanation * 大きなシステムでも 説明できる事柄は僅かで 予測も覚束ない Meta-physica-Physica H. Diels(ed.), , Commentaria in Aristotelem Graeca, Berlin: Reimer. Sorabji, R., 2005, The Philosophy of the Commentators AD. A Sourcebook (Volume 1: Psychology; Volume 2: Physics; Volume 3: Logic and Metaphysics), London, Ithaca, NY: Duckworth, Cornell University Press. 18
19 註釈 書物を通じた学問の在り方 : 註釈 テキスト中心 人文主義の伝統 眼光紙背に徹す 眼光紙背に透る 行間を読む read between the lines ( 書を読むとき 字句を解釈するばかりでなく 行間にひそむ深い意味までよく理解することのたとえ ) 19
20 Simplicius (c. 490-c. 560 CE) In his commentary on Aristotle's Physics Simplicius quotes at length from Eudemus's History of Geometry which is now lost. Simplicius wrote a commentary on Euclid's Elements which survives in an Arabic translation. Simplicius attempted the proof of the parallel postulate. Commentary on Aristotle's De Caelo by Simplicius. This is a14th century manuscript. 20
21 Ernst Bloch, Vorlesungen zur Philosophie der Renaissance, Suhrkamp, 1972.( ルネサンスの哲学 2005, 白水社 ) 世界書物の解読 : 自然という書物 カンパネラは自然という書物の中に 彼の三つの基本原理を探し求め その解読を試みた (p.70) ブロッホはガレリオのうちに この世界の解読の一つの極限をみいだす ガリレオは 自然という書物は数学で書かれているのであり 数学でなければ解読できないと指摘した 21
22 Mathesis Universalis( 普遍数学 ) Hypothetical universal science modeled on mathematics envisaged by Descartes and Leibniz, a kind of a unified theory about nature 22
23 ニュートン ( ) の Principia 自然哲学の数学的原理 (Principia Mathematica Philosophiae Naturalis) Newton's own copy of his Principia, with hand-written corrections for the second edition 23
24 古典的世界観 実在論 機械論 決定論 合理論 経験論 因果論 客観的知識 24
25 数学的な知識 Platonism David Hilbert ( ) 論理主義 形式主義 直観主義 公理系 形式系 記号系 形式主義とプラトン主義の数学理論の解釈 25
26 世界の数学化 単位の設定 測定 数量化 ユークリッド幾何学 デカルトの解析幾何学 解析学 確率論 統計学 点と線 : 粒子と運動 集団 : 分布と頻度 26
27 註釈から観察 実験へ 27
28 実験 観測 註釈の際の経験と実験や観測の経験 註釈するテキストと自然の中のデータ 正確な実験 観測 : 測度と測定 科学主義 実証主義 経験主義 プラグマティズム 道具主義 28
29 役割の変更 書物の役割 : 主役の研究対象から記録 報告の一手段へ 実験 観察の役割 : 脇役 道具から主役 研究の要へ 書物という窓を通じて考えられる世界 圧縮された経験を通じて観られる世界 29
30 書物と経験 読む経験 あるいは 経験を読む 書く経験 あるいは 経験を書く 他人の経験を読む 自分の経験を書く ( 記す ) 他人の知識 情報を読む ( 知る ) 自分の知識 情報を書く ( 伝える ) * 他人の経験を知る 自分の経験を感じる 30
31 演繹と経験 人文科学 存在する対象を演繹する 本質を公理化する 演繹することが科学的な営み 経験はきっかけやヒント 書物 テキストこそ重要 自然科学 表現する技術としての演繹 公理を満たすなら何ものでもよい 科学知識の表現としての演繹 演繹は表現技術 実験 観察こそが重要 31
32 文献の背後 (1)Darwin and Wallace 32
33 Darwin と Wallace の考えはよく似ていた Darwin began formulating his theory of natural selection in the late 1830s, but he went on working quietly on it for twenty years. During those years he corresponded briefly with Wallace, who was exploring the wildlife of South America and Asia. Wallace supplied Darwin with birds for his studies and decided to seek Darwin's help in publishing his own ideas on evolution. He sent Darwin his theory in 1858, which, nearly replicated Darwin's own. 33
34 Delicate arrangement Charles Lyell and Joseph Dalton Hooker arranged for both Darwin's and Wallace's theories to be presented to a meeting of the Linnaean Society in Darwin had been working on a major book on evolution and used that to develop On the Origins of Species, which was published in Wallace, on the other hand, continued his travels and focused his study on the importance of biogeography. 34
35 文献の背後 (2)Lambert A. J. Quetelet ( ) a Belgian astronomer, mathematician, statistician and sociologist. He founded and directed the Brussels Observatory and was influential in introducing statistical methods to the social sciences. 平均的人間 35
36 James Clerk Maxwell ( ) James Clerk Maxwell had been impressed by John Herschel s influential essay on Quetelet s work in the Edinburgh Review (1850). During the1870s, Maxwell introduced his gas theory using analogies from social statistics. The first point, a crucial one, was that statistical regularities of vast numbers of molecules were quite sufficient to derive thermodynamic laws relating the pressure, volume, and temperature in gases. 気体分子運動論 統計力学 36
37 Ludwig Eduard Boltzmann ( ) an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory at a time when that scientific model was still highly controversial. S=klogW ( エントロピーの公式 ) 37
38 文献の背後 (3)G. Mendel( ) He gained posthumous fame as the figurehead of the new science of genetics for his study of the inheritance of certain traits in pea plants. Mendel showed that the inheritance of these traits follows particular laws. The significance of Mendel s work was not recognized until MENDEL, G., 1866 Versuche über Pflanzen-Hybriden. Verh. Naturforsch. Ver. Brünn 4: 3 47 (first English translation in 1901, J. R. Hortic. Soc. 26: 1 32; reprinted in Experiments in Plant Hybridization. Harvard University Press, MA, 1967). 38
39 Ronald Aylmer Fisher ( ) an English statistician, evolutionary biologist, eugenicist and geneticist. He was described by Anders Hald as "a genius who almost single-handedly created the foundations for modern statistical science," and Richard Dawkins described him as "the greatest of Darwin's successors". 39
40 Mendel-Fisher Controversy ( 理論に合わないデータ 合い過ぎるデータ ) In 1936 R.A.Fisher asked the question, "Has Mendel's Work Been Rediscovered?" The query was intended to open for discussion whether someone altered the data in Gregor Mendel's classic 1866 research report on the garden pea, "Experiments in Plant-Hybridization." Fisher concluded, that the statistical counts in Mendel's paper were doctored in order to create a better intuitive fit between Mendelian expected values and observed frequencies. Fisher, R. A. (1936). Has Mendel's work been rediscovered?, Annals of Science 1:
41 文献の背後 (4) 獲得形質 Jean-Baptiste Pierre Antoine de Monet, Chevalier de la Marck ( ), known as "Lamarck", was a French naturalist. 動物がその生活の中でよく使う器官は次第に発達する 逆に 使われなければ 次第に衰え 機能を失う そこで 彼は獲得形質が子孫に伝わると考えた < 用不用説 > 41
42 Friedrich L. August Weismann ( ) ヴァイスマンは生殖質説を提唱し 多細胞生物の遺伝は生殖細胞 つまり精子や卵子によって引き起こされと主張した 彼がソーマ細胞と呼んだ体細胞は遺伝には無関係とした これはラマルクの獲得形質の遺伝に反対する考えであり セントラル ドグマと基本的に同じ考えである 42
43 Paul Kammerer ( ) Austrian biologist who studied and advocated the now abandoned Lamarckian theory of inheritance the notion that organisms may pass to their offspring characteristics they have acquired in their lifetime. Arthur Koestler, The Case of the Midwife Toad, London: Hutchinson, 1971( サンバガエルの謎 石田敏子訳 岩波現代文庫 2002.) 43
44 Trofim Denisovich Lysenko ( ) 科学と政治の混同 He rejected Mendelian genetics in favor of the hybridization theories of Ivan V. Michurin. His unorthodox experimental research in improved crop yields earned the support of Stalin. In 1940 he became director of the Institute of Genetics within the USSR's Academy of Sciences. Scientific dissent from Lysenko's theories of acquired inheritance was outlawed in 1948, and for the next several years opponents were purged from held positions, and many imprisoned. His work was officially discredited in the Soviet Union in
45 ラマルク再登場??? E. J. Steele Somatic Selection and Adaptive Evolution: On the Inheritance of Acquired Characters 2d edition, 1981 If the thesis advanced in this book can be corroborated by experiments currently being carried out in a number of laboratories around the world, it will signify an intellectual revolution and a landmark in the history of science. E. J. Steele here suggests that on the basis of his own immunological research, the theory originally put forward by Lamarck 170 years ago and subsequently rejected the notion that organisms may transmit characters acquired in their lifetimes to their offspring may in fact be right. In the new postscript to the second edition, Steele presents his latest findings and replies to the enormous body of criticism his research has engendered. 45
46 免疫寛容性の遺伝 (Soma to germ-line feedback) In the 1970s the immunologist E. Steele and colleagues, proposed a neo-lamarckian mechanism to try to explain why homologous DNA sequences from the VDJ gene regions of parent mice were found in their germ cells and seemed to persist in the offspring for a few generations. The mechanism involved the somatic selection and clonal amplification of newly acquired antibody gene sequences that were generated via somatic hyper-mutation in B-cells. The mrna products of these somatically novel genes were captured by retroviruses endogenous to the B-cells and were then transported through the blood stream where they could breach the soma-germ barrier and retrofect (revers transcribe) the newly acquired genes into the cells of the germ line. An interesting attribute of this idea is that it resembles Darwin's own theory of pangenesis, except in the soma to germ line feedback theory, pangenes are replaced with realistic retroviruses. Lamarck's Signature: how retrogenes are changing Darwin's natural selection paradigm. Edward J. Steele, Robyn A. Lindley, Robert V. Blanden. Perseus Books,
47 文献の背後 (5) Sokal affair "Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity", published in the Social Text Spring/Summer 1996 ニューヨーク大学のソーカル教授 ( 物理学 ) が上記の論文を捏造した事件で Science Wars の典型として物議を醸した 論文は 量子力学が社会的 言語的につくられたものである と主張するものだった 投稿した雑誌は学術雑誌で ポストモダンの文化研究を目的としていた ソーカルはこの雑誌の知的厳密さをテストしようと投稿し 論文の見掛けの良さ 編集者たちの思想に合致する といった点を露呈しようとした ソーカルは出版されると同時に自らの論文が捏造であることを雑誌 Linga Franca で公表した * ピルトダウン人の捏造と比較してみよ ( 情報の捏造 人骨の捏造 ) 47
48 情報と知識 情報理論 :Shannon, Mathematical Theory of Communication Claude E. Shannon: A Mathematical Theory of Communication, Bell System Technical Journal, Vol. 27, pp , , Claude E. Shannon and Warren Weaver: The Mathematical Theory of Communication. The University of Illinois Press, Urbana, Illinois, 情報量という単位 : 情報の数量化 知る と 知らせる や 伝える 知識 (justified true belief) の自然化 : その第一歩が知識の情報化 48
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