Some Aspects of the Philosophy of Science in Japan

By Hiroshi NAGAI

I

Philosophy in its strict sense had not been in Japan until her mod ern age, which broke out at Meiji Revolution about one hundred years ago. It must be remembered that the proper notion of philosophy has its historical origin in ancient Greece and that its development is performed on the basis of Greek tradition in Western Europe. From this point of view we Japanese have been in quite different circum stances from those of European peoples, whose philosophies, I presume, for all varieties in their character and trend, are united in a common mental circle, so that they are on intimate terms with one another. Of course, as generally recognized, it is an irresistibly clear fact that Buddhism and Confucianism had influenced intrinsically on the mental life of Japanese people for a long time, but their doctrines may not be called philosophic in the proper sense. We prefer to consider them respectively a sort of religious speculation or peculiar worldly Wisdom rather than as philosophy. This state of affairs will be said to be due to the special historical and geographical conditions in which our country was so long situated that we could hardly take any chance of international contact with European peoples and their philosophical thoughts. As the leading and decisive one of those conditions we can especially point out the political and social influences of the feudal

-63- 64 government, which was established by the Tokugawas and lasted for almost three hundred years; its political absolutism strictly prohibited our countrymen living in four small islands from taking foreign informations. But in 1867 the feudal government was overthrown and thus a new age had dawned. Obtaining the liberty of thought and belief 'we opened our eyes to the outer world and began to endeavour to import various kinds of products of European civilization, such as political social institution, literature, art, technology, industry, education etc. Science and philosophy were also not exceptional, and these things were esteemed as eminent representations of the mental activities of Europeans. This consideration caused our admiration for oversea countries. Under these historical circumstances our antecessors in mod ern age displayed vigorous energies to introduce the oversea cultures into their mother country. Yet, in spite of all their endeavour the effects were not so easily brought in the domain of mentality as in that of materiality. Although the enlightened Japan ingeniously imi tated modern scientific technic and could mobilize it in filling up her national power, she could not therefore necessarily comprehend the mental essence of science and philosophy in the Western World. Accordingly, science and philosophy, being abstracted of their bistorical background and necessity, were rather understood in a formal or superficial appearance. Between science and philosophy an inner and inseparable union had always existed in the western history of ideas, where, I believe , science was not only scientific, but also essentially philosophic and the notion of science deeply depended upon that of philosophy . It may be said that the ideal of philosophy as science is the traditional property of the western philosophy and that it is this characteristic that lacks in our own history of intellect. Of course, even in Western Europe the inseparable alliance maintained between them seems to have been weakened gradually. Above all, from the end of the eighteenth century , -64- 65

separated from philosophical foundations science seems to have begun to develop itself in its own technical aspects; yet, science still remains there an object of considerable interest of many philosophers as well as philosophy is universally interested among mathematicians and scientists. The idea of the philosophy of science, I think, is one of the most important expressions of the European intellect. Were this idea abstracted, there would be little space for its principal activity. Taking this into consideration, it would not be so much difficult to understand how the philosophy of science has not grown so naturally in Japan as in the Western World. As a matter of fact, our philosophy is the newly imported one and its history is made ony in the last one hundred years. Hence we have also had few native philosophers originally creative and epockmaking, such as Fr. Bacon in England, Descartes in France and Leibniz in Germany. At the beginnings of our modern age, the western philosophies accepted by our earlier thinkers were those of English empiricism, e.

g. the philosophies of J. Bentham, J. S. Mill and H. Spencer, and at the same time some sorts of French philosophy were welcome. We were mentally instructed and disciplined by those philosophies. The ideas of the western philosophy, however, were not able to be appre hended in their historical connection and essential characteristic; they were rather received as a practical means to social action or individual welfare, for our old custom of thought was still maintained and its inertia deprived us of theoretical activity of pure reasoning. Con fucianism was still the supreme inward lawgiver of our thinking and an antithesis between Confucian doctrine and philosophy, contrasting each other in their main character, could not so easily disappear. This being admitted, it should not be surprised if our advancement of learning was not smoothly and steadily effected. On the contrary, the newly introduced philosophy had: given rise to great confusion for a time, which was promoted with increasing information about. the various doctrines of the western, philosophy. In fact, there appeared

-65- 66 many Japanese translations of the works of western philosophers, and up to present days we have had the translations of their chief works; even those of Greek and mediaeval philosophers, especially the dia logues of Plato and some works of Aristotle. It would not be unjust to say that of the eminent works of European thinkers there is none which has not been translated into our own language today. The influence of English empiricism was not lasting; the philosophy of German idealism was soon introduced, too, and after a conflicting discussion on the superiority which was expected to belong to any one of them, the latter won the day. What is the significance of this practical fact? Why was German idealism easier to understand than English empiricism? Was it not due to the historical tradition of our thought which had been based on a certain metaphysical speculation of Buddhism? We can really find that many philosophical terms of the idealism used in translations were borrowed from the words of Buddhist scriptures. In addition to this, we might peculiarly premise even the complicated conditions of our society on which our traditional art of thinking was built up. Nevertheless, so far as these conditions are concerned, a further investigation will be postponed to be left to another penetrating analysis. For the present, it is one of the most important facts for us that German idealism has been really most fa miliar with our modern thinkers and that it has enabled them to satisfy their desire to gain acquaintance with philosophy itself. After this clearing of the ground, we can explain the strange situation in which our academic philosophy has been so long determined; during the last fifty years or so German idealistic philosophy has held the leadership among our researchers, and at distinguished universities in Japan most students have been interested in German philosophy and have inquired into the problems of it. It will be no exaggeration to say that the majority of our leading philosophers owe their thought to German idealism today, e. g. the philosophy of Kant and that of Hegel. And yet, this trend is set forward by Neo-Kantian philosophy

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and even by the phenomenology of E. Husserl in some different con nection.(1) This statement may be surprising, but we shall scarcely

be able to neglect this obvious fact; we must notice that this salient fact was necessary at least until our defeat in the Second World War. Although a large number of explanations and translations of the works of the western philosophers were issued, which, as previously professed, were not always restricted to those of German philosophers, our own philosophy did not make much advance. This granted, what next? What is the real meaning of our endeavour in the last one hundred years? Have we not been only subject to the imported western philo sophy? These questions are too grave to be overlooked. If the subjec tion, however, were all for us, I think we should feel far more uncer tainty about our own abilities to philosophizing than we actually do feel. Even if we felt the uncertainty, we should be confident in our -selves . The justification of this confidence might not be unreasonable. We agree with saying that it is difficult to find any creative philoso pher among us, but it does not mean that there exists none; in fact, -we have fortunately one philosopher of that sort , who is the most celebrated and unusual thinker in modern Japan. His name is Kitaro Nishida. Born at a small village in the northern part of Japan in 1870, he -was Professor of philosophy at Kyoto University from 1910 to 1928 , and died in 1945. His work was immense, his thought was original or radical, and his influence was so fundamental and universal that our philosophical climate was determined by him almost for thirty years.(2) In addition, he is also the founder of the Kyoto School and his system of philosophy is called the Nishida-Philosophy (in Japanese the Nishida-Tetsugaku; Tetsugaku here means philosophy and it must be

(1) Kant's chief works are translated into our own language respectively by different scholars and it is the same with Fichte, Schelling, Hegel and other German philosophers of modern age. For instance, Kant's Kritik der reinen Vernunft is admirably translated by T. Amano.

-67- 68 noticed that this word as a term in a translation is not found in old Japanese). But we must now restrict our survey to what is refered to the philosophy of science in the principles of Nishida; so far as it is concerned we will explain the fundamental ideas of his philosophy. A Study of Good, his first principal book, was published in 1911. In this book which is generally well read for a long time among us, he declared to maintain the view of the philosophy of pure or immediate experience. On the one hand, of course, this idea was borrowed from William James, to whose philosophical principles he devoted himself. On the other hand, however, it was derived from his Zen-Exercise, a. kind of ecstatic practice usually held by many Buddhists of the Zen-Sect in Japan. We cannot neglect that the motive of his thinking was essentially religious; his religious mentality is evident in his discussions of reality, knowledge, human life and other universal problems of philosophy.(3) Hence it might be true to say that an inner union of the western philosophy and the Buddhist spec ulation was performed by him for the first time in our history of intellect and that thus our own philosophy had begun to develop itself on its proper ground. If it proves to be the case, what is the so-called pure experience? According to Nishida, pure experience must be the most fundamental and immediate principle of philosophy, on which not only the true

(2) His complete works of 18 volumes was published after his death from 1946 to 1953 (Tokyo, Iwanami) . Some of his papers were translated into German, but the most part of them has never been translated into Europeann language, hence his thought, I think, is little known among European people . Among his earliest friends we can find Sakae Kimura , a well known. physicist, and Daisetz Suzuki, a famous religionist in our country; above all, the latter affected the inner life of Nishida (cf . T. Shimomura, Nishida. in His Youth, 1947). (3) Of course, it is worthy to mention especially that in his youth Nishida. had read through almost every kind of works of the western philosophers , the titles of which were written down in his diary; he was not only a radical thinker, but also an extensive reader .

-68- 69 reality depends, but also does all our knowledge. In other words, it is rather reality itself and at the same time knowledge itself. In this sense, therefore, he urges that it precedes ourselves and not vice versa. Then pure experience may be said to be the primitive unity going before any subject-object differentiation, because object is already that which stands against subject of knowledge and in the opposite direction subject must presume beforehand anything which it intends to know. None of these alternatives ought to be the first principle of philosophy. Since subject and object are both in an alternative relation, each of these is the derivative and not the primitive. Here Nishida orientates a radical empiricism, which is neither a mere empiricism nor any kind of idealism. In his later days sometimes he called it the absolute positivism or realism, too. And thus pure experince is the primitive fact ,of the world , which connot be deduced from anything else and yet can set forth every differentiation in the world of itself; it is nothing but an intuitive datum of our experience. All the defferentiations of the world are considered as self-developments of this unique datum, which is in turn reduced into the greater unity of reality through those differentiations. Therefore, reality in itself must be always an infinite process of unity through all its differentiations, while the more advan ced differentiation, the greater unity. In this relation it may be said that reality and appearance are ultimately the same thing. We can see here something that is similar with the doctrine of Hegelian dialectic or that of coincidentia oppositorum in the metaphysics of Nicolaus Cusanus, because pure experience is in its essence nothing else than an identity . of contradiction, which, according to Nishida, is only to be intuited immediately. But here intuition has nothing to do with aesthetic or mystical one; it is rather ontological in its nature. Such was the starting point of Nishida. He had elabolated unceasingly his initial thought to his last day. The dialectic nature of pure exper ience was deepened to that of acting intuition, one of the most impor tant ideas of the Nishida-Philosophy.(4) He maintains that every

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knowledge, of what kind it may be, is founded on this original intui

tion, which must be the organon of understanding of the true reality.

Action is in its ontological character temporal and intuition is in the same way spatial. It must be remembered here that his concept of intuition is principally distinct from that of Kant and even that of

Bergson. Acting intuition, therefore, is dialectic identity of time and space in its concrete meaning. Moreover, if we scrutinize the logical form of this intuition, we can find the principle of identity of absolute contradiction, which is also one of his most important ideas. Can we understand how absolute contradiction will be identified ? There is indeed nothing commensurable between two poles of this contradiction. How does it happen that these absolutely contradicted poles must be coincided with one another in their desperate opposition? So far as we concern with the usual principle of identity, we are not sure of answering this question. Looking straight at this difficulty, Nishida seems to introduce illuminatedly the concept of absolute nothing (it would better be translated into German, das absolute Nichts, than into English), which originated in the old Buddhist speculation. We should now say that the principle of identity of absolute contradiction is the logic of acting intuition itself, which Nishida calls the logic of place or field (in Japanese, Basho). In addition, the concept of place is

ontologically extended to that of historical world, the most concrete and actual world, where we are born, live and die. We individuals

are ontologically considered as self-determination of the world, and we are all the creative elements of the creative world. Again, there must be

the logical relation of identity of absolute contradiction between the

individuals and the world. We ought to hold that his meditation on

(4) I am afraid that acting intuition may be too strange to perceive in its diction; it is indeed not easy for me to translate this term into English. It should here be understood by the translation that action is incited and put on by intuition, and intuition is in turn enlaged by action simultaneously; it is of dialectic nature as such a thing.

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this subject has an affinity to that in the monadology of Leibniz, whom Nishida esteems exceedingly.

Being a systematic thinker Nishida investigates the principles of the philosophy of science. He seems to have a considerable talent for mathematics, in which he is at least interested. 'Understanding of Mathe matics and Logic' (1912), a paper on the philosophy of mathematics, is found in his earliest documents.(1) But, in Intuition and Reflexion in Self-Consciousness (1917), his tremendous book, he exerts all his powers to explain the basic principles of mathematics and science from his standpoint. We can see that he is there much influenced by Fichte and H. Cohen. In fact, he often refers to Fichte's idea of Tathandlung and Cohen's logic of Ursprung. The term of self-consciousness is used here not in a psychological sense, but in a logical and ontological one, which has a sort of affinity to that of Fichte or Hegel. Mathematics is neither a product of mere intuition nor of reflexion; mathematical knowledge is rather composed of those two moments which are oppositely distinguished from each other, because intuition is simulta neous and reflexion is successive. Then, if these two opposite directions are to be united, we ought to demand a higher and more fundamen tal principle of knowledge. Nishida now assumes that self-conscious ness alone will satisfy the demand; it is regarded as the most funda mental principle of an agreement or assimilation of the object with the thinking subject. And thus self-consciousness, uniting intuition and reflexion, develops itself productively. An infinite process in the system of mathematics as a dynamic unity of self-consciousness will be completed in this way. This assertion, however, as it may be suggested, is likely to fall into a sort of subjectivism.

As a matter of fact, his thinking was to some extent under the

(1) Nishida, Worlds 1 st Vol., 250 sqq.

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influence of Neo-Kantianism in those days. It is verified by the fact that Contemporary Philosophy of New Idealism, his book on Neo - Kantianism, was published in 1917, the same year when the above mentioned book on self-consciousness was issued. But it is beyond dispute that Nishida's main theme was and has been nothing but objecting against every kind of subjectivism; self-consciousness is no more individual, but rather universal to him. In other words, it must be rather the constructive principle of the world. This being true, mathe matics is to be considered as a formal development of the world; the world now again goes before subject-object contradiction. Upon this we may realize that self-consciousness is of the same nature as that of pure experience or acting intuition. The world has various forms of development effected by the system of self-consciousness, so that it is a system of various worlds in itself; the world of mathematics must be one of these worlds.(2) The world of nature or the so-called empirical world must also be founded on the system of self-consciousness, since the knowledge of physical world cannot be reduced to mere sensations or perceptions. It may be said that self-consciousness as a unity of value and being, i. e. meaning and fact, enables us to have the knowledge, of the external world. Therefore, we can see that Nishida held neither empiricism nor idealism; he intended to unite, as he professed, Bergson's intuitionism and the transcendentalism of Neo - Kantians in his creative system of self-consciousness. With regard to the philosophy of science, the above-mentioned work is one of his most important issues. But we do not consider his opinion more in detail. In his later days he discussed on various problems of mathematics and natural science from his standpoint of the logic of place or identity of absolute contradiction, where mathematics and science were considered

as the abstract and formal expressions of the creative world .(3) The creative world develops itself according to the logic of place , which is

(2) Nishida confesses in the preface of his book that he was affected this . view by J. Royce's The World and the Individual (Vol . I; Supplementary Essay).

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the necessary form of self-determination of the world. Hence this world is also logically called the dialectic universal by himself. For all his efforts, however, we cannot help confessing that the effects of those are negative or implicit. The philosophy of science was not necessarily cultivated by Nishida in its proper region. Upon this we have a sufficient reason to call for the name of Hajime Tanabe, who was also Professor of philosophy at Kyoto University as Nishida's successor from 1919 to 1945 and is now working briskly as one of leading philosophers in our country. At first under the influence of Nishida, Tanabe devoted himself to a critical explanation or foun dation of the knowledge of mathematics and natural science. In exe cution of the task, he held the view of critical philosophy of Kant, and supporting the viewpoint of Neo-Kantianism he declared that the subject of the philosophy of science is nothing but critique of the scientific knowledge. Of course, he was not wholly subject to Neo - Kantianism, but being a most acute critic he had an intention to gain the principle of his own critical philosophy. Nevertheless, we should say that in spite of his intention he was a friend of Neo-Kantians in those days; his leading ideas were evidently supplied from the criti cism of Marburg school or Baden School. In fact, he was affected by the philosophy of H. Cohen, and when Tanabe published his Philosophy of Science (1918), a most elaborated and systematically well 'arranged book, our endeavour to build the philosophy of science really began. Tanabe also translated Poincare's La valeur de la science into Japanese. It will be perceived how he is learned in mathematics and natural

(3) He issued many papers concerning the principles of mathematics and natural science as follows: ' Experiential Science', 1939. ' The Physical World', 1944. 'Space' , 1944. ' Logic and Mathematics', 1944. ' Philosophical Foundations of Mathematics', 1945. 'On the Principle of Life , Philosophy of Biology', 1945. These papers are collected in the 9th and 11 th volumes of his works.

-73- 74 science. When we become aware of the fact that there are few philo sophers learned in science in our country, this cannot be too exaggerated; he is no doubt an eminent thinker being worthy to be reckoned as a philosopher well acquainted with science. In this sense his philosophy of Science is an epockmaking monument in our history of the philoso

phy of science. Furthermore, this book was followed by his second book, A Study of the Philosophy of Mathematics (1925), in which he urgued scrupulously the principles of mathematics. From his critical standpoint much depending on H. Cohen and P. Natorp, he constructed a system of the philosophy of mathematics and contributed to advance ment of it. We will explain some of his chief ideas.

In the first part of his book Tanabe gives the philosophical foun

dations of mathematics. At first, he discusses the method of the phil osophy of mathematics and claims to adopt the viewpoint of transcen dental-logical development of number concepts, where natural number is the most basic. Tanabe asserts that the so-called transcendental

method as developmental understanding of knowledge is the only one way by which the fundamental concepts and axioms of mathematics will be logically founded and synthetically constructed. Therefore, the

transcendental-logical principles of mathematics is more concrete than those of logicism or mathematical logic which is held by B. Russell and G. Frege. Such is his method. From this point of view he makes the concept of natural number clear and then gradually advances to further explanations of the concepts of other numbers, such as negative,

fractional, irrational and imaginary. The concept of number grows more and more universal in the process of this development. In the

procedure of these arguments the principle of infinitesimal calculus is founded, too. Here Tanabe accepts the theory of infinitesimal of H.

Cohen who considers it as intensive quantity generating continuum,

and he sees the essence of the transcendental thinking in it. So far

as this is concerned, Cohen's presumption must be esteemed superior

to that of Russell. Defending Cohen against Russell he dares to say

-74- 75 that Cohen's ideas concerning the relation between intensive quantity and physical reality have an everlasting significance. With regard to the infinite, he touches upon the profound problems of the set theory erected by G. Cantor, and after explaining some aspects of transfinite numbers he concludes that the theory of infinite set is founded on the property of our thinking and the inner fact of consciousness. But it may be remembered at the same time that a system of transfinite numbers as self-representative system is not only expression of the nature of our consciousness, but also that of the true reality. And then, according to Tanabe, a cardinal number expressed as alef zero is nothing but representation of the whole process of self-consciousness. In this system it goes a cardinal number before an ordinal, and a transfinite ordinal number co corresponding to alef zero is an ideal limit of self-consciousness. And so transfinite numbers are possible only at the ideal limit of construction of our thinking; the existence of the manifold which is really possible to think of must be restricted to that of finite natural numbers. The theme of the second part of the book is logical foundations of geometry, where the fundamental concepts of Euclidean, projective and non-Euclidean geometries are explained. Now, again, his view is based on the same principles as those in the preceding arguments of arithmetic and analysis, and he concludes that geometrical space, how ever abstract it may be, ought to be reduced to the constructive images produced in the logical thinking of transcendental subject. Consequently, the truth of geometrical knowledge may be ascribed to the transcendental ideality of space in itself. However, it must be noticed that there are some defects not to be overlooked, which are pointed out by himself. Firstly it concerns with his methodology; above all, he has nothing of the practical meaning of the so-called axiomatic method in modern mathematics which D. Hilbert proposed. Tanabe confesses that there exists much to supply in his understanding of this method. Moreover, the philosophical significance of ideal and

-75- 76 complex numbers is there still untouched; he promises to complete his system some day.(4) And besides, the problems of foundations of mathematics awakened by the intuitionism of Brouwer and H. Wey1 are not yet taken into account, and he also does not thoroughly inquire concerning an inner relation between non-Euclidean geometry and

Einstein's theory of relativity. After these masterly treatises on mathematics and natural science Tanabe devoted himself to the establishment of his own principle of philosophy, which would be extended to almost all the problems of philosophy and justified by their explanations. Although he was formerly under the decisive influence of Nishida he now began to create his own thought, which overcame the Neo-Kantian subjectivism. What is then the principle of his philosophy? He calls it absolute dialectic himself. As we see, Nishida created his own dialectic which was called the logic of identity of absolute contradiction or that of place. Although Tanabe was under the influence of Nishida and his absolute dialectic had something similar to Nishida's logic a fundamental distinction soon became appearent, and he rejected the latter with a will through a severe criticism. Where is then the importance of the criticism? Tanabe prohibits himself from acting intuition, because it utterly destroys the essence of dialectic which is based on the real contradic tion of time. Since acting intuition should be rather considered as a sort of spatial intuition it cannot present the true identity of real contradiction, but escapes from it. We must maintain the essence of dialectic in the contradictory characteristic of time itself. And if it proves to be the case, the logic of place would be of nature of disgust ing intuition. Consequently it should be considered ultimately as a kind of identity-logic. In addition to this, acting intuition is aesthetic or mystical because of its spatiality; hence action in its strict sense would be weakened and annihilated in spatial intuition. How can we

(4) This promise, as we shall see, is fulfiled in his book recently published.

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then grasp the real meaning of action in its very activity? Answering this question Tanabe proposes that true action must be of nature of absolute conversion through time; time is essentially most dialectic in the radical denial of itself, which he calls absolute denial or das absolute Nichts. In this sense true action means absolute mediation itself, in which the past and the future ought to be united dialectically through mutual conversion. And thus the present is always the real centre of action; action is essentially temporal, yes, time itself. In those senses the subject of true action is considered as the actor of absolute mediation. We can say that his absolute dialectic is the logic of this mediation. The so-called absolute denial is the real logic of absolute mediation itself and at the same time that of true action. It is in this way that Nishida's logic is replaced by the logic of absolute mediation, where time is superior to space and is necessarily real for its own sake. On these grounds Tanabe is now esteemed as the greatest thinker succeeding Nishida in our country, and his philosophy is naturally called the Tanabe-Philosophy today. Whereas Nishida subordi nates action to intuition (spatiality), Tanabe seeks for action in its& activity (temporality), excluding intuitive and contemplative moments, Therefore, his dialectic is the actual logic of absolute mediation; both mediator and mediation are ultimately the same thing in their dialectic conversion. As he really confesses it has a more concrete meaning than Nishida's logic. But Tanabe's philosophy of science was postponed for a time, since he became more interested in other problems of philosophy. Neverthe less, it remained serious in his mind, and it may be proved by his, book titled Between Philosophy and Science (1937), wherein were collected. his philosophical papers on natural science, especially on the relativity theory and quantum mechanics.(6) He scrutinizes the relation between

(5) Of these papers we have to mention 'The Philosophical Meaning of Quantum Mechanics' and 'Matter Concept in Greek Philosophy and New Physics'.

-77- 78 the fundamental concepts of new physics and the ontological essence of his absolute dialectic. After the Second World War, however, his dialectic was more deepened and his philosophy of science was more elaborated. He proposed his general viewpoint in his lectures, Intro duction to Philosophy (Vol. III, 1950) and in particular discussed some basic problems of classical mechanics in his paper, 'Dialectic of Classical Mechanics' (1949). But he interprets the philosophical meaning of the theories of new physics by his dialectic; this is now closely connected with his world-view of radical historism, and the word of radical here means that dialectic character of conversion of temporal action. The structure of historical time is really dialectic in its nature; he calls his standpoint absolute criticism, too. It is natural that the title of his recent book is Development of Mathematics in Historism (1954), which must be perceived in the proper sense of his absolute-critical dialectic. The book was followed further by his supplementary trea tises: Inquiry into a New Methodology of Theoretical Physics (1955) and Dialectic of the Theory of Relativity (1955).

Tanabe now reflects on his earlier ideas of philosophy of mathema tics and natural science and overcomes the various defects involved in them, which we fomerly noticed. We can find here that he confronts with the difficult problems of foundations of mathematics and new theoretical physics. At first, the formalism of Hilbert and the intuition ism of Brouwer are criticized from his viewpoint of historism. He makes us clear that there is certainly an intuition on which mathema tics is grounded. This intuition, however, is determined by radical historism which is said to express the essential characteristic of actual world. Mathematics cannot escape from the historical interpretation of the actions of the mathematicians who really construct it, because they are determined by the historical development of mathematics in their own constructive activities. It must be the same with physics.

As to mathematics, on the one hand, the axiomatic method is too for mal to grasp this truth. But on the other hand, the intuitionism is

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too narrow to realize the same truth. Above all, the formalism of Hilbert must have something necessarily to be supplied with radical historism or dialectic of absolute mediation, because there must be active conversion between axiom and intuition in mathematics, which is deep -rooted in the historical interpretation of history itself. From this point of view he attempts to manifest the ontological essence of topology, seeing a new method of the philosophy of mathematics in it, because topology is like a mathematical expression of historism. And thus he proposes a new idea of the topological set theory basing on historism. Besides these discussions he gives a philosophical explanation of the concept of . Dedekind section and objects against the foundations of mathematics by Z. Suetuna, one of our leading mathematicians, whose viewpoint will be soon explained. In his first treatise on theoretical physics Tanabe points out the significance of the theory of functions of complex variables and its topological characteristic in theoretical physics, because the four-di mensional world in the special theory of relativity demands the intro duction of imaginary numbers. Considering the inner and essential relation between the mathematical forms and the physical world, he gets a new insight into the physical theory of relativity (of Einstein and Minkowski), where time is represented with a imaginary number. The physical meaning of the theory of functions of complex variables may be appreciated by this reflexion, and he favours here Riemann's ideas. In fact, he points out philosophically that there exists the necessary correspondence between the theory of functions of complex variables and the special theory of relativity. If this correspondence is to be explained by means of philosophical thinking and such a task is worthy to perform, the logic of historism should be the unique way to be followed. As historism is dialectic in its nature, it might be concluded that the theory of complex numbers is also dialectic in its philosophical structure. In this sense it can develop the real meaning of the physical world which is represented in the relativity theory.

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The unity which we expect to be accomplished between the relativity theory and the quantum theory will get some clue philosophically in this meditation, too. Accordingly, he promotes his ideas more concretely in his second supplementary treatise. And now he investigates, how the special theory of relativity principally relates to the general theory of it. According to Tanabe, the latter is not a simple generalization of the former; the relation of those must be mediated by dialectic. Upon this it seems reasonable to say that there exists really the dialectic of absolute conversion in the development of the relativity theory itself. This granted, we can probably get a new perspective of the

quantum theory, where a concept of quantum of time plays an im portant role. Thus again he repeats the philosophical excellence of the mathematical theory of complex numbers which may be applied to new

physics. The real understanding of the present-day problems of natural science will be taken in such a way, and this art of understanding alone will make it possible to grasp the essence of human knowledge of natural world. But we may spare the detail of his thought.(6) For the present we must content ourselves with his notable name in our history of the philosophy of science.

We have now examined the main currents of historical development

of the philosophy of science in our country. We departed from a critical discussion of the concept of philosophy gained by the earlier

thinkers of our modern age. I think it must be a necessary preparation

for our treatise.

As to mathematics and natural science we have had many eminent

specialists, but they have not always got philosophical insight into

the intellectual essence of them. Nevertheless, fortunately we are

(6) A more precise English explanation of these treatises is given by the author in another place (cf. H. Tanabe, 'Dialectic of the Theory of Relativ

ity, The Journal of Philosophical Studies, Vol . XXX‡Z, No. 12, 1955).

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‡V 81 somewhat rid of the defect of our mental attitude by the works of some sensible thinkers among us; they paid attention to the history of science and devoted themselves to historical investigations of philo sophical 'ideas of science in the Western World. From this viewpoint their activities contrast with the efforts of Tanabe who has constructed a logical system of the philosophy of science. It must be remembered that the historism of Tanabe is nothing but a systematic principle which is not historical in a general sense, but rather logical. On the contrary they attach importance to the very history of science and its ideas. For instance, G. Miyake, a keen philosopher at Kyoto University, has followed the fundamental ideas of mathematics (the infinite, continuum etc.) and natural science from ancient Greece to the end of the eighteenth century, and has analysed the basic characteristics of the western philosophy inseparably combining with those ideas. Formation of Science and the Natural World, his great book, was published in 1940, in which he collected his significant papers produced in many years. And his second book was A History of Ideas of the Philosophy of Mathematics, which appeared in 1947.

As to mathematics in particular and natural science in general, we can find an elegant book, Philosophy of the History of Science (1941), whose author is T. Shimomura. His argument is as follows. Mathematics is used to be considered as a formal science. This formality, however, is not a primitive feature of mathematics, but a derivative; there must exist a philosophical background foregoing to the establishment. of the so-called formal mathematics. It is indeed true that in ancient Greece a logical and philosophical reflexion on. the fundamental concepts of human knowledge went before the accomplishment of mathematical science. The logical investigations cultivated by Socrates, Plato and Aristotle was a necessary condition of the formation of Greek mathe matics which converged into Euclid's Elements. This is also essentially the same with modern mathematics. Upon this Shimomura exemplifies his presumption in detail throughout the whole history of mathematics

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and justifies his theme from the viewpoint of history of mind (Geistes geschichte). Although mathematics is abstract and formal in itself it must be considered as an expression of the histroical mind and inter preted as such a thing. Hence formation of mathematics as science (i. e. history to mathematics) was the most individual event of European history of ideas which inherited the Greek mentality distinguished obviously from our own. For that reason it may be said that the yenri method discovered by Seki Kowa (1642-1708),(1) one of our greatest mathematicians, is principally distinct from the method of Newton and Leibniz. For all his technics of high degree, Seki could never give any definition of a circle. Consequently our modern mathematics is also an imported one in our new age; it is wholly independent of Seki's idea. The same argument is further found in Shimomura's Formation and Structure of the Theory of the Infinite (1944), which scrutinizes the historical development of the theory of the infinite and, above all, displays the philosophical structure of the infinite represented in the set theory of Cantor. He disputes the serious prob lems of foundations of mathematics, criticizes the intuitionism of Brouwer and the formalism of Hilbert, and then prefers the latter rather than the former. The formalism, however, is not necessarily sufficient to a solution of the problems, so that he proposes to remake its standpoint. From his point of view, Hilbert's idea which should be completed in an ideal form must be that of symbolism, which is essentially distinct from a mere formalism. A symbol which he wears in his mind might be an expression of the world which is possible and actual at the same time. Thus his symbolism, as he really professes, is rather ontological or metaphysical. He is confident of that in this

consequence he can gain a new view of foundations of mathematics . Historical researches of science have also been made by others. We can mention K. Ogura, J. Sugai, S. Yajima, Y. Kondo etc . Their

(1) Cf. F. Cajori, A History of Mathematics, 80. Cajori calls it yendan; this statement is not suitable.

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works are more positivistic than those of the preceding researchers and intend to describe the scientific facts of the past and lay much stress on the practical and technical factors in the historical develop ment of science; the social basis of science is also held in esteem. For that reason it may be noticed that an analysis of the philosophical ideas which caused the development of science is not sufficiently given in their works. Ogura is well known by his studies of the social history of mathematics, in which he displays his erudition. Yajima has studied in the history of modern physics, and Kondo has also given his works on the history of mathematics. A History of Geometrical Thought (1946) and An Introduction to History of Mathematical Thought (1947), Kondo's diligent works, have contributed to advancement of historical studies

of science. The works of others, among whom we can find H. Mita and M. Hara, may be comprehended in those tendencies.(2) As a gen eral description of the whole history of science, S. Honda's History of Scientific Thought (1955) is worthy to remember. As to the present writer, he issued Formation of the Modern Philosophy of Science (1955). He researches into the inner and inseparable unity of philosophy and science from the Renaissance to the end of the eighteenth century and gives an account of the philosophical basis on which modern science really developed in its earlier days. He lays importance on the ontological-constructive elements of mathematics, which played an essential role in building up modern science, where mathematics was not a mere subjective form of knowledge, but did exist as an objective and creative form of being, i. e. a sort of world-view as the so-called universal mathematics. Yet, this idea of mathematics decayed in the last half of the eighteenth century, and philosophy began to separate from science, while science itself was about to advance independently. And we can see a reflexion of that inclination in the transcendental

(2) It must be remembered that the Association for the Study of History of Science was previously established in our country and that the Journal of History of Science has been issued.

-83- 84 philosophy of Kant. We may owe one of the difficulties involved in the present-day idea of the philosophy of science to the philosophical attitude of Kant. Therefore, the philosophy of Kant ought to be dis puted in preparation for a pursuit of a new idea of the philosophy of science today. Such is a chief motive of the present writer.(3) What is the real meaning of the philosophy of science? It is a fact that we cannot answer this question without disputation. The philo sophy of science is really not only a matter of philosophers, but also that of scientists; it will interest scientists rather than philosophers.

We may rather say that science does demand a sort of philosophy when its foundation becomes problematic and that any speculative or tran scendental philosophy has nothing to do with it. From this viewpoint, the philosophical thinking of mathematicians or scientists will really be much instructive for us. We see how much they have contributed to the idea of the philosophy of science in the Western World. But in our country, the matter is not all the same; scientists in general do not take much interest in philosophical problems. However, some mathematicians and scientists are exceptional, and we can find that in the last twenty years or so they have made an effort to explain the fundamental problems of mathematics and science. Above all, Z. Suetuna, one of our most ingenious mathematicians today, has radically discussed the profound problems of foundations of mathematics. Suetuna introduces the idea of acting intuition into his mathematical researches, which is derived from the Nishida-Philosophy. In Mathematics and its History (1944) and Mathematics and Logic (1947), his aspiring works, Suetuna considers the essence of mathematics in its historical development and arrives at a conclusion that there exists fundamental intuition which is really acting at the basis of mathematical thinking. But this intuition is self-contradictory in its nature, and yet on this

(3) He issued A Study in Leibniz' Philosophy of Sciences (1954), in which he explained the ontological principle of universal mathematics of Leibniz in detail.

- 84- 85 ground alone mathematical thinking can develop itself creatively. Acting intuition, an original unity of obvious contradiction, therefore, cannot be reduced to any logic; being an evident fact of mathematical thinking, it goes before logic. From his point of view, action is temporal and intuition is spatial, and mathematical thinking is based not only on action, but also on intuition; it is temporal and spatial at the same time. Consequently, mathematics should not be an oper ation of mere abstract forms deprived of any content; it must always have a concrete meaning to be determined by acting intuition, which is indeed the constructive principle of real thinking of every mathe matician. But intuition does not here mean what is usually meant by the so-called intuitionists, for it is wider than mere intuition. On the contrary, however, Suetuna protests against the abstractness of the formalism, too, restricting mathematics to that which has definite contents verified by acting intuition. He calls it the real mathematics which may be extended to the general analysis. As to mathematical induction, he distinguishes a concept of 'some' from that of 'some definite' and prohibits the former from absolute application. Thus he proposes that natural numbers and the linear continuum must be the elemental or ultimate facts on which the real mathematics depends. The whole of natural numbers can be comprehended as a set of definite elements based on acting intuition; otherwise it could not be the completed whole. In fact, mathematicians always hold the system of all natural numbers as a finished entity, and it is an evident truth. This evidence does not depend on mere temporal-serial action, but does on acting intuition which is temporal-spatial or serial-existent. Accordingly Suetuna dares to say that the whole of natural numbers and the linear continuum are the very bases which should sustain all mathematics in concreto. Mathematical existence in its strict sense must be always considered as a set of definite elements founded on those bases. Now he aims at a system of the real mathematics distinguished from the formal one, and by practically improving of its meaning he

-85- 86 claims to reintroduce the law of excluded middle which the intuition ists have banished. In Foundations of Mathematics (1952), his notable book collecting his papers on the basic problems of mathematics for several years, he searches for the constructive principles of real math ematics in concreto by means of his own philosophy. We can find there the originally significant meditations on natural and real numbers, sequen ces and functions, continuous functions, and integral and differential.

How can we found the continuum and the whole of real numbers?

Suetuna answers this perprexing question as follows. A number is con sidered as a finite or infinite decimal; the infinite decimals which do not represent rational numbers should be called irrational numbers.

Thus the continuum of numbers or real numbers are to be defined as the totality of infinite decimals (0. a1, a2, a3, •c). The matter would be better expressed if we observed it on the so-called number

axis. Then the problem is: how can we really hold the whole process of an infinite decimal? In other words, how does it really happen that we are convinced of an existence of the limit of sequence ‡T1, ‡T2, ‡T

3, •c , In, •c of intervals on the number axis, each of which is contained in the preceding one? The limit is nothing but a point to which these intervals do converge. Generally speaking, how can we really see an infinite process coming to an end? So far as we adhere to the intuitionistic viewpoint, we cannot arrive at the existing limit.

Then, we are forced to see the whole throughout the infinite process simultaneously. Acting intuition alone which underlies our mathematical thinking enables us to practise it; otherwise an existence of the limit

would be only possible and not actual. In this way, indeed, we can

transcend the finite standpoint and grasp the very existence of the

whole and the continuum of real numbers represented as infinite

decimals. It can be said in this sense that infinite decimals are real

numbers. Consequently the real number system, which expresses the

property of acting intuition itself, is temporal and spatial; in this

system rational and irrational numbers are contradictorily united

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through their distinct opposition. This is the reason, I believe, why Suetuna proposes to adopt the linear continuum and the whole of

natural numbers as his bases in foundations of mathematics.(4) Besides Suetuna, of course, there are some eminent mathematicians who try to seek the philosophical characteristic of mathematical

science. It must be remembered that they have contributed much to advancement of our philosophy of mathematics. S. Iyanaga published his refined work, The World of Pure Mathematics in 1942. Elemental Concepts ofModern Mathematics, his most significant book, was also issued in 1946, to which we owe much of general understanding of modern mathematics. Y. Yoshida is distinguished for his aesthetic essays on mathematics and Y. Akizuki is celebrated as the author of An Outline of Modern Algebra (1941). K. Ono's What is Mathematics P (1943) and S. Shiraishi's Philosophy of Number and Continuum (1943) are also the remarkable documents. And recently K. Nakamura has inquired into the history of modern mathematics and has practically clarified the real thinking of earlier mathematicians, such as Descartes, Pascal, Leibniz and others. In addition to this, he is well known among us as the excellent translator of Hilbert's Grundlagen der Geometrie. As to historical essays, especially we cannot oversee Topics on the History of Modern Mathematics (1933), a brilliant issue of T. Takagi who is our world-famous mathematician. It is really one of the most prominent books full of deep insight in our country.

But, we must remember that S. Kuroda, a most keen mathematician,

(4) His inquiry concerning this problem will be found more precisely in the present journal. His German paper was already printed: Suetuna, Uber die Glundlagen der Mathematik, 2. Mitteilung, Proc. Japan Academy 27, 1951. Tanabe who utterly rejects the so-called acting intuition has criticized the viewpoint of Suetuna in his Development of Mathematics in Historism, and Suetuna has responsed to the objection. Corresponding to Suetuna's theory S. Ohe has studied in the epistemological problems of mathematics and natural science. His General Theory of Knowledge (1953) is an interesting book, in which he has set forth a new idea.

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has also made a great effort to advance foundations of mathematics. He

follows the intuitionists and tries to reconstruct formal logic by means of intuitionistic logic. According to him, mathematics has its proper

intuition in itself, which cannot be deduced from formal logic, hence

mathematics ought to be built up by its inner laws which are found out as generally evident in real activities of mathematical thinking.

Thus formal logic must be meditated in the natural way, that is to say, in the intuitionistic way. On these grounds he intends to introduce

the intuitive and formal modus for each logical operation, and by exam ination of each logical inference he concludes that the double denying is identified with Widerspruchsfreiheit and the law of exacluded middle with Brouwer's law of absurdity of absurdity of the law of excluded middle. Upon this the understanding of formal logic may be changed; separation of formal logic into intuitionistic and formalistic (classical) logic will no more be maintained. There must be only one formal logic which may be called intuitionistic in the historical diction, if it contains even the formalistic logic. In Mathematics such an expansion of the intui tionistic mathematics is really possible. Hence Kuroda asserts that, by considering all the modi of words as formal, the number theory and the infinitesimal calculus will be constructed in the intuitionistic mathe matics without any alteration of other inference procedures. Therefore, the intuitionistic mathematics will comprise the greater part of classical mathematics, such as theory of groups, theory of topological space etc.(5) Generally speaking, our physicists, I suppose, do not feel so much interest in the philosophy of science as do our mathematicians . But once J. Ishiwara and T. Terada had endeavoured to popularize the

(5) His papers on these researches are found in Science (Kagaku) and Foundations of Science (Kisokagaku). Above all, we can refer his German paper: Intuitionistische Untersuchungen der formalistischen Logik, Nagoya Mathematical Journal, Vol. 2, 1951. As to Kisokagaku, this journal was issued from 1947 to 1953 and contributed to our studies of the philosophy of science . Many remarkable papers by mathematicians and scientists are contained in it .

- 88- 89 theories of new physics. And in the present day H. Yukawa, our most celebrated physicist, is also a learned philosophical thinker and his philosophy of physics is regarded as the most instructive. He has indeed written down much of general informations about modern physics, in which we can see an expression of his philosophical thinking. We owe our general understanding of quantum mechanics to Introduction to Quantum Mechanics (1947), which is his masterpiece. The more popular books on his ideas . of the philosophy of physics are issued by himself, which are recently collected in his selected works.(6) S. Watanabe argued how time can be grasped from the standpoint of modern physies in his Time (1948). This problem is treated philosophically and much space is spared for an examination of Bergson's theory of time. We must also mention S. Tomonaga's The World-Picture of Quantum Theory (1949) and K. Fushimi's The World- Picture of Relativity Theory (1950). These writings are characteristic in their popularity, clarifying the essence of modern physics in readable fashion; as such they are short of philosophical content. In a different tendency, however, S. Sakata and M. Taketani inquire into the present- day problems of the so-called natural dialectic and try to found modern physics on their dialectic principles. Although their arguments are of interest philosophically, the physical meaning of natural dialectic, I think, is somewhat uncertain. The philosophy of physics is now encouraged in these circumstances. With regard -to the philosophy of biology, physiology and psychology, we have not yet anything to notice with the exception of some cases. Meanwhile the analytic philosophy has given rise to a considerable interest among our younger generation

(6) Of these books we may choose as follows: Recent Views of Matter, 1939. Law of Natural Things, 1943. Introduction to Theoretical Physics, 1946. The Invisible, 1946. Views of Matter and World, 1948. Thinking and Observation, 1949.

-89- 90 nowadays; we now receive it mainly from the philosophy of U. S. A. Throughout the previous discussions we have given a sketch of main currents of the philosophy of science in Japan and have pointed out some important thoughts of it. But it is true that the philosophy of science has not necessarily been a serious problem of our intellect; mathematicians, scientists and philosophers have not held the common ground, separating themselves from each other. A sort of sectionalism, I dare say, has prevailed in our intellectual climate. However, in the last ten years this climate has been much altered, and the desire for the philosophy of science has more and more increased. This tendency has converged to the establishment of the JAPAN ASSOCIATION FOR PHILOSOPHY OF SCIENCE in 1954, which is now composed of hundreds of members of researchers in the domain of the philosophy of science in our country. The mathematicians, physicists, biologists, psychologists and philosophers who take interest in the foundations of science are almost included in it. And thus our Association has issued its journal in Japanese, which counts up to 6 numbers today. The editors of the journal are S. Kuroda (mathematics), G. Miyake (philosophy), S. Ohe (philosophy), H. Oka (biology), T. Shimomura (philosophy), Z. Suetuna (mathematics), S. Takagi (psychology), Y. Yamanouchi (physics) and H. Yukawa (physics). We must be grateful to the UNION INTERNATIONALE DE PHILOSOPHIE DES SCIENCES, which has excited us to arrive at the present stage , and we do expect a further advance to come through international intercourse of intel lectual activities.

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