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モナド

ギリシア語のモナス monas(単位,一なるもの)に由来する概念。単子と訳される。古代ではピタゴ

ラス学派やプラトンによって用いられ,近世ではニコラウス・クサヌスやブルーノが,モナドを世界を

構成する個体的な単純者,世界の多様を映す一者としてとらえた。これらの先駆思想を継承して,

ライプニッツは彼の主著《モナドロジー》において独自の単子論的形而上学思想を説いた。ライプニ

ッツは物理的原子論を批判して,宇宙を構成する最も単純な要素すなわち自然の真のアトムは,不

可分で空間的拡がりをもたぬ単純者であり,いわば〈形而上学的点〉とも言うべきものであると主張

した。モナドは意識的もしくは無意識的知覚を有する魂に類似したものであり,それぞれに固有の

観点から宇宙のいっさいの事象を表出する個体的な実体である。しかしおのおののモナドは相互

に他から独立であり,モナドはそこから物が入ったり出たりする〈窓〉をもたない(無窓説)。モナドの

作用は自己の内的原理のみにもとづいて展開され,モナド相互の間には予定調和の原理に従う観

念的関係しか存しない。ライプニッツによれば宇宙においていっさいは生命的はたらきによってみ

たされており,物質のどのような微細な部分にも生命がある。モナドはかかる宇宙の生命的活動

の原理であり,神の超自然的はたらきによってのほかは不生不滅である。誕生は生命の展開(現勢

化)であり,死は生命の収縮(潜勢化)にすぎない。《モナドロジー》のこのような形而上学思想に含ま

れる最大の困難は,真の実在である不可分の単純者(モナド)からいかにしてわれわれが経験する

物体的合成体が形成されるか,合成体は見かけの存在にすぎぬか,またはそこには真の統一が

あるか,等の問題であった。ライプニッツは〈実体的紐帯〉の説によってこれに答えようとしたが,そ

れは十分説得的なものではなく,今日まで種々の論議を呼び起こしている。モナドの概念はその後

多くの思想家によって用いられ,例えばルヌービエの《新モナドロジー》(1899),M. ネドンセルの

〈モナド的相互人格性〉の思想,フッサールの〈モナド的相互主観性〉の説等に見ることができる。

増永 洋三

(c) 1998 Hitachi Digital Heibonsha, All rights reserved.


ライプニッツ

ドイツの哲学者,数学者。歴史学,法学,神学などについても重要な業績を残し,政治家,外交官など実務家としても活躍した。ライプチヒに生まれ,ライプチヒ大学で哲学を,イェーナ大学で数学を,アルトドルフ大学で法律を学んだ後,マインツ侯国の前宰相ボイネブルク Johann Christianvon Boyneburg(1622‐72)と相識り,1670年侯国の法律顧問官となる。侯国の外交使節として72年以降パリに滞在したが,このパリ派遣は,彼自身の起草になる〈エジプト計画〉(フランスの対外拡張政策,特にオランダ侵攻を阻止し,エジプト征服を勧めることによって,ひいてはドイツの安全を図ろうとするもの)を,ルイ14世に奏上することが直接の目的であった。この試みは実現しなかったが,彼はフランスの学者グループに仲間入りし,またイギリスにも渡り,R. ボイルを知るなどして刺激を受けた。オランダでのスピノザとの会見を経て,76年末ドイツに帰国,以後生涯変わることなくハノーファー家に司書官,顧問官として仕える。その間,ハノーファー家の系譜の歴史学的探求,そのためのイタリア旅行,ヨーロッパ各地でのアカデミー設立(自身1700年設立のベルリンのアカデミーの初代総裁となった),さらにカトリックとプロテスタント両教会の間の融和統一等の仕事に尽力する。そ

の膨大な著作の大半は,現在においても未刊の断片的草稿のままに,ハノーファーの〈ライプニッツ文庫〉に日の目を見ずに保存されている。刊行されたもののうちまとまりのある主要な著作は,《形而上学叙説》(1686),《新人間悟性論》(1704),《弁神論》(1710),《単子論》(1714)等である。


[哲学]

ライプニッツ哲学の根本的特質は普遍的調和(予定調和)の思想と個体主義にある。論理・認識思想に関しては,思考のアルファベットと結合法の思想にもとづく普遍学の理念,および認識の経験論的理説と合理論的理説を独自に統一した表出説が重要である。自然学思想ではライプニッツに特有の力動的な活力の概念の発見(力動説)のうちに,デカルトの静力学的自然学に取って代わるべき新たな力学説の成立を見ることができよう。これらを基礎として単子論的形而上学思想(モナド)が確立されるに至った。ライプニッツが物体の形相的要素とみなす根源的力は,物質における運動の力動的原理であり,自然現象の連続性と多様性の条件である。すなわち宇宙が秩序も統一も欠く混沌ではなく,また多様な変化の認められる余地のない同質的集塊でないために,物質のうちに根源的力がなければならず,実体の活動が多様な変化の現象を可能にするのでなければならない。ライプニッツは原子論(アトミズム)の批判によっても同一の結論に達した。真に実在するものは不可分であり不滅である。真に〈一なる〉存在でないものは,真に〈存在する〉ものではない。同質的で無限に可分的な物質的アトムは理性に反する。実体の不可分性は形相の不可分性である。それゆえ形相的アトムは魂に類似したものとして把握されうる。すなわち生命,エンテレケイア,魂が物質の最小の部分のうちにも存在するのである。この意味でライプニッツの形而上学説は汎心論もしくは汎生命論とも呼ばれうる。なお,彼の哲学はライプニッツ=ウォルフ学派により,一面的にではあるが継承された。増永 洋三


[数学,自然学]

ライプニッツは,大学時代にはほんの初等的な幾何学・算術を学んだにすぎなかったが,学位論文《結合法論考》(執筆1666)における普遍記号法の理念は後年,数学・論理学の革新を計る際開花することになる。数学における能力はパリ滞在期に大きく飛躍する。当時アカデミー・デ・シアンスの中心的科学者であったホイヘンスやローヤル・ソサエティの知識人たちによってヨーロッパの第一線の知的世界に導かれたためである。最初の数学の天分は計算機作製において示された。この計算機は加減乗除の四則演算が可能となるように計画されたものであった。また

73年以降,求積法・接線法の研究を急速に発展させ,手初めにパスカルの無限小幾何学についての著作から示唆を受けて円の算術的求積に成功し,円周率の無限級数展開に関する〈ライプニッツ公式〉(?I/4=1-??+?”-??+……)を得た。さまざまな求積問題・逆接線問題にとり組む中から,76年秋までには今日の微分記号 d や積分記号∫を用いる微分積分法の概念に到達したものと思われる。この成果は84年から徐々に公表された。ライプニッツ的微分積分法の特質はすぐれた記号法によった点にある。今日の位相幾何学の考え方にも通ずる《位置解析について》の書簡をホイヘンスあてにつづっている(1679)が,ホイヘンスはこれに好意的でなかった。このように同時代人は必ずしも代数的普遍記号法の理念を歓迎したわけではない。ニュートンなどイギリスの数学者たちがライプニッツ的数学を受け入れたがらなかった理由の一つも,このような記号法的特質のためであった。だが,96年のロピタルの微分法の教科書《曲線の理解のための無限小解析》がライプニッツ思想にもとづいて書かれたのをかわきりに,ベルヌーイ兄弟,バリニョン Pierre Varignon(1654‐1722)など大陸の数学者たちはライプニッツ的記号数学を普及させた。ライプニッツ的形式

主義は論理学の変革にも力を及ぼし,論理学は論理計算に改変させられた。この試みは19世紀末以降,数学的論理学者たちによって再評価された。彼はまた二進法,行列式の考えにも到達していたことが今日ではわかっている。

自然学においては,デカルト学派が運動量(質量と速度の積 mv)保存の法則を動力学の世界にもち込もうとしたのに反対し,保存されるのは〈活力〉(mv2)であると主張,活力論争をひき起こした。デカルトと同じく機械論的哲学を基本的には支持しながらも,独断的な機械論には反対であったものと思われる。ニュートン学派の S. クラークとも論争し,ニュートン的神,絶対時空概念を批判した。彼の相対的時空論は現代の相対性理論的観点から高く評価されている。ライプニッツ哲学はカント以降ほとんど見捨てられたものの,以上のような個々の科学的言明は後代に大きな影響を及

ぼしたわけである。佐々木 力(c) 1998 Hitachi Digital Heibonsha, All rights reserved.


THE MONADOLOGY

http://www.rbjones.com/rbjpub/philos/classics/leibniz/monad.htm

by Gottfried Wilhelm Leibniz

translated by Robert Latta

1. The Monad, of which we shall here speak, is nothing but a simple substance, which enters into compounds. By 'simple' is meant 'without parts.' (Theod. 10.)

2. And there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregatum of simple things.

3. Now where there are no parts, there can be neither extension nor form [figure] nor divisibility. These Monads are the real atoms of nature and, in a word, the elements of things.

4. No dissolution of these elements need be feared, and there is no conceivable way in which a simple substance can be destroyed by natural means. (Theod. 89.)

5. For the same reason there is no conceivable way in which a simple substance can come into being by natural means, since it cannot be formed by the combination of parts [composition].

6. Thus it may be said that a Monad can only come into being or come to an end all at once; that is to say, it can come into being only by creation and come to an end only by annihilation, while that which is compound comes into being or comes to an end by parts.

7. Further, there is no way of explaining how a Monad can be altered in quality or internally changed by any other created thing; since it is impossible to change the place of anything in it or to conceive in it any internal motion which could be produced, directed, increased or diminished therein, although all this is possible in the case of compounds, in which there are changes among the parts. The Monads have no windows, through which anything could come in or go out. Accidents cannot separate themselves from substances nor go about outside of them, as the 'sensible species' of the Scholastics used to do. Thus neither substance nor accident can come into a Monad from outside.

8. Yet the Monads must have some qualities, otherwise they would not even be existing things. And if simple substances did not differ in quality, there would be absolutely no means of perceiving any change in things. For what is in the compound can come only from the simple elements it contains, and the Monads, if they had no qualities, would be indistinguishable from one another, since they do not differ in quantity. Consequently, space being a plenum, each part of space would always receive, in any motion, exactly the equivalent of what it already had, and no one state of things would be discernible from another.

9. Indeed, each Monad must be different from every other. For in nature there are never two beings which are perfectly alike and in which it is not possible to find an internal difference, or at least a difference founded upon an intrinsic quality [denomination].

10. I assume also as admitted that every created being, and consequently the created Monad, is subject to change, and further that this change is continuous in each.

11. It follows from what has just been said, that the natural changes of the Monads come from an internal principle, since an external cause can have no influence upon their inner being. (Theod. 396, 400.)

12. But, besides the principle of the change, there must be a particular series of changes [un detail de ce qui change], which constitutes, so to speak, the specific nature and variety of the simple substances.

13. This particular series of changes should involve a multiplicity in the unit [unite] or in that which is simple. For, as every natural change takes place gradually, something changes and something remains unchanged; and consequently a simple substance must be affected and related in many ways, although it has no parts.

14. The passing condition, which involves and represents a multiplicity in the unit [unite] or in the simple substance, is nothing but what is called Perception, which is to be distinguished from Apperception or Consciousness, as will afterwards appear. In this matter the Cartesian view is extremely defective, for it treats as non-existent those perceptions of which we are not consciously aware. This has also led them to believe that minds [esprits] alone are Monads, and that there are no souls of animals nor other Entelechies. Thus, like the crowd, they have failed to distinguish between a prolonged unconsciousness and absolute death, which has made them fall again into the Scholastic prejudice of souls entirely separate [from bodies], and has even confirmed ill-balanced minds in the opinion that souls are mortal.

15. The activity of the internal principle which produces change or passage from one perception to another may be called Appetition. It is true that desire [l'appetit] cannot always fully attain to the whole perception at which it aims, but it always obtains some of it and attains to new perceptions.

16. We have in ourselves experience of a multiplicity in simple substance, when we find that the least thought of which we are conscious involves variety in its object. Thus all those who admit that the soul is a simple substance should admit this multiplicity in the Monad; and M. Bayle ought not to have found any difficulty in this, as he has done in his Dictionary, article 'Rorarius.'

17. Moreover, it must be confessed that perception and that which depends upon it are inexplicable on mechanical grounds, that is to say, by means of figures and motions. And supposing there were a machine, so constructed as to think, feel, and have perception, it might be conceived as increased in size, while keeping the same proportions, so that one might go into it as into a mill. That being so, we should, on examining its interior, find only parts which work one upon another, and never anything by which to explain a perception. Thus it is in a simple substance, and not in a compound or in a machine, that perception must be sought for. Further, nothing but this (namely, perceptions and their changes) can be found in a simple substance. It is also in this alone that all the internal activities of simple substances can consist. (Theod. Pref. [E. 474; G. vi. 37].)

18. All simple substances or created Monads might be called Entelechies, for they have in them a certain perfection (echousi to enteles); they have a certain self-sufficiency (autarkeia) which makes them the sources of their internal activities and, so to speak, incorporeal automata. (Theod. 87.)

19. If we are to give the name of Soul to everything which has perceptions and desires [appetits] in the general sense which I have explained, then all simple substances or created Monads might be called souls; but as feeling [le sentiment] is something more than a bare perception, I think it right that the general name of Monads or Entelechies should suffice for simple substances which have perception only, and that the name of Souls should be given only to those in which perception is more distinct, and is accompanied by memory.

20. For we experience in ourselves a condition in which we remember nothing and have no distinguishable perception; as when we fall into a swoon or when we are overcome with a profound dreamless sleep. In this state the soul does not perceptibly differ from a bare Monad; but as this state is not lasting, and the soul comes out of it, the soul is something more than a bare Monad. (Theod. 64.)

21. And it does not follow that in this state the simple substance is without any perception. That, indeed, cannot be, for the reasons already given; for it cannot perish, and it cannot continue to exist without being affected in some way, and this affection is nothing but its perception. But when there is a great multitude of little perceptions, in which there is nothing distinct, one is stunned; as when one turns continuously round in the same way several times in succession, whence comes a giddiness which may make us swoon, and which keeps us from distinguishing anything. Death can for a time put animals into this condition.

22. And as every present state of a simple substance is naturally a consequence of its preceding state, in such a way that its present is big with its future; (Theod. 350.)

23. And as, on waking from stupor, we are conscious of our perceptions, we must have had perceptions immediately before we awoke, although we were not at all conscious of them; for one perception can in a natural way come only from another perception, as a motion can in a natural way come only from a motion. (Theod. 401-403.)

24. It thus appears that if we had in our perceptions nothing marked and, so to speak, striking and highly-flavoured, we should always be in a state of stupor. And this is the state in which the bare Monads are.

25. We see also that nature has given heightened perceptions to animals, from the care she has taken to provide them with organs, which collect numerous rays of light, or numerous undulations of the air, in order, by uniting them, to make them have greater effect. Something similar to this takes place in smell, in taste and in touch, and perhaps in a number of other senses, which are unknown to us. And I will explain presently how that which takes place in the soul represents what happens in the bodily organs.

26. Memory provides the soul with a kind of consecutiveness, which resembles [imite] reason, but which is to be distinguished from it. Thus we see that when animals have a perception of something which strikes them and of which they have formerly had a similar perception, they are led, by means of representation in their memory, to expect what was combined with the thing in this previous perception, and they come to have feelings similar to those they had on the former occasion. For instance, when a stick is shown to dogs, they remember the pain it has caused them, and howl and run away. (Theod. Discours de la Conformite, &c., ss. 65.)

27. And the strength of the mental image which impresses and moves them comes either from the magnitude or the number of the preceding perceptions. For often a strong impression produces all at once the same effect as a long-formed habit, or as many and oft-repeated ordinary perceptions.

28. In so far as the concatenation of their perceptions is due to the principle of memory alone, men act like the lower animals, resembling the empirical physicians, whose methods are those of mere practice without theory. Indeed, in three-fourths of our actions we are nothing but empirics. For instance, when we expect that there will be daylight to-morrow, we do so empirically, because it has always so happened until now. It is only the astronomer who thinks it on rational grounds.

29. But it is the knowledge of necessary and eternal truths that distinguishes us from the mere animals and gives us Reason and the sciences, raising us to the knowledge of ourselves and of God. And it is this in us that is called the rational soul or mind [esprit].

30. It is also through the knowledge of necessary truths, and through their abstract expression, that we rise to acts of reflexion, which make us think of what is called I, and observe that this or that is within us: and thus, thinking of ourselves, we think of being, of substance, of the simple and the compound, of the immaterial, and of God Himself, conceiving that what is limited in us is in Him without limits. And these acts of reflexion furnish the chief objects of our reasonings. (Theod. Pref. [E. 469; G. vi. 27].)

31. Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false; (Theod. 44, 169.)

32. And that of sufficient reason, in virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us. (Theod. 44, 196.)

33. There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible: truths of fact are contingent and their opposite is possible. When a truth is necessary, its reason can be found by analysis, resolving it into more simple ideas and truths, until we come to those which are primary. (Theod. 170, 174, 189, 280-282, 367. Abrege, Object. 3.)

34. It is thus that in Mathematics speculative Theorems and practical Canons are reduced by analysis to Definitions, Axioms and Postulates.

35. In short, there are simple ideas, of which no definition can be given; there are also axioms and postulates, in a word, primary principles, which cannot be proved, and indeed have no need of proof; and these are identical propositions, whose opposite involves an express contradiction. (Theod. 36, 37, 44, 45, 49, 52, 121-122, 337, 340-344.)

36. But there must also be a sufficient reason for contingent truths or truths of fact, that is to say, for the sequence or connexion of the things which are dispersed throughout the universe of created beings, in which the analyzing into particular reasons might go on into endless detail, because of the immense variety of things in nature and the infinite division of bodies. There is an infinity of present and past forms and motions which go to make up the efficient cause of my present writing; and there is an infinity of minute tendencies and dispositions of my soul, which go to make its final cause.

37. And as all this detail again involves other prior or more detailed contingent things, each of which still needs a similar analysis to yield its reason, we are no further forward: and the sufficient or final reason must be outside of the sequence or series of particular contingent things, however infinite this series may be.

38. Thus the final reason of things must be in a necessary substance, in which the variety of particular changes exists only eminently, as in its source; and this substance we call God. (Theod. 7.)

39. Now as this substance is a sufficient reason of all this variety of particulars, which are also connected together throughout; there is only one God, and this God is sufficient.

40. We may also hold that this supreme substance, which is unique, universal and necessary, nothing outside of it being independent of it,- this substance, which is a pure sequence of possible being, must be illimitable and must contain as much reality as is possible.

41. Whence it follows that God is absolutely perfect; for perfection is nothing but amount of positive reality, in the strict sense, leaving out of account the limits or bounds in things which are limited. And where there are no bounds, that is to say in God, perfection is absolutely infinite. (Theod. 22, Pref. [E. 469 a; G. vi. 27].)

42. It follows also that created beings derive their perfections from the influence of God, but that their imperfections come from their own nature, which is incapable of being without limits. For it is in this that they differ from God. An instance of this original imperfection of created beings may be seen in the natural inertia of bodies. (Theod. 20, 27-30, 153, 167, 377 sqq.)

43. It is farther true that in God there is not only the source of existences but also that of essences, in so far as they are real, that is to say, the source of what is real in the possible. For the understanding of God is the region of eternal truths or of the ideas on which they depend, and without Him there would be nothing real in the possibilities of things, and not only would there be nothing in existence, but nothing would even be possible. (Theod. 20.)

44. For if there is a reality in essences or possibilities, or rather in eternal truths, this reality must needs be founded in something existing and actual, and consequently in the existence of the necessary Being, in whom essence involves existence, or in whom to be possible is to be actual. (Theod. 184-189, 335.)

45. Thus God alone (or the necessary Being) has this prerogative that He must necessarily exist, if He is possible. And as nothing can interfere with the possibility of that which involves no limits, no negation and consequently no contradiction, this [His possibility] is sufficient of itself to make known the existence of God a priori. We have thus proved it, through the reality of eternal truths. But a little while ago we proved it also a posteriori, since there exist contingent beings, which can have their final or sufficient reason only in the necessary Being, which has the reason of its existence in itself.

46. We must not, however, imagine, as some do, that eternal truths, being dependent on God, are arbitrary and depend on His will, as Descartes, and afterwards M. Poiret, appear to have held. That is true only of contingent truths, of which the principle is fitness [convenance] or choice of the best, whereas necessary truths depend solely on His understanding and are its inner object. (Theod. 180-184, 185, 335, 351, 380.)

47. Thus God alone is the primary unity or original simple substance, of which all created or derivative Monads are products and have their birth, so to speak, through continual fulgurations of the Divinity from moment to moment, limited by the receptivity of the created being, of whose essence it is to have limits. (Theod. 382-391, 398, 395.)

48. In God there is Power, which is the source of all, also Knowledge, whose content is the variety of the ideas, and finally Will, which makes changes or products according to the principle of the best. (Theod. 7, 149, 150.) These characteristics correspond to what in the created Monads forms the ground or basis, to the faculty of Perception and to the faculty of Appetition. But in God these attributes are absolutely infinite or perfect; and in the created Monads or the Entelechies (or perfectihabiae, as Hermolaus Barbarus translated the word) there are only imitations of these attributes, according to the degree of perfection of the Monad. (Theod. 87.)

49. A created thing is said to act outwardly in so far as it has perfection, and to suffer [or be passive, patir] in relation to another, in so far as it is imperfect. Thus activity [action] is attributed to a Monad, in so far as it has distinct perceptions, and passivity [passion] in so far as its perceptions are confused. (Theod. 32, 66, 386.)

50. And one created thing is more perfect than another, in this, that there is found in the more perfect that which serves to explain a priori what takes place in the less perfect, and it is on this account that the former is said to act upon the latter. 51. But in simple substances the influence of one Monad upon another is only ideal, and it can have its effect only through the mediation of God, in so far as in the ideas of God any Monad rightly claims that God, in regulating the others from the beginning of things, should have regard to it. For since one created Monad cannot have any physical influence upon the inner being of another, it is only by this means that the one can be dependent upon the other. (Theod. 9, 54, 65, 66, 201. Abrege, Object. 3.)

52. Accordingly, among created things, activities and passivities are mutual. For God, comparing two simple substances, finds in each reasons which oblige Him to adapt the other to it, and consequently what is active in certain respects is passive from another point of view; active in so far as what we distinctly know in it serves to explain [rendre raison de] what takes place in another, and passive in so far as the explanation [raison] of what takes place in it is to be found in that which is distinctly known in another. (Theod. 66.)

53. Now, as in the Ideas of God there is an infinite number of possible universes, and as only one of them can be actual, there must be a sufficient reason for the choice of God, which leads Him to decide upon one rather than another. (Theod. 8, 10, 44, 173, 196 sqq., 225, 414-416.)

54. And this reason can be found only in the fitness [convenance], or in the degrees of perfection, that these worlds possess, since each possible thing has the right to aspire to existence in proportion to the amount of perfection it contains in germ. (Theod. 74, 167, 350, 201, 130, 352, 345 sqq., 354.)

55. Thus the actual existence of the best that wisdom makes known to God is due to this, that His goodness makes Him choose it, and His power makes Him produce it. (Theod. 8, 78, 80, 84, 119, 204, 206, 208. Abrege, Object. 1 and 8.)

56. Now this connexion or adaptation of all created things to each and of each to all, means that each simple substance has relations which express all the others, and, consequently, that it is a perpetual living mirror of the universe. (Theod. 130, 360.)

57. And as the same town, looked at from various sides, appears quite different and becomes as it were numerous in aspects [perspectivement]; even so, as a result of the infinite number of simple substances, it is as if there were so many different universes, which, nevertheless are nothing but aspects [perspectives] of a single universe, according to the special point of view of each Monad. (Theod. 147.)

58. And by this means there is obtained as great variety as possible, along with the greatest possible order; that is to say, it is the way to get as much perfection as possible. (Theod. 120, 124, 241 sqq., 214, 243, 275.)

59. Besides, no hypothesis but this (which I venture to call proved) fittingly exalts the greatness of God; and this Monsieur Bayle recognized when, in his Dictionary (article Rorarius), he raised objections to it, in which indeed he was inclined to think that I was attributing too much to God- more than it is possible to attribute. But he was unable to give any reason which could show the impossibility of this universal harmony, according to which every substance exactly expresses all others through the relations it has with them.

60. Further, in what I have just said there may be seen the reasons a priori why things could not be otherwise than they are. For God in regulating the whole has had regard to each part, and in particular to each Monad, whose nature being to represent, nothing can confine it to the representing of only one part of things; though it is true that this representation is merely confused as regards the variety of particular things [le detail] in the whole universe, and can be distinct only as regards a small part of things, namely, those which are either nearest or greatest in relation to each of the Monads; otherwise each Monad would be a deity. It is not as regards their object, but as regards the different ways in which they have knowledge of their object, that the Monads are limited. In a confused way they all strive after [vont a] the infinite, the whole; but they are limited and differentiated through the degrees of their distinct perceptions.

61. And compounds are in this respect analogous with [symbolisent avec] simple substances. For all is a plenum (and thus all matter is connected together) and in the plenum every motion has an effect upon distant bodies in proportion to their distance, so that each body not only is affected by those which are in contact with it and in some way feels the effect of everything that happens to them, but also is mediately affected by bodies adjoining those with which it itself is in immediate contact. Wherefore it follows that this inter-communication of things extends to any distance, however great. And consequently every body feels the effect of all that takes place in the universe, so that he who sees all might read in each what is happening everywhere, and even what has happened or shall happen, observing in the present that which is far off as well in time as in place: sympnoia panta, as Hippocrates said. But a soul can read in itself only that which is there represented distinctly; it cannot all at once unroll everything that is enfolded in it, for its complexity is infinite.

62. Thus, although each created Monad represents the whole universe, it represents more distinctly the body which specially pertains to it, and of which it is the entelechy; and as this body expresses the whole universe through the connexion of all matter in the plenum, the soul also represents the whole universe in representing this body, which belongs to it in a special way. (Theod. 400.)

63. The body belonging to a Monad (which is its entelechy or its soul) constitutes along with the entelechy what may be called a living being, and along with the soul what is called an animal. Now this body of living being or of an animal is always organic; for, as every Monad is, in its own way, a mirror of the universe, and as the universe is ruled according to a perfect order, there must also be order in that which represents it, i.e. in the perceptions of the soul, and consequently there must be order in the body, through which the universe is represented in the soul. (Theod. 403.)

64. Thus the organic body of each living being is a kind of divine machine or natural automaton, which infinitely surpasses all artificial automata. For a machine made by the skill of man is not a machine in each of its parts. For instance, the tooth of a brass wheel has parts or fragments which for us are not artificial products, and which do not have the special characteristics of the machine, for they give no indication of the use for which the wheel was intended. But the machines of nature, namely, living bodies, are still machines in their smallest parts ad infinitum. It is this that constitutes the difference between nature and art, that is to say, between the divine art and ours. (Theod. 134, 146, 194, 403.)

65. And the Author of nature has been able to employ this divine and infinitely wonderful power of art, because each portion of matter is not only infinitely divisible, as the ancients observed, but is also actually subdivided without end, each part into further parts, of which each has some motion of its own; otherwise it would be impossible for each portion of matter to express the whole universe. (Theod. Prelim., Disc. de la Conform. 70, and 195.)

66. Whence it appears that in the smallest particle of matter there is a world of creatures, living beings, animals, entelechies, souls.

67. Each portion of matter may be conceived as like a garden full of plants and like a pond full of fishes. But each branch of every plant, each member of every animal, each drop of its liquid parts is also some such garden or pond.

68. And though the earth and the air which are between the plants of the garden, or the water which is between the fish of the pond, be neither plant nor fish; yet they also contain plants and fishes, but mostly so minute as to be imperceptible to us.

69. Thus there is nothing fallow, nothing sterile, nothing dead in the universe, no chaos, no confusion save in appearance, somewhat as it might appear to be in a pond at a distance, in which one would see a confused movement and, as it were, a swarming of fish in the pond, without separately distinguishing the fish themselves. (Theod. Pref. [E. 475 b; 477 b; G. vi. 40, 44].)

70. Hence it appears that each living body has a dominant entelechy, which in an animal is the soul; but the members of this living body are full of other living beings, plants, animals, each of which has also its dominant entelechy or soul.

71. But it must not be imagined, as has been done by some who have misunderstood my thought, that each soul has a quantity or portion of matter belonging exclusively to itself or attached to it for ever, and that it consequently owns other inferior living beings, which are devoted for ever to its service. For all bodies are in a perpetual flux like rivers, and parts are entering into them and passing out of them continually.

72. Thus the soul changes its body only by degrees, little by little, so that it is never all at once deprived of all its organs; and there is often metamorphosis in animals, but never metempsychosis or transmigration of souls; nor are there souls entirely separate [from bodies] nor unembodied spirits [genies sans corps]. God alone is completely without body. (Theod. 90, 124.)

73. It also follows from this that there never is absolute birth [generation] nor complete death, in the strict sense, consisting in the separation of the soul from the body. What we call births [generations] are developments and growths, while what we call deaths are envelopments and diminutions.

74. Philosophers have been much perplexed about the origin of forms, entelechies, or souls; but nowadays it has become known, through careful studies of plants, insects, and animals, that the organic bodies of nature are never products of chaos or putrefaction, but always come from seeds, in which there was undoubtedly some preformation; and it is held that not only the organic body was already there before conception, but also a soul in this body, and, in short, the animal itself; and that by means of conception this animal has merely been prepared for the great transformation involved in its becoming an animal of another kind. Something like this is indeed seen apart from birth [generation], as when worms become flies and caterpillars become butterflies. (Theod. 86, 89. Pref. [E. 475 b; G. vi. 40 sqq.]; 90, 187, 188, 403, 86, 397.)

75. The animals, of which some are raised by means of conception to the rank of larger animals, may be called spermatic, but those among them which are not so raised but remain in their own kind (that is, the majority) are born, multiply, and are destroyed like the large animals, and it is only a few chosen ones [elus] that pass to a greater theatre.

76. But this is only half of the truth, and accordingly I hold that if an animal never comes into being by natural means [naturellement], no more does it come to an end by natural means; and that not only will there be no birth [generation], but also no complete destruction or death in the strict sense. And these reasonings, made a posteriori and drawn from experience are in perfect agreement with my principles deduced a priori, as above. (Theod. 90.)

77. Thus it may be said that not only the soul (mirror of an indestructible universe) is indestructible, but also the animal itself, though its mechanism [machine] may often perish in part and take off or put on an organic slough [des depouilles organiques].

78. These principles have given me a way of explaining naturally the union or rather the mutual agreement [conformite] of the soul and the organic body. The soul follows its own laws, and the body likewise follows its own laws; and they agree with each other in virtue of the pre-established harmony between all substances, since they are all representations of one and the same universe. (Pref. [E. 475 a; G. vi. 39]; Theod. 340, 352, 353, 358.)

79. Souls act according to the laws of final causes through appetitions, ends, and means. Bodies act according to the laws of efficient causes or motions. And the two realms, that of efficient causes and that of final causes, are in harmony with one another.

80. Descartes recognized that souls cannot impart any force to bodies, because there is always the same quantity of force in matter. Nevertheless he was of opinion that the soul could change the direction of bodies. But that is because in his time it was not known that there is a law of nature which affirms also the conservation of the same total direction in matter. Had Descartes noticed this he would have come upon my system of pre-established harmony. (Pref. [E. 477 a; G. vi. 44]; Theod. 22, 59, 60, 61, 63, 66, 345, 346 sqq., 354, 355.)

81. According to this system bodies act as if (to suppose the impossible) there were no souls, and souls act as if there were no bodies, and both act as if each influenced the other.

82. As regards minds [esprits] or rational souls, though I find that what I have just been saying is true of all living beings and animals (namely that animals and souls come into being when the world begins and no more come to an end that the world does), yet there is this peculiarity in rational animals, that their spermatic animalcules, so long as they are only spermatic, have merely ordinary or sensuous [sensitive] souls; but when those which are chosen [elus], so to speak, attain to human nature through an actual conception, their sensuous souls are raised to the rank of reason and to the prerogative of minds [esprits]. (Theod. 91, 397.)

83. Among other differences which exist between ordinary souls and minds [esprits], some of which differences I have already noted, there is also this: that souls in general are living mirrors or images of the universe of created things, but that minds are also images of the Deity or Author of nature Himself, capable of knowing the system of the universe, and to some extent of imitating it through architectonic ensamples [echantillons], each mind being like a small divinity in its own sphere. (Theod. 147.)

84. It is this that enables spirits [or minds- esprits] to enter into a kind of fellowship with God, and brings it about that in relation to them He is not only what an inventor is to his machine (which is the relation of God to other created things), but also what a prince is to his subjects, and, indeed, what a father is to his children.

85. Whence it is easy to conclude that the totality [assemblage] of all spirits [esprits] must compose the City of God, that is to say, the most perfect State that is possible, under the most perfect of Monarchs. (Theod. 146; Abrege, Object. 2.)

86. This City of God, this truly universal monarchy, is a moral world in the natural world, and is the most exalted and most divine among the works of God; and it is in it that the glory of God really consists, for He would have no glory were not His greatness and His goodness known and admired by spirits [esprits]. It is also in relation to this divine City that God specially has goodness, while His wisdom and His power are manifested everywhere. (Theod. 146; Abrege, Object. 2.)

87. As we have shown above that there is a perfect harmony between the two realms in nature, one of efficient, and the other of final causes, we should here notice also another harmony between the physical realm of nature and the moral realm of grace, that is to say, between God, considered as Architect of the mechanism [machine] of the universe and God considered as Monarch of the divine City of spirits [esprits]. (Theod. 62, 74, 118, 248, 112, 130, 247.)

88. A result of this harmony is that things lead to grace by the very ways of nature, and that this globe, for instance, must be destroyed and renewed by natural means at the very time when the government of spirits requires it, for the punishment of some and the reward of others. (Theod. 18 sqq., 110, 244, 245, 340.)

89. It may also be said that God as Architect satisfies in all respects God as Lawgiver, and thus that sins must bear their penalty with them, through the order of nature, and even in virtue of the mechanical structure of things; and similarly that noble actions will attain their rewards by ways which, on the bodily side, are mechanical, although this cannot and ought not always to happen immediately.

90. Finally, under this perfect government no good action would be unrewarded and no bad one unpunished, and all should issue in the well-being of the good, that is to say, of those who are not malcontents in this great state, but who trust in Providence, after having done their duty, and who love and imitate, as is meet, the Author of all good, finding pleasure in the contemplation of His perfections, as is the way of genuine 'pure love,' which takes pleasure in the happiness of the beloved. This it is which leads wise and virtuous people to devote their energies to everything which appears in harmony with the presumptive or antecedent will of God, and yet makes them content with what God actually brings to pass by His secret, consequent and positive [decisive] will, recognizing that if we could sufficiently understand the order of the universe, we should find that it exceeds all the desires of the wisest men, and that it is impossible to make it better than it is, not only as a whole and in general but also for ourselves in particular, if we are attached, as we ought to be, to the Author of all, not only as to the architect and efficient cause of our being, but as to our master and to the final cause, which ought to be the whole aim of our will, and which can alone make our happiness. (Theod. 134, 278. Pref. [E. 469; G. vi. 27, 28].)

THE END


© created: 4/12/94; modified 24/12/95

大学名 東亜大学

氏名 井上龍介氏名(ローマ字) INOUE,Ryuusuke

職名 助教授所属学部・学科・講座名 デザイン学部;デザイン学科

担当科目 哲学;倫理学現在の専門分野西洋近世哲学

研究活動

「身体的存在としてのモナド」『東亜大学研究論叢』第16巻第2号 (1992年)「モナドロジー」その他の著作や書簡で、ライプニッツが身体性(物体性)をどのように理解しているか、また彼の考案した概念装置を用いて身体性を解釈するとき、どのような展望が拓かれうるか、ということを考察する。

「創造されなかったアダムたち」『東亜大学経営学部紀要』第2号 (1994年)ライプニッツの可能世界論には、「分身」または「相似者」についての議論が含まれている。この一見奇矯な概念の存在理由と理論的射程とについて究明する。

「本質から実存へ?」『東亜大学研究論叢』第20巻第1号(1995年)「内部性」と「外部性」、「境界領域」といった概念装置を駆使して、ライプニッツのオプティミズムにおける「創造のアルゴリズム」を解析する。『日常生活の謎解き』(共著)学術図書出版社,(1993年)第三章「<不在の現実>としてのユートピア」を執筆した。

キーワードモナド;可能世界;予定調和;最善性;偶然的命題主要所属学会日本哲学会;広島哲学会

記入年月1996年1月9日

市川 哲彦, ``非正格関数型言語におけるデータベース更新と遅延検索,'' 情報処理学会データベースシステム研究会報告, Vol. 95, No. 65, Jul. 1995, pp. 193--200. (In Japanese).

Abstract

非正格な関数型プログラミング言語 Haskell 向けに,状態モナドによる実行順序制御を用いたデータベース操作インターフェースを実装した.このアプローチの最も単純な実装では,データベース操作が参照透過になる反面,基本処理が状態遷移の過程で行なわれるために,検索の記述が命令的になるという欠点がある.本稿ではトランザクション制御の自然な拡張としての版管理機能を用いることにより,この問題を軽減する試みについて報告する.

http://hyalos.is.ocha.ac.jp:8080/~ichikawa/paper/dbs95/dbs95-absj.html

単子的邪擬似~君主制とモナド~NTT出版刊季刊「Inter Communication」no.25 1998年夏号Reserch and Creationpp10-12

<掲載テキスト>の英訳文は●Englishをクリックするとご覧になれます。


15 Reserch and Creation単子的邪擬以 Monadic Jaggie

<掲載テキスト>君主制とモナド...●English

<掲載作品>音の心1997Meaning (Soul of sound)

「430個の変曲点のある単一曲線」と「608個の変曲点のある単一曲線」の二作品同所配置1997

Placement of 2 pieces in the same location:"Single curved line with 430 inflection points" and "Single curved line with 608 inflection points"

二九字二九行の文字座標型絵画第一番1997

Letter-coordinates-type painting of 29 letters by 29 lines,No. 1

二九字二九行の文字座標型絵画第二番1997

Letter-coordinates-type painting of 29 letters by 29 lines,No. 2

768個の変曲点のある単一曲線1997Single curved line with 768 inflection points

4760個の変曲点のある単一曲線1997Single curved line with 4760 inflection points

プロフィール写真付き掲載


●主要自筆原稿及び活動トップ頁に戻る

Copyright : (C)1997-1998 HIDEKI NAKAZAWA/ALOALO INTERNATIONAL禁無断転載

E-mail : nakazawa@aloalo.co.jp

http://www.aloalo.co.jp/nakazawa/980511~jihitsu/980603tanshi.html

D3 北野孝志 「フッサールにおけるモナド概念と相互主観性」1996年『中部哲学会年報』28号

第9回(昭和40年度)科学哲学大会プログラム

時:昭和40年10月23~24日所:千葉大学文理学部千葉市弥生町

主催科学基礎論学会、アメリカ哲学研究会、科学論理学会

後援日本哲学会


10月23日(土)

研究発表・質疑討論(10:00~17:30)

第1部(数理・論理・言語)第1会場(921番教室)

10:00~12:001.高塚頼寿現代宇宙数学の論理的構成と論理的演繹的方法

2.松下伊勢松証明対象の束構造と同型な証明形式

3.村田全解析集合論における N.Lusin の“哲学”

4.河嶋元吉M.Freche の nombre paracomplexe について

15:00~17:305.正村史朗モナド相位の規制について

6.藤田晋吾ヴィットゲンシュタインにおける論理形式の概念について

7.坂井秀寿様相論理について―Lewis の体系をめぐって

8.川野洋コンピュータと言語

9.佐久間鼎ロゴスということ

第2部(知識・科学・技術)第2会場(931番教室)

10:00~12:001.田中治認識主観は客観

2.井上一美体系にあらわれる認識論の影響について

3.飯森豊経験科学におけるモデルについての一考察

4.植田清隆エネルギー変換構造II―“Lagrange の方程式”の意味とその問題点

15:00~17:305.黒崎宏検証の立場より見たる自由と決定論

6.沢井濤哉causa efficiens の一問題

7.浅野芳広法則性の表現をめぐる諸問題

8.広松渉マッハの空間理論―ニュートンとアインシュタインをつなぐ環

9.東節男科学における宿命的限界について

第3部(価値・行動・歴史)第3会場(941番教室)

10:00~12:001.岡昌宏貨幣価値と価格

2.江藤肇オペレーションズ・リサーチにおける価値論

3.小田切瑞穂価値の科学

4.安藤唯一意識について

15:00~17:305.青木孝悦「異常」をどのように考えるか

6.大羽蓁人間行動における恒常性と transactionism

7.岡本栄一条件づけの論理的構造

8.能見義博動物の探索行動について

9.福鎌達夫「ひと」と“person”

特別講演1(13:00~14:30)大山正(北海道大学助教授)行動科学としての心理学の研究法

懇親会(18:00~20:00)山本芳弘(千葉大学助教授)アメリカの諸大学を歴訪して

―スライドを中心に―(帰朝報告)


10月24日(日)(10:00~17:30)シンポジウム

第1部(10:00~12:00)第4会場(712番教室)

〔司会〕碧海純一(法学・哲学)行動科学の現代的課題

問題提出者吉村融(哲学)―序説・文明論的展望―、

高田洋一郎(数理心理学)、田中靖政(政治心理学)

武者小路公秀(政治学)、関寛治(政治学)

第2部(15:00~17:30)第4会場(712番教室)

〔司会〕大江精三(哲学)科学的人間像の諸相

問題提出者池原止戈夫(数学)、山内恭彦(物理学)、石田周三(生物学)

岡本彰祐(大脳生理学)、石田英一郎(文化人類学)

特別講演2(10:00~14:30)第4会場(712番教室)

中村元(東京大学教授)東洋思想と科学的思惟


市川 哲彦, ``プログラミング言語 Haskell 上のデータベース操作インターフェースの実装,'' 情報処理学会データベースシステム研究会報告, Vol. 94, No. 62, Jul. 1994, pp. 201-208. (in Japanese).Abstract

純粋な関数型プログラミング言語 Haskell 向けに,monad を用いた実行順序制御と多重定義関数を基本操作とするデータベース操作インターフェースを設計・実装した.データベース操作はすべて monad によって制御されているので,参照透過である.また,基本操作を Persistent class に関連付けられた多重定義関数として定義することにより,実装の詳細を隠蔽するデータ独立性を実現し,多様関数と静的型付けの利用とを可能にしている.

The Haskell 1.4 Library Reporttop | back | next | contents


10 Monad Utilities

module Monad (

join, mapAndUnzipM, zipWithM, foldM, when, unless, ap,

liftM, liftM2, liftM3, liftM4, liftM5

) where

join :: (Monad m) => m (m a) -> m a

mapAndUnzipM :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])

zipWithM :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]

foldM :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a

zeroOrMore :: (MonadPlus m) => m a -> m [a]

oneOrMore :: (MonadPlus m) => m a -> m [a]

when :: (Monad m) => Bool -> m () -> m ()

unless :: (Monad m) => Bool -> m () -> m ()

ap :: (Monad a) => (m (a -> b)) -> (m a) -> m b

liftM :: (Monad m) => (a -> b) -> (m a -> m b)

liftM2 :: (Monad m) => (a -> b -> c) -> (m a -> m b -> m c)

liftM3 :: (Monad m) => (a -> b -> c -> d) ->

(m a -> m b -> m c -> m d)

liftM4 :: (Monad m) => (a -> b -> c -> d -> e) ->

(m a -> m b -> m c -> m d -> m e)

liftM5 :: (Monad m) => (a -> b -> c -> d -> e -> f) ->

(m a -> m b -> m c -> m d -> m e -> m f)

These utilities provide some useful operations on monads.

The join function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

The mapAndUnzipM function maps its first argument over a list, returning the result as a pair of lists. This function is mainly used with complicated data structures or a state-transforming monad.

The zipWithM function generalises zipWith to arbitrary monads. For instance the following function displays a file, prefixing each line with its line number,

listFile :: String -> IO ()

listFile nm =

do cts <- openFile nm

zipWithM_ (\i line -> do putStr (show i); putStr ": "; putStrLn line)

[1..]

(lines cts)

The foldM function is analogous to foldl, except that its result is encapsulated in a monad. Note that foldM works from left-to-right over the list arguments. This could be an issue where (>>) and the "folded function" are not commutative.

foldM f a1 [x1, x2, ..., xm ]

==

do

a2 <- f a1 x1

a3 <- f a2 x2

...

f am xm

If right-to-left evaluation is required, the input list should be reversed.

The when and unless functions provide conditional execution of monadic expressions. For example,

when debug (putStr "Debugging\n")

will output the string "Debugging\n" if the Boolean value debug is True, and otherwise do nothing.

The monadic lifting operators promote a function to a monad. The function arguments are scanned left to right. For example,

liftM2 (+) [0,1] [0,2] = [0,2,1,3]

liftM2 (+) (Just 1) Nothing = Nothing

In many situations, the liftM operations can be replaced by uses of ap, which promotes function application.

return f `ap` x1 `ap` ... `ap` xn

is equivalent to

liftMn f x1 x2 ... xn

10.1 Library Monad

module Monad (

join, mapAndUnzipM, zipWithM, zipWithM_, foldM, when, unless, ap,

liftM, liftM2, liftM3, liftM4, liftM5

) where

join :: (Monad m) => m (m a) -> m a

join x = x >>= id

mapAndUnzipM :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])

mapAndUnzipM f xs = accumulate (map f xs) >>= return . unzip

zipWithM :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]

zipWithM f xs ys = accumulate (zipWith f xs ys)

zipWithM_ :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m ()

zipWithM_ f xs ys = sequence (zipWith f xs ys)

foldM :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a

foldM f a [] = return a

foldM f a (x:xs) = f a x >>= \ y -> foldM f y xs

when :: (Monad m) => Bool -> m () -> m ()

when p s = if p then s else return ()

unless :: (Monad m) => Bool -> m () -> m ()

unless p s = when (not p) s

ap :: (Monad m) => m (a -> b) -> m a -> m b

ap = liftM2 ($)

liftM :: (Monad m) => (a -> b) -> (m a -> m b)

liftM f = \a -> [f a' | a' <- a]

liftM2 :: (Monad m) => (a -> b -> c) -> (m a -> m b -> m c)

liftM2 f = \a b -> [f a' b' | a' <- a, b' <- b]

liftM3 :: (Monad m) => (a -> b -> c -> d) ->

(m a -> m b -> m c -> m d)

liftM3 f = \a b c -> [f a' b' c' | a' <- a, b' <- b, c' <- c]

liftM4 :: (Monad m) => (a -> b -> c -> d -> e) ->

(m a -> m b -> m c -> m d -> m e)

liftM4 f = \a b c d -> [f a' b' c' d' |

a' <- a, b' <- b, c' <- c, d' <- d]

liftM5 :: (Monad m) => (a -> b -> c -> d -> e -> f) ->

(m a -> m b -> m c -> m d -> m e -> m f)

liftM5 f = \a b c d e -> [f a' b' c' d' e' |

a' <- a, b' <- b,

c' <- c, d' <- d, e <- e']


The Haskell 1.4 Library Reporttop | back | next | contents

April 4, 1997

KMSF-MONAD Architecture new stuff(totally under construction)

KMSF-MONAD is formerly known as the KMSF-ADO (Autonomous Distibuted Object). KMSF-MONAD is an acronym for the Mobile Object Network with Autonomy and Diversity.


細野晴臣/ザ・ベスト・オブ・インストゥルメンタル・ミユージック・オブ HOSONO HARUOMl "CALM"

1.ダウン・トゥ・ザ・アース

2.プリオシン海岸

3.ダーク・サイド・オブ・ザ・スター

4.フォシエル・オブ、フレーム

5.ザ・トラック・オン・ザ・シー

6.マジンガー"H"

7.別離のテーマ

8.MABUl DANCE

9.ノルマンディア

10.MAKlNG 0F M0NAD MUSlC 3・6・9

11.ザ・マン・オブ・チャイナ

12.トウ・ジ・エア

(49'02")

TE‐コンチネンタル [25CH‐4]\2,348 (88.9.21)


NON STANDARD / MONAD SPECIAL SAMPLER

CD[型番CDS-10402]

1991年?月??日発表

プロモ 0 曲名 アーティスト 0

1. Carnaval 哀しみのカーナヴァル MIKADO

2. 瞳はサンセット・グロウ SHI-SHONEN

3. Pasio WORLD STANDARD

4. China bees WORLD STANDARD

NON STANDARD LABELの12インチシングルは一般向けにはとうとうCD化されませんでした。そういう意味でやはりこのNON-STANDARD/MONADSpecial Samplerは貴重なものでしょう。これは全てCD一般未発売の12インチシングルより収録されているのです。ヴァージョンは12インチのもと同じものです。 Shunichi Tanaka's Home Page

(tanaka@math.kyushu-u.ac.jp)

論理・束・位相

Monoids :monoidはobjectが1個であるカテゴリ-である.そのarrowsの全体Mは(単位元をもつ)半群をなす.objectsはMが作用するsets(M-sets),arrowsはMの作用を保つM-sets間のmaps(M-maps)とするカテゴリ- M-Setsが基本的なカテゴリ- Setsからどのように組み立てられるか調べることによりmonadの概念に到達する.

Lattices :posets(半順序集合)のカテゴリ-論はすべての図式が可換であること,同型な対象は等しいことから単純な構造をもつ.

Frames and Locales 1998.6.23

finite meetと任意のjoinをもつ束で無限分配法則をみたすものをframeという.位相空間の開集合の全体に包含関係で半順序を入れたものはframeである. frame morphismはfinite meetと任意のjoinを保つmapのことをいう.Framesはobjects はframes 全体,arrows はframe morphismsであるようなカテゴリ-である.そのopposite categoryをLocalesという.点のない位相空間であるロカールは層,トポス,領域理論において基本的な位相概念である.

References LinksFCS Seminar(辻下徹氏のホームページ)FCS=Formal Methods in Complex Systems Research 基盤研究B「形式的方法による複雑系数理の基礎研究」(代表者:辻下徹氏)ホームページ The Hypertext Bibliography Project

Topology at Imperial College,Department of Computing 九州システム情報技術研究所

高良弘志,Topos入門 MkLinux ==>数理学研究科ホームページ

Monads

カテゴリ- Xのendofunctor T,自然変換 \eta:1X->T,\mu:T2-> T が

\mu T\mu = \mu \muT (associative law)

\mu \etaT = 1T = \mu T\eta (identity law)

をみたすとき組 (T,\eta,\mu) をX上のmonadという.

Mをsetとし,T(X)=M \times X とする.(T,\eta,\mu) がSetsのmonadであれば,Mはmonoidであり,monadはmonoidに対して構成したものと一致する.実際1点集合S={*}を考え,\etaS(*)=(e,*)とおく.\eta は自然変換なので,任意の集合Xの任意の元に対して,\etaX(x)=(e,x) が成立する.Mの2元に積が定義できることも同様である.

カテゴリ-XTを,objectsを組(X,h:TX->X) で

h \etaX = 1X

h \muX = h Th

をみたすものとし,(X,h)から(X',h')へのarrowをmap f:X->X'で

f h = h' Tf


1997平成9年度 算譜意味論 講義録 東京大学大学院理学系研究科情報科学専門課程

(講師: 木下 佳樹 yoshiki@etl.go.jp) 単位取得のためのレポートについて

出席した人で, 単位の必要な人はレポートを出してください. 課題をここにおきます. レポート作成中に講義の内容について質問がわいたら講師宛メイルで質問してくださって結構です (yoshiki@etl.go.jp).

レポートは, できるだけ電子メイルで講師宛直接提出してください. 期限は8月31日

とします. 数学記号が厄介なら TeX などで書いて, PostScript にしたものを送ってください. どうしても紙に書きたい人はしようがないので, 情報科学科の事務室に提出しても受けつけますが, その場合には, 期限を早めて 8月15日 とします. いずれにしても, 期限に遅れた場合, 間にあえば遅れても成績を付けますが, 必ず成績を付けるという保証はしません.

ミラーについてこのページと関連ファイルのコピーを萩谷研のマシン ( ftp://nicosia.is.s.u-tokyo.ac.jp/pub/staff/yoshiki および http) にも置かせてもらいました. こちらへは手でコピーしているので, バージョンが古くなっていく可能性がありますが, 先日のように電総研からダウンロードできないときは, 萩谷研においてあるものを使ってください.

講義内容シラバスには

表示的意味論およびそこで使われる領域理論, 圏論の講義を行う. 時間があれば, データ精製についての最近の成果も紹介する.

と載せてもらったと思いますが, 内容は圏論に偏りそうです. 一通り圏論の入門を終えた後, 圏論のデータ型の理論への応用を紹介しようか, と考えています. データ精製の話までできるかどうか...

第一回 (1997.5.14)

講義ノート [PostScript] [dvi]圏と函手の定義と例 1997.5.23 に更新しました. 実は最後の部分は第二回に話した部分だったりする. 寄り道の話 すべての集合の集合, 空集合からの写像・空集合への写像 同値関係, 同値類についても, 急いで話した.

第二回 (1997.5.21)

講義ノート [PostScript] [dvi] 随伴の四つの等価な定義 まだ書き足りないので, 後に更新するかも知れません. 寄り道 単射と全射を要素を使わないで定義する. 寄り道その2 同型射について.

第三回 (1997.5.28)

講義ノート [PostScript] [dvi] 随伴の例, 表現可能函手と米田の補題 道草

集合の直積 (×) は結合法則を満たさない!

第四回 (1997.6.4)

極限 (limit) と余極限 (colimit), その例, 極限の存在の必要十分条件 (Freyd の随伴函手定理は話せなかった)

講義ノート [PostScript] [dvi]

第五回 (1997.6.11)

単子 (monad) の理論: Eilenberg-Moore 圏, Kleisli 圏 (Beck の定理と代数系との関係の詳しい話はできなかった)

第六回 (1997.6.18)

再帰的定義の不動点意味論 (filtered colimit の保存)

まず, 函数の再帰的定義の不動点意味論をωCPOとω-鎖を保存する汎関数を用いて説明した. 次に, データ型の再帰的定義の不動点意味論を filtered colimit を持つ圏と filtered colimit を保存する函手について説明した. ω-鎖は filtered colimit の特別な場合なので, ωCPO は, filtered colimit を持つ圏の特別な場合ともなる.

第七回 (1997.6.25)

一階述語論理, λ計算の圏論的モデルをみたすものとする.


==>index

Roget's Thesaurus: Entry 193 (Littleness)

Make sure you have read the copyright information for this Project Gutenberg thesaurus, as well as the description of the thesaurus.

#193. Littleness.-- N. littleness &c. adj.; smallness &c. (of quantity) 32; exiguity, inextension[obs]; parvitude[obs], parvity[obs]; duodecimo[obs]; Elzevir edition, epitome, microcosm; rudiment; vanishing point; thinness &c. 203.

dwarf, pygmy, pigmy[obs], Liliputian, chit, pigwidgeon[obs], urchin, elf; atomy[obs], dandiprat[obs]; doll, puppet; Tom Thumb, Hop-o'-my- thumb[obs]; manikin, mannikin; homunculus, dapperling[obs], cock-sparrow.

animalcule, monad, mite, insect, emmet[obs], fly, midge, gnat, shrimp, minnow, worm, maggot, entozoon[obs]; bacteria; infusoria[obs]; microzoa[Microbiol]; phytozoaria[obs]; microbe; grub; tit, tomtit, runt, mouse, small fry; millet seed, mustard seed; barleycorn; pebble, grain of sand; molehill, button, bubble.

point; atom &c. (small quantity) 32; fragment &c. (small part) 51; powder &c. 330; point of a pin, mathematical point; minutiae &c. (unimportance) 643.

micrometer; vernier; scale.

microphotography, photomicrography, micrography[obs]; photomicrograph, microphotograph; microscopy; microscope (optical instruments) 445..

V. be little &c. adj.; lie in a nutshell; become small &c. (decrease) 36, (contract) 195.

Adj. little; small &c. (in quantity) 32; minute, diminutive, microscopic; microzoal; inconsiderable &c. (unimportant) 643; exiguous, puny, tiny, wee, petty, minikin[obs], miniature, pygmy, pigmy[obs], elfin; undersized; dwarf, dwarfed, dwarfish; spare, stunted, limited; cramp, cramped; pollard, Liliputian, dapper, pocket; portative[obs], portable; duodecimo[obs]; dumpy, squat; short &c. 201.

impalpable, intangible, evanescent, imperceptible, invisible, inappreciable, insignificant, inconsiderable, trivial; infinitesimal, homoeopathic[obs]; atomic, subatomic, corpuscular, molecular; rudimentary, rudimental; embryonic, vestigial.

weazen|!, scant, scraggy, scrubby; thin &c. (narrow) 203; granular &c. (powdery) 330; shrunk &c. 195; brevipennate[obs].

Adv. in a small compass, in a nutshell; on a small scale; minutely, microscopically.

人工知能向きオブジェクト指向言語Monad

Monad: An Object Oriented Language for Artificial Intelligence

石橋勇人, 矢崎朋夫, 西田豊明, 堂下修司 H.Ishibashi, T.Yazaki, T.Nishida, S.Doshita

Abstract

Monad is an object oriented language designed for building AI systems. AI language should provide the user with a means for organizing knowledge in a flexible and modular manner. Towards this end, it would also be useful to allow the user to write programs without worrying about control structures. To achieve these goals, we have incorporated into Monad the following features: (1) The user can program methods as rule based production systems. He can write easily not only non-deterministic programs but also deterministic programs. (2) The user can use patterns to catch messages. He can use such messages that contain two or more selectors and contain no selector (only arguments). The order of the selectors and arguments is optional. (3) The user can make use of multiple inheritance and specify searching path. The specification is done by special purpose reserved variable. It is also possible to combine methods defined in the super classes. (4) The user can define event-driven methods which will be invoked when a certain condition holds. By using this facility, it is easy to keep consistency of information in objects. We have developed the Monad interpreter in Interlisp-D on 1100 SIP and confirmed that it is effective for AI programming.

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Earthen Vessel Productions

Microcurrent Catalog

Third Quarter, 1998


M.E.N.S.-i Super CM.E.N.S. IVFreedom Micro Pro

M.E.N.S. IIM.E.N.S. 2000+4

Microcurrent Instruments

Earthen Vessel Productions is proud to be the master distributor of MONAD microcurrent instruments. MONAD has been developing and manufacturing microcurrent instruments longer than any other company in the industry--over two decades. Their experience shows--with instruments that combine intuitive design with ingenious electronic engineering. MONAD microcurrent instruments are being used by Chiropractors, Physical Therapists, Acupuncturists, Occupational Therapists, Sports Trainers, Medical Doctors and Surgeons in hospitals, clinics, offices and training rooms all over the world. These health care professionals know what a valuable, effective, safe and comfortable modality microcurrent is, and that MONAD has helped lead the way in its maturation.

Please take some time to get familiar with the different instrument models. As always, if you have any questions, please don't hesitate to contact us. We look forward to hearing from you.


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Maja Mileinski Leibniz in kitajska filozofija

Èlanek obravnava Leibnizov odnos do kitajske filozofije, ki ga je oblikoval na poznavanju Yijinga in neokonfucijanske filozofije. Njegov glavni vir so bila dela figuristov, jezuitov zgodnjega osemnajstega stoletja, ki so gradila na preprieanju o skupnem izvoru elove?tva. Leibnizova teorija monad ima mnogo skupnega s kitajsko korelativistieno filozofijo, poleg tega pa je tudi v analizi trigramov klasienega kitajskega filozofskega dela Yijing odkril potrditev za svoj binarni sistem. Dejstvo, da so Kitajci ?e vsaj pred 4500 leti imeli matematieni sistem in gojili disciplino racionalnosti in logike, je Leibniza pripeljalo tudi do teze, da bi naj ?e stari Kitajci imeli naravno religijo, ki jo je Leibnizov ueenec Christian Wolff razumel kot ateizem. Z Leibnizom in Wolffom se je v zgodovini evropske filozofije za dve stoletji prekinil odprt in sprejemljiv odnos do neevropskih filozofskih tradicij, in konealo se je kratko obdobje sreeanja evropskih filozofov s kitajskimi filozofskimi deli. V Evropi pa se je filozofija vzpostavila kot ≫zahodna≪ filozofska tradicija.


Maja Mileinski Leibniz and the Chinese philosophy

The paper discusses Leibniz's approach to Chinese philosophy, which was built on his knowledge of Yijing and neo-Confucian philosophy. His main sources were the works of the Figurists, early eighteen century Jesuits, that held the conviction that there is a common background to all humankind. Leibniz's theory of monads is very close to Chinese correlativistic philosophy. In addition to this, in his analysis of the Yijing trigrams, Leibniz also discovered confirmation for his binary system. The fact that 4500 years ago the Chinese possessed a mathematical system, as well as engaged in a discipline of rationality and logic, brought Leibniz to the thesis that the ancient Chinese practised a sort of natural religion, which was understood by Leibniz's student Christian Wolff as atheism. With Leibniz and Wolff, the brief encounter of European philosophers with Chinese philosophical works came to a close, and the approach it opened up to the non-European philosophical traditions in the history of philosophy was suspended for two centuries. In Europe, philosophy reestablished itself as a ≫Western≪ philosophical tradition.

http://www.zrc-sazu.si/www/fi/Vestnik/SINOP396.HTM

Monarchy and Monad

Ancient Egyptian history and long Chinese history can be clearly interpreted as the history of the rise and fall of monarchies; on the other hand, Western history can be understood as a pendulum which swang, having monarchy as an axis, between two poles of the material-oriented people-glorified age and the ideology-oriented monotheism-dominating age. Direct democracies seen in ancient cities were destroyed by the blind populace, and after the absolute monachies which were maintained by Roman emperors, there arrived the Middle Ages, which were centuries of God having the popes as mediators. Then Crusade caused the stream to turn back, and the theory of the divine right of kings gave absolute monarchism a chance to flourish again, and then individualistic anarchism appeared after tumultuous revolutions. The one who embodied the situation by putting color-dots evenly on canvas was a pointillist Seurat.

But let us stop and think: Anarchism's condition as non-structuralism ought to be as primitive as to react easily to any biological impulses. It was the very monarchy made by blood relatives that appeared as the result of the law of the jungle and gene's self-expanding reproduction function through generation. Monarchs, like an emperor portrayed by Arcimboldo, took all existing things in their empires as the structural elements (dots), and formed an unbroken line of sovereigns.

Ubiquitous coexistence of self-awareness of reductionistic arbitrariness, which is the characteristic of the 20th century's art and science, and its converse, tautology, suggests nothing but another Socratism itself which incarnates anarchism as cynicism. It is the age of the blind populace, but a material atom in atomism originally has no meaning in itself. Can this no-meaningness be re-integrated into a meaningful red circle by blood?

The following two exactly correspond, that is, that Archimedes who discovered mensuration by replacing the jaggie with points of inflection and tangents was a disciple of an atomist Democritus, and that Leibniz, the founder of modern infinitesimal calculus, invented a binary-system calculator and advocated monadology, a theory on a monad which well corresponded to a spiritual atom. Picture elements of bitmap CG restart to restore meaning to an individual, reversely going by way of the materialization of integers by Leibniz and the fractionation of the world by Seurat. Democracy is not self-evident.

http://www.aloalo.co.jp/nakazawa/980511~jihitsu/980716MonarchyMonad_Eng.html

SUKI: The Sence of Multi-VernacularJunji Ito Commissioner

The prime objective of the Japanese pavilion exhibition is not so much to display individual works as to show the philosophical links implicit in their disposition. It is intended to prove that a metaphysical harmony can be created among works from different times and speces by what is an essentially architectural idea, and taht this particular idea emerged from an accumulation of aesthetic sensibilities peculiar to our culture. This idea has consistently determined our contacts with others, as well as the absorption and release of the energy of other cultures within our own.

This idea is not something that possesses a solid structure created from any particular element, but is built on a number of diverse and overlapping ideas linked in a continuum either circumstantially or like constellations. The link itself is the idea. Therefore, the individual works displayed in this exhibition, while symbolic of numerous allegories, have been thrown off of their time-space axes by their mutual interchangeability. Because of the diversity of the constellatory links among thses works, judgments basd on specific art genres of the Modernist past are not relevant. Visitors will find, in the abstraction-promoting concreteness of the exhibition itself, a passage that causes them to embark on spiritual wanderings like the nomads of the plains.

This wandering, as we experience it in our daily life, began at least 400 years ago, with the first encounter of the East and West, and it begins in the "present," 400 years later. For, on the linear time-axis of the suki aesthetic, everything coexists in the time unit of the experiential "present". This "present," which is free to roam within an enormous span of time, has stimulated even the minutest particles within that great sweep of time, generating thereby the motion of its continuity. And it continues to demonstrate that this motion functions in the infinite expanse of time even earlier than that.

Around the time piero della Francesca, painter of the "ideal city," was seeking the truth in the proportions of artificial representation amid the Renaissance of Europe, in Japan, the merchant tea master Sen no Rikyu formalized the act of making and drinking tea into the artistic discipline known as wabi-cha. Since then, chanoyu (the tea ceremony), and its aesthetic of suki, have been engaged in experiments to discover the invisible truth in the ceaseless links of the "critique" implicit in nature. On the supposition that the truth can be found in the state of "nothingness" that assimilates all phenomena, the earliest experiment consisted of transplanting untouched nature into the artificial city. The simple drinking of a bowl of tea without any formal rituals in this architectural environment called sukiya was an allegory of as-yet-unseen "truth," a representation of the composition of natural elements in a spatial continuum. Within that space, the collected components--plants, water, earth, architecture, utensils, painting, calligraphy, light, air, etc.--contain fragments of the truth of "nothingness" continuously converging and dispersing in that continuum, ih the process of achieving a conceptual represetation of the whole. The same is true of the forms of different cultures introduced through utensils. The landscape gardening perfected by Rikyu's predecessor Muso Kokushi (Soseki, 1275-1351), displaying a principle of passage in the sense of Walter Benjamin, that was architecturally adopted in the conceptual development of sukiya and continues to impinge on our daily lives even now. Nature, which plays the greatest part in this principle, is not there simply to be given a certain concrete form but as a means of seeking the principle of its forms and of maintaining the quality of mutual criticism in the continuum. Nature also permeates the human-made objects--structures, utensils, ornaments--and in the exchange of critiques, it calls for reappraisal of the metaphysical qualities of those objects.

Sukiya is the structure for examining the multiple directions, as seen in the compound eye, of the abstruse, complex, and intricate labyrinth or fictive nature that we have used over a long period of time as our criteria for forms and their arrangement, indeed, that we have relied upon for the structure of our very thought. It is the conceptual and methodological result of an idea of search for the truth that had drifted across a whole continent, allegorized in the everyday act of drinking tea.

Within the sukiya (tearoom), pathways are strictly prescribed and the space (emptiness) so arranged that there are always two points of view in which "tea" is exchanged. Those who arrive by way of the roji, which is an metaphor for the passage to gedatsu (discarding of the self and attainment of the state of selflessness), and those who have already achieved gedatsu--the guests (kyaku) and the host (teishu), respectively--never view anything from the same direction. In other words, everything (whether it be something natural or something artificial) is always exposed to plural appraisals from different directions, This means that things are perceived in multiple layers of imagery and conception and thereby deprived of their own peculiar and physical value. The resulting crisis of meaning produces value splits in which a real constellation (or relativity) appears. In this constellation, everything--past, present, and future, customs, arts, the whole of space and its parts--loses its borders and becomes merely an element of which the constellation is composed. Thus, the aesthetic of suki (which means literally, "gather numbers") represents a continuum of critique formed by fractal curves and surfaces. the word suki itself evokes many other meanings--"to like [something]," "transparency," even "a spade [which digs up things]," and so on, meaning ultimately, the conceptual whole of various related images.

The continuum of critique (represented by suki), however, keeps on changing and taking on new forms as small parts of it change, so that, just as we confront nature, we are compelled to maintain a cybernetic perception of any given situation. This device for producing beauty, or the system of relativity by the nature of its structure, does not reject things created in a different culture. The reason we do not reject them is that the device is a curve of infinitely continuing critique, the very continuation of which shapes our thought. It assimilates new elements, then transforms itself to construct a new constellation, and create now forms and arrangements. In this sense, suki represents a composite of the structures of various cultural dialects; in other words, the composite structure itself constitutes our own dialect (vernacular). The system thus penetrates all aspects and phenomena of our daily life and even eschews the realm of "aesthetic" in the pure conceptual sense.

In the 1980s, the emergence of post-modernism and neo-expressionism brought a number of new themes into the fields of art and design, and the one that had the most symbolic and practical impact was the revival of the "vernacular," the return to particularistic, indigenous themes in reaction to modernism's universalism. In the course of modernism's unconditional embrace of all things new and innovative from the eighteenth century onward, the indigenous and vernacular were rejected, producing in the twentieth century a society in which everything is envelopecd by industrialization (modernization). As Ivan Illich wrote in his definition of modernization about the dissolutiom of vernacular values, even culture, which derives from the world "cult" (rituals, beliefs) was made the target of change. In other words, in the process of separating and distancing society from the vernacular Values that centered around religion that was to be achieved as the liberation from magic (Max Weber), cultures, too, forced into a qualitative shift from value by affiliation to value by achievement (ability). The post-modernist revival of vernacular themes, occurring against the backdrop of overstandardization propagated by modern distribution systems, the collapse of communism, and the revival of religions, therefore, can be seen as the rise of a kind of "cultural fundamentalism" in reaction to Modern civilization.

At the same time, however, because of the vacuum of history and developments in information distribution, the vernacular is far less clear than before. Even the stereotypical division of East and West, for instance, is no longer valid, because "easts" and "wests" have been formed or dismantled with regions themselves. These are times when what matters most is not so much that which is solid and discreet, but what embraces or aims for the "multi-vernacular."

In these circumstances, the semblance of internationalization that has been built up on the basis of an environment that is well equipped informationally, as well as economically and politcally, harbors the potential for creating truly global culture for the first time in history. But there is one serious problem: the over-diversification of "beauty" accompanying the acknowledgement of the particularity of individual cultural regions and the expansion of information systems linking ever-wider areas. Moreovr, it is not simply a question of recognizing those particularistic systems. Each culture has its own complex structure, with its own dynamics, as has been acknowledged from the 1980s. That complexity is an important issue as far as it concerns the appreciation of beauty, because it is a concept that has always been closely linked to indigenous culture. Standards of what is beautiful, which onece enjoyed the status of the absolute for each particular region, now face the imminent threat of extinction in the context of informational relativity. It may even be said, in fact, that visual beauty has already lost its absoluteness. If so, if "beauty" is caught in this swirl of relativity, how should was attempt to perceive it? what sort of mutual relationships should be constructed for aesthetics? Amid the paradigm shifts going on in international society today, this is one of our most serious dilemmas, for "beauty" is the final conceptual property of humankind that can be used to establish perceptual relationships transcending national boundaries.

The suki concept of space and its aesthetic setting are for perceiving new metaphysical qualities through the creation of a relativity among various individualities (vernaculars) while maintaing their diversity. This idea could be very useful to us in this time of the chaotic diversification of "beauty." Indeed, once information starts flowing randomly and freely across the disciplines through multi-media networks, the philosophical value of suki will be all the greater.

Jacques Derrida described his idea of deconstruction as reexamining traditional values and reinventing them from within the old structures. Rikyu, too, sought to "follow rules and observe norms to perfection, then break or move away from them without forgetting the basics" (the concept of shu-ha-ri, literally, "defend, destroy, depart"), although he was more radical because action and form accompany each other, and even involve matters of daily life.

Fritjof Capra, author of The Tao of Physics, saw in the interactions of elemental particles the union of all phenomena as taught in Oriental mysticism. If Capra is right, perhaps Rikyu was a practical applier of universal concepts through the teachings of Zen Buddhism, who persisted in the arrangement (agencement) of fragments--utensils--brought from a variety of cultures, but who knew how to create a new, unified tension transcending their individual vernaculars.

It is amazing, considering the huge gap in time, to find Rikyu-esque concepts and aesthetics like suki in the ruminations of the contemfporary writers now attempting to construct a framework for thought following the breakdown of the Modern ideology. And we might carry the comparison with the lineage of progressive Western thought even further back, to Gottfried Wilhelm Leibniz, who described what he called "preestablished harmony," a state when monads (a monad being the ultimate physical and mental unit of which entities composed) unrelated to each other and each constituting an independent world, present a state in which they seem to be mutually related. Taking the position of subjective idealism, Leibniz believed the source of harmony among monads was God. Rikyu, meanwhile, described the essence of the relationship among separate entities as "nothingness" or "selflessness."

One might attribute the divergence of their views to the differences between the monotheistic and the polytheistic views, but "nothingness" in chanoyu and in Zen is an absolute chaos to be seen beyond an animist state and its metaphysical condition, and this chaos synthesizes all detalis without denying any. Chanoyu was an effort to gain an empirical and therefore universal idea by replacing the totality of these deeds with the passage of temporal and spatial processes.

Thus chanoyu is a highly condensed ritual for attaining a Zan-like state of mind. It might be described as a device for arousing equal visual, linguistic, and physical stimuli in a context of interactive information exchange through which to conceptualize a utopian condition whicih does not exist there either visually or representationally but is etched in the memory of the individual's unconscious. In this sense, all the things "arranged" there, despite differences in the time or space where they were made, represent "beauty" with a "functoin" and designe for the realization of something magical or metaphysical. It follows that beauty expressed in form is incomplete by itself and is conceptually completed only when the display, itself a critical act, is linked with physical perception and imagery. That is why suki, though comceived against a premodern historical backdrop, never loses its "contemporaneity."

The exhibition in the Japanese pavilion this year is presented using the suki technique in order to temporally and spatially liberate the perspective of modern art, not so much from sectarianism, evolutionism, dualism, or universalism, as from mono-valued, fixed preconceptions, and to revive the utopian ideas that once sustained avant garde art.

In order to apply suki, an aesthetic with a methodology for creating overall relativity without stifling individuality comparable to the constellations in the night sky, to an even more comprehensive environment, we began whth the acknowledgment that all areas of creative endeavor in Japan today are realms of art. The basic structural axes in this view are tradition, design (and folkways), and technology, for it is at the intersection of these three axes that the new "beauty" evolving toward the twenty-first century is located. This structure, furthermore, can probably be understood as applying to circumstances that can be found in many other parts of the world. We therefore regard these three as the X, Y, and Z axes in this exhibition, presenting the leading and most creative works on each axis comprehensively, stereoscopically, and in a suki fashion, hoping to express thereby how we see the universal situation and identihy the direction it is moving in. This endeavor is both our challenge to the territorially-bound Modernist "art" and our proposition on "beauty" for the twenty-first century and after.

The exhibition begins with the installation of Jae Eun Choi, at whic the visitor embarks on a path into space with no borders and no weight. The path is made of unvarnished wood that circles the entire pavilion. The viewer is free to choose between the position of "guest" and that of "host." If the position of "guest" is chosen, the visitor first encounters the presentation on the axis of design (and folkways), Scattered over the expanse of water covering the exhibition site are cardboard placards carrying images identified with the artist. The idea of the work is that it is created on the canvas of the city of Tokyo.

In the Edo period, it is said, the ukiyo-e artists, or those who were in charge of the actual production of prints--the woodcutters, printers, and publishers--would, in the final stage of printing, remove the finest and bestmade of the blocks. This drastic step was taken out of consideration for the immensely complex environment of the city in which the finished work was to be appreciated. Deliberately, we tend to favor minimal expressions in art because the premise for appreciation of them is reality itself, which is not minimal at all. The works of Katsuhiko Hibino, which have won the unconditional support of the younger generations in Tokyo, vividly reflects this tradition. His abbreviated style is what we call suku.

Following Hibino's works along the water's edge, the vistior comes upon a huge waterfall. The Fall, by Hiroshi Senju, was produced with traditional paints called iwa-enogu, several hundred kilograms of it. The cascade, in concert with the water on the floor, transcends the border between real space and fictive space. The images that seem to be false actually possess the realistic materiality of minerals and washi (Japanese paper), while the water that seems to be substantial is really false in the images reflected on it. This interctive exchange between the real and the false is the aestheticism we have maintained traditionally, and the dual structure of Benjamin-like criticism can be seen there. In this sense, what is represented in this space by Senju is not a "painting" in the usual concept of an artwork, but nature inself.Only when a work possesses this dimension of nature, can it acquire an infinite sense of time stretching in the direction of both past and future.

The infinite volume of time and space, such as represented in The Fall, is then futurologically compressed by Yoichiro Kawaguchi, High-definition images composed through precision computer graphics synthesize time and space according to the principle of suki, condensing life generated within a computer, In Life City, all formes are expressed in movements, and the substances with which it is made are mysterious and difficult to identify as organic or inorganic, but appeal directly to the senses. Through the experience of realizing it, we are surprised at the perceptions and memories dormant within ourselves. This work is evidence that metaphysical qualities can exist in artificial objects, not only of the age of analog technology but carrying on into the society of digital environments.

Passing by Kawaguchi's city, the viewer comes around to the microcosm of cells by Choi. These clusters of microorganisms collected with the organic material of washi from the soil of various parts of the world liberate from mystery the "living body" obsessed by the concept of evolution in the progress of modernism. The images of the cells photographed here firmly express the impulse of all living things for symbiosis as well as the interactive communication of this impulse that fills our environment. The chaos of life exists not for the selection/elimination process but for the expansion of the positive, gathering process. Each individual cell is a metaphor for contemporary society that, at the same time, can signify its ideal state because the development of its free movement corresponds with our subconscious memory, The critique conveyed here is reexamination of the environment as a living entity, which is exactly what Rikyu sought to communicate in the sukiya style by bringing nature unadulterated into the midst of the city.

The different forms of expression of the environment as a living entity by Kawaguchi and Choi are linked precisely because of the connection between their critiques. Such a critical and perceptual link is possible because at the core lies an absolute and unappraisable chaos of "nothingness" or "selflessness." The metaphor for this mandala-like perception of the universe is the completely empty space that is invariably found in the center of the sukiya (tearoom), as well as in this exhibition site, Precisely because of this "nothingness" void of all worldly values, everything can maintain equal relativity.

Conversely, there ought to be some tension toward the building of relations in each and every detail that symbolizes such relativity. The form depends on this very tension. Kengo Kuma, who is in charge of the space design for the exhibition, insists taht the continuous space using water and complex pathways is needed to visually reproduce the intense relativity shared by these forms. That is the meaning of presenting the complex passages of sukiya.

The architecture, though it is generally classified in the category of design, is therefore just as important as the artworks exhibited in it. The graphic art direction by Ikko Tanaka and the lighting direction by Haruki Kaito are integral parts of the whole. Suki, after all, involves not only free bonds but equal quality of all the elements.

In the movement repudiating modernism, many attempts have been made to interpret the points of convergence between art and design and their relationship. Most of the debate, however, while carried out under the guise of de-modernization, does not go much beyond the outlining of relationships and definition of differences. That very situation shows the gravity and duration of the modernist schism in the world of form. Within that schism, form was deprived of the cultural dimension and converted for the expression of individual egos and their collisions.

Now we cannot even remember for certain what we expected of the art of form. At the end of the last century, William Morris proposed that in order to regain the blessed age of the art of form, we would have to reaffirm not the formulas but the structure of relativity. In this sense, it seems to me, the methodology and the idea of suki that was born in our culture has contemporary relevance in its structural allowance for a complex of vernaculars.

Suki arranges all forms and languages, or space and time, in a mandala like homogeneous universe, and cha (the tea ceremony) puts the process into a continuous and complex performance. This was the method employed by Marcel Duchamp, too, in shedding light on the philosophical processes of form. For that reason alone, it is worth examining against the cultural situation today.

Apart from its ritual origins, the development of the tea ceremony was a product of the cultural confrontation between Eastern and Western cultures.

By evoking the aesthetic of suki, we have achieved the perception ofborderless by subsuming all the constituent forms in the arrangement (agencement) and the process.

Four hundred years since Sen no Rikyu, the world again facing chaos amid the tide of de-modernism, it behooves us to reevaluate the relativity of forms as well as viewpoint from which cultures can be freely synthesized.

Chaji

The act of "preparing tea to entertain guests" was refined and ritualized, adding elements of play, of the arts of performance, and of exacting etiquette to form what we know of today as chanoyu (tea ceremony). Its dimension as spiritual discipline was enhanced through close contact with Zen. Through its games of competitive sensibility, it nurtured distinctively Japanese aesthetics that have been maintained in modern times.

Chaji (serving of tea with a full meal) is the most formal and fundamental performance of chanoyu that provides the special stage upon which the host can perform for assembled guests. It is conducted in a variety of modes depending on the time of day and other conditions. The seven main styles (chaji nanashiki) are shogo no chaji (noon tea), asa chaji (morning tea), yobanashi no chaji ("evening conversation" tea), akatsuki no chaji (dawn tea), hango no chaji (tea following a meal), atomi no chaji ("follow-up" tea), and rinji (fuji) no chaji (extra or irregular tea).

Chaji generally cosists of two parts, the first, shoiri (shoza; first course), and the second, goiri (goza: second course). Before the shoiri, plain hot water is served to the guests, who are then received by the host (mukaetsuke) where they are seated waiting. They then proceed to the chashitsu (tearoom). After the first course, the guests are ushered out to wait again (nakadachi), during which drastic changes are made in the chashitsu before the guests are brought in once again for the goza. It is a four-hour drama of entertainment in two acts.

The season is a very important factor determining the mode of the chaji. The setting and decoratoin of the rooms as well as the menu of the meal that is served vary according to the season, and in all these preparations, the originality, innovativeness, and aesthetic sensibilities of the host are tested.

Soan chashitsu

The chashitsu is the architectural setting for performance of chanoyu. In the history of architecture, a certain type of building generally grows larger and more splendid in the course of its development, but the chashitsu, by contrast, grew smaller and more austere in the process of its refinement. Its ultimate form is the soan chashitsu.

The concept of wabi was originally identified and incorporated into chanoyu by tea men who were members of the Buddhist priesthood. Sen no Rikyu, who studied under them, systematized their ideas and developed their ultimate spatial expression in the form of the soan chashitsu.

The which is small is small, and tht which is large, and it is a violation of common sense to call the small large. However, the soan chashitsu emerged to demonstrate, in line with the teachings of Zen, that we can be awakened to the infinity of the universe and freedom by breaking out of the shackles of conventional views. Rikyu perfected this idea while fully developing an aesthetic sensibility that was all his own.

Machiai

The machiai is a room where guests invited to a chaji gather, tidy their attire, and wait until all attending are present and ready. If the roji (garden leading to the tearoom) represents the space in front of the chashitsu, the machiai should be the waiting room (hikaeshitsu), It is the place where guests can relax while, as they wait, the mental tension in anticipation of the coming chaji builds.

Roji

The roji is the garden through guests move from the machiai to the chashitsu. It is both garden and pathway, but not merely a space to pass through or to appreciate and enjoy. In wabi-cha, the chashitsu is intended to be a neutral space remote from the mundane world, an infinite universe. In this space, every person is required to be an ordinary person (without title, rank, or statsu); to be himself. The roji is a device through which guests expose themselves and become ordinary before entering the chashitsu.

One of the things Rikyu invented is roji zori (sedge sandals used in the roji). All the guests change into a pair of roji zori to move through the roji, so that the sound of the footsteps does not indicate the quality of footwear or the social status of the person approaching. This practice is a natural outcome of Rikyu's effort to perfect the function of the roji.

Nijiriguchi

The chanoyu guest walks through the roji and passes into the chashitsu through the designated entrance, the low nijiriguchi. Rikyu came upon the idea of the nijiriguchi so that a guest would have to crawl to go in and out of the soan chashitsu. Together with the sword rack set in front of the nijiriguchi, it was considered effective as a way of forcing the guest to experience the most practical and direct experience of passage, completing the process of leaving worldly affairs behind and entering the neutral space of the chashitsu, thus becoming an ordinary person. This low entranceway serves not only to force the guest to move into the room in a humble posture, but accentuates the dramatic encounter with the shitsurai (decoration) of the room, particular that in the tokonoma.

Tokonoma

The tokonoma is an alcove for the display of flowers, candle holders, incense burners and other artifacts. It became a fixed part of Japanese rooms during the Momoyama periood, when people began to appreciate fine calligraphy and paintings in the form of hanging scrolls, because it was suitable for displaying a scroll to be appreciated with the piety that had once been reserved for sacred Buddhist paintings. It is therefore usually raised slightly higher than the floor.

In wabi-cha, which was strongly influenced by Zen, the meaning of the scroll hung in the tokonoma is very imprtant. What position and angle the tokonoma, and the scroll within it, will be first encountered by the guest, therefore, is a key question for the entire performance and presentation of the chaji in a soan chashitsu. A great deal of consideration is thus given to the dimensions of the nijiriguchi and the tokonoma, and their positions and derections vis-a-vis each other.