The Significance of Einstein’s Theory of Relativity in Nishida’s “Logic of Field”
By Hisaki, Hashi
(ProQuest: … denotes non-USASCII text omitted.) Nishida Kitaro (1870-1945), one of the most famous philosophers of the Kyoto School, has become well known in Europe through his works on religious philosophy and ethics.1 Yet the interdisciplinary aspect of his philosophy has received much less attention. Aiming at a comprehensive system of philosophy, Nishida strove toward a system of thinking in which thought and practice are united. In this context, the contents of volume 6 of his Complete Works are remarkable. They consist of writings on the philosophy of mathematics and science, where Nishida presented his own position on the establishment of a connection between philosophy and science.2 In this article I attempt to explain Nishida’s approach to philosophy, for example how he was stimulated by the research findings of contemporary physicists and how he constructed his philosophical theory with reference to the physics of his day. In order to concentrate on this discourse-the Theory of Relativity and the Logic of Field-various other topics of Quantum Theory, its controversial theses and hypotheses, interpretations of Quantum phenomena, physics, and social phenomenology, psychology, et cetera, are not treated here.
Basic Principles of Nishida’s Philosophy of Science
Nishida’s philosophy of science is largely different from the analytic philosophy and physicalism of the twentieth century. The position of physicalism is constructed on the fundamentals of contemporary physics.3 Seeking to explain each new item in physics research, some scholars translate mathematical formulas and theorems of physics into the speculative language of philosophy and posit constructive, predicative logical explanations for the new findings in this research. The objects of explanation are physical data that can be definitively described and explained in original physics with mathematical formulas. Problems outside this field, such as how an anthropos recognizes a universal truth for humankind, or in which way s/he can gain knowledge of her/his own life and experiences, are not treated in physicalist philosophy.4
Contrary to physicalism, Nishida considered that field which is not treated in original physics, namely the translation of physical theory to anthropological philosophy. His philosophy cannot be separated from the problem of how we gain insight to grasp the universal truth in our lives. According to Nishida, our self is constructed from body and consciousness as a dimension of oneness. Nishida’s cognition of natural science shows the following features: At first our self intensively considers the phenomenon of physis. This way of thinking must be free of any kind of subjectivism. The field of self-consciousness joins with the existing phenomenon of physis. This results in a dimension of oneness providing a wide cognition in which physics and the philosophy of life and humankind are recognized as anthropological knowledge.
Nishida grasps this dimension, in which a physical thinking self combines with physical phenomena, as a “field” of cognition. Nishida originally borrowed this term (basho, field, Ort) from Plato’s term xora (chi…rhoalpha).5 In the development of this concept Nishida further extended it:
1. The Field is a physically localized, material field of being (…deltarhoalpha in Plato).
2. The Field is a place in which principles develop and come into being (chi…rhoalpha in Plato’s sense).
3. The Field is a position of things, where their existence can be explained in a logical and predicative way (topov, as in the sense of Aristotle).
The synthetic unity of these three aspects forms Nishida’s concept of “field.” His “Logic of Field” serves to realize a critical reflection of various cognitions. The unity of various cognitions is grasped as a synthetic apperception in the Field of consciousness by a thinking self in a life and its practice. This Field does not mean selfconsciousness in the usual sense. In Nishida’s terminology the Field includes not only cognitions of declared objects, but also the cognition and recognition of the thinking and acting anthropos as itself. The thinking and acting self joins with the phenomena of nature, so that an absolute dimension of oneness enters the Field, in which cognitions and the whole being of nature are included as itself.
In this sense, the principle position of Nishida’s philosophy of science can be distinguished from Bertrand Russell’s method of analytical philosophy. In his mathematical philosophy Russell presented the opinion that the idea (idelta…alpha) in the sense of Plato cannot be proved through positivistic data and the analytical method of thinking. According to Russell, thought is led by the principle that each of its objects may be constructed through the principles of mathematical logic. Mathematical logic is free from contradiction, and each element of thinking is connected to the others. The collected elements are able to set up the “World of Universals.” Universalia, a term borrowed from Scholastic philosophy, presents the universal idea in which the substance of things (essentia) is included in the connection to realistic being.
According to Russell, objects of experience can be constructed by including the following factors: sense-data, physical material, and sensation. The analytical method of thinking uses these factors to construct the World of Universals.6 For Russell, the idea in Plato’s sense can be depicted only in the world of our thinking. It is possible to illustrate an idea in our projection of consciousness, but the being and the substance of an idea cannot be proved through the data of positivistic science.7 How an anthropos gets an idea from the phenomenon of being and what kind of meaning an idea has for the life of an anthropos are not central subjects in Russell’s analytical thought. But this tendency should not be considered a factor lacking in his philosophy; it should be understood as a basic principle of analytical thought. Analytical philosophy aims at the predicative logical construction of positivistic factors. Truth is found in logical construction, and it must be proved in every detail. Factors of reflection are objective positive data, which can be proved by science. The thinking Self, the subject of consciousness as itself, is not taken up as a central theme for analytical objects by Russell. In the thought of Russell the existence of our self must be issued as an analytical object. For this purpose the existence of self must be taken up as a topic of analysis in psychology or medicine.
In contrast to Russell, Nishida makes anthropological reflection the central part of his philosophy. It is interesting to note that, since his early works, Nishida had held the following position: when our self as thinking subject combines objects of cognition in an apperceptive unity in our consciousness, we can say that this results from a subjectivist cognition, because the entire field of cognition is illuminated from the position of our self- consciousness as an autonomous thinking and apperceptive subject.8 In contrast to this, objectivist cognition is derived from a field of existing objects: if our self exists apart from subjective sensations, it is opened to the larger field of objects’ phenomena in the entire physis. The contents of self-consciousness are transformed into the field of existing objects. All objects of cognition have aspects that are perceived from the existing object as itself. According to this position Nishida means that physical cognitions are without any exception “objectivist cognitions.”
Nishida presented his position in a such a way that comprehensive cognition does not come from just one of the selected fields of science. Truly comprehensive cognition should not use only one aspect of the two types of cognition, namely subjectivist or objectivist cognition. Comprehensive knowledge can only arise as a relation between subjectivist and objectivist cognition. In understanding Nishida’s position we can see that it can be clearly distinguished from the physicalist or scientist positions.9 The meaning of the Logic of Field in Nishida’s “Sixth Inquiry” (included in the Complete Works, vol. 11) is presented through the basic idea that physics as a cognitive science helps us to reflect the contents of cognition in our consciousness. The thinking self in physics becomes free of any kind of subjectivism. The philosophically thinking self then takes a further step in a direction that is accompanied by the following question: what kind of meaning does physical knowledge have for humankind as a being with comprehensive insight? With this step our self continues toward comprehension, which includes the subjectivist and objectivist cognitions as a dimensional world of whole truth. Each side of cognition joins with the other side and strives for the associative unity of subjectivist and objectivist cognition.
The Logic of Field and its Meaning in the Philosophy of Nature and Science
Nishida examines every step of physical research in connection with the anthropological and self-conscious perspective. Let us take the construction of physical coordinates as an example. One of the easiest acts is to define a zero point of the coordinates. This act is not only recognized as a decision for the point 0, but it also provides the starting point for our thinking in the construction of a “field of our physical cognitions.” Our consciousness of a physical thinking self makes up a Field associated with the three aspects of Field quoted in the last section: 1. a Field of physical localization, or hedra (…deltarhoalpha)
2. a Field that includes the potential to develop principles in the striving for truth, or xora (chi…rhoalpha), and
3. a Field as topos (tau…rhopis) for logical and predicative explanations.
Self-consciousness opens into the central problem of recognizing this Field for cognition. Nishida always includes this aspect in his philosophy of nature and science, as the perspective on anthropological reflection should not be excluded from natural philosophy.
In this context there is an interesting model for understanding Nishida’s way of thinking.10 A part of his thought is similar to the dialectic in Hegel’s Enzyklopadie (1830), in the chapter on “natural philosophy” ([section] 253 ff.). We can see Hegel’s position in the following summary:
Space and Time cannot be conceptually identified with each other. From the perspective of Time as an idea, Space is incommensurate with Time. Vice versa, Time is in dialectical contradiction to Space as an idea. The dialectical contradiction between Space and Time is remarkable in every spatial localization as being here and in the temporal punctuality as being now.11
Nishida adopted the formal character of Hegel’s logic, namely a dialectical construction, to develop an explanation of ideas. But the contents of Nishida’s Logic of Field are quite different from Hegel’s logic. Let us look at Nishida’s position in the following summary:
Space is grasped as a dimension of being something; time is grasped as a period of being something. Our self as a thinking and living subject performs this recognition. Things that can be recognized include not only objects of cognition outside our bodies, but also our self-consciousness itself. The existence of our body as being here and the existence of time as being now are displayed in a contrasted relation. Simultaneously we can say that this contrast is issued as a united recognition of time and space, in which we recognize the form and the contents of our self-consciousness as itself. There is a unity which includes the three contents of existing space, existing time and existing self, which recognizes this unity in various directions: space-time, time-space, unity of space and recognizing self, unity of time and recognizing self.12
The complete synthesis of these elements is defined in Nishida’s terminology as follows: the absolute contradictory identity of space- time-self at the absolute contemporary point of here and now.13
In figure 1, dimensional space is shown in the circle, which is widened in the horizontal direction [s]. Time is shown by the vertical axis [t ]. Dimensional space [s] is recognized in passing time. Their unity is noted with [s']. Time [t] is recognized in dimensional space, while their unity is noted with [t']. The center of the circle [f] is the focal point of existing consciousness of our self. [F] (where an arrow pierces [f]) represents a focus of the consciousness of being and acting self: in a field of consciousness ([f]) the [F] represents our being as dimensional self-recognition in the unity of space and time.
It must be remarked that the whole system is issued as a Field of self-cognition, which is illuminated by self-conscious activity. Space-time-self, the three contents, are combined and recognized as an idea: the absolute contradictory identity.
An explanation of one of the more familiar parts of the Theory of Relativity was suggested by Hermann Minkowski. He demonstrated that a physical concept of time-space could be described with a combination of four infinitesimal points (x^sub 1^, x^sub 2^, x^sub 3^, x^sub 4^, or ct).14 This result was well known in Nishida’s philosophical circle and seminar. The consideration of time and space as an inseparable unity is relevant to the actual development of his reflections. But we should not hurry to the conclusion that Nishida’s position on the Logic of Field was derived directly from Minkowski’s observations on physical phenomena and his physical concepts. The reality was different, and the following point distinguishes Nishida’s position from that of Minkowski. Minkowski’s description of space-time was defined as rigidly physical knowledge. The infinitesimal unity of the factors of space-time is intended for the localization of various physical phenomena spread along the path of a light beam. Further problems of any kind were not objects of research for Minkowski. For example, how do we understand the significance of this localization for our existing selfconsciousness, and in which way of thought is our cognition constructed from different factors (time, space, self); these are outside the thematic field of physics as a rigid science.
The Origin of the Theory of Relativity
It is well known that there is a remarkable difference between the classical theory of Galileo and Einstein’s Theory of Relativity. In the former, the speed of light is a relative value. It is always changing according to the physical movement of the observer. If a physical body moves toward a light in an inertial system, the speed of light becomes faster for a stationary observer outside the moving body. Vice versa, when a physical body travels away from a light, the light’s speed becomes slower when observed from a stationary external position.15 But this classical principle of the speed of light was cast into doubt by Michelson and Moley’s experiment and finally disproved at the end of the nineteenth century.16 Based on Galileo’s classical principle, Michelson and Moley tested the prediction that two different values for the speed of light could be measured, depending on the direction of the earth’s rotation. When the direction of light coincides with the direction of the moving earth, the speed of light should slow down for the observer at the location of the experiment. If the light is beamed against the direction of the earth’s rotation, its speed should be higher for an observer on earth. The light beamed from a starting point A is separated, by a half-mirror at point M, to both directions, B and C. The beam is reflected at the points B and C, so that it returns through the mirror M to an exit point D. If the direction of global rotation is unknown, it would be expected that an interference be displayed at the exit point D. For physicists at that time it was possible to predict, because the direction of rotation would have an influence on both of the different directions of light, A-M-B-M-D and A-M-C-M-D. (See figure 2; illustration by Wada Sumio.)17 But the result of this experiment was a surprise: no interference was registered. The light was spread in straight lines in all directions. The form of this spread was independent of the condition of the light’s source.
A number of physicists tried to resolve this contradiction with a coherent interpretation. We can present one of these hypotheses as follows. The route of a spreading light differs on a case-by-case basis. A different value is derived depending on whether or not the course of light coincides with the earth’s rotation. But during the period of spreading, a light shows absolutely the same value. Hendrik Antoon Lorentz tried to explain this reality by proposing that the bar used to measure the route of spreading light undergoes a proportional contraction in a horizontal direction if a physical body moves against the ether of the earth. This interpretation presented a hypothesis that the ether influences a proportional contraction for a physical moving body. But it reveals a self- contradiction in Maxwell’s thesis: in a vacuum, a ray spreads in all directions in straight lines; the form of a light’s spread is independent of the physical condition of a light’s source. If we accept the existence of ether as matter, which only transmits electromagnetic changes and has no further influence on a molecular system, then we would have to accept that the earth’s ether would remain stationary vis-a-vis all the other parts of the universe.18 Even admitting the material existence of ether, it was clear that the hypothesis was unacceptable. Lorentz sought to explain the contraction by proposing that the elastic character of moving electrons can cause this proportional contraction. This hypothesis also failed, due to the difficulty of its being proven.19
Einstein noted the result of Michelson and Moley’s experiment. Physical theory proceeds from the elements of experiments and their consistency. If an experiment repeatedly disproves a conventional axiom, it must be recognized that the old theory is invalid and should be modified. Galileo’s principle of the relative speed of light was disproved by Michelson and Moley. It would therefore have to be changed. Yet Einstein included part of Lorentz’ hypothesis in his own theory. This was the so-called Lorentz Contraction. A measuring bar traveling with a physical body experiences a proportional contraction if it is moved in a straight line in the same direction. This contraction does not depend at all on the earth’s rotation. A ray of light spreads in all directions at the same time, absolutely independent of the condition of the moving physical body. Accordingly, one had to recognize a new fact: the new principle of physics should be constructed on the axiom that the speed of light is not variable; it is a natural constant. The basic physical principle does not change, even if the movement of a physical body or its representation in a system of coordinates can be changed. Einstein made this principle the starting point in the development of his new theory. He also derived from this the basic part of his Special Theory of Relativity.20 Measured from a stationary system, the bar fixed to a moving body experiences a proportional contraction in its horizontal direction (Lorentz’ Contraction: [the square root of]1 – (v/c)^sup 2^). During this contraction, a clock fixed to this physical moving body becomes slower. Time slows down during the Lorentz Contraction; this is the phenomenon of time’s dilatation. The path of light is calculated as a multiplication of the contracted bar and the clock that slows down during the physical movement. The value of this multiplication coincides with the multiplication of the bar and the clock in a resting position. This is logical because the former system experiences proportional contraction along its length and a proportional dilatation in its temporal value. This yielded a new rule in Relativity Theory, whereby the following rules of classical physics must be rejected:
1. There is no difference between two clocks that measure the time of the same physical event. The coincidence of time for these clocks is absolute. The “same time” at the “same physical occasion” is absolute and unchangeable. It is independent of the physical condition of the clock, that is, whether it is resting or moving.
2. The length between two points on a rigid bar in physical space is absolutely the same, regardless of its physical condition, that is, whether the measuring bar is in a condition of movement or rest.21
The name “Relativity Theory” resulted from the fact that the measure of length and the measure of time show variable values according to their physical movement. Against these relative values of time and space, the speed of light remains an absolute natural constant; here, we can say that Einstein’s new theory represented an opposite position to Galileo’s classical principle.
Relativity Theory’s Approach to Reason and Cognition
To illustrate the new principles of Relativity Theory there is the following often-cited phenomenon. We imagine a train traveling through darkness. We then beam a light from the center of this train. The ray is caught at the front of the train. At the same time the ray is caught at the back of the train, because the light is spread to all directions in space, independent of the movement of the light’s source. Let us name this point of time (t). The same phenomenon is observed by someone near the railroad. It appears to her that the light arrives earlier at the rear of the train, because this part is traveling toward the light’s source, (t’). The front part of the train is departing from the source of the light, so it catches the ray later than the rear: (t”).22
This phenomenon is calculated in classical physics using the addition theorem of the speed of light, as follows. For an observer near the railroad the ray arrives at the back part of the train with a speed (c + v), while the front of the train receives the light at a different speed (c – v). Yet we have seen that this addition theorem was disproved by Michelson and Moley’s experiment: the value of the speed of light is definitive and invariable as a natural constant. How can we explain this appearance of light that is spread at an absolute speed to all directions yet received at various times? This discrepancy is due to the different positions of observers and according to the various physical conditions of movement of each observer. The “same time” is not the same-a typical case of contradiction in Relativity Theory.
There is a reasonable explanation for this fact. Each physical body is valid as a different physical system. Each body in an inertial system has a completely different value according to its motion and according to the position of physical observation. The difference appears in the values of length (x), and time (t). A different value appears according to the motion of the physical body. But the speed of the spreading light is absolutely the same; it does not experience any kind of change.23
An inertial system consists of a physical body at rest, physical system A, and the other body, physical system B. B is moving in a straight line in the same direction. Both systems are described in classical physics using only one coordinate system: (x, y, z, t). Both physical systems are measured in the same way in classical physics. In Relativity Theory this rule is refuted. System A is represented by the coordinates (x, y, z, t), and system B is represented by the other coordinates (x’, y’, z’, t’). But this change of measurement is not arbitrary; it is based on a regulative relation. The relation of (x) to (x’) and the relation of (t) to (t’) is regulated by the proportional value of measurement. If (x) represents 1, (x’) is [the square root of]1 – (v/c)^sup 2^. If (t) represents 1, (t’) is 1/[the square root of]1 – (v/c)^sup 2^. The multiplication of (x – t) and (x’ . t’) yields the same value, whereas the measure of length and time of the two systems is different. The field’s measure is regulated by the parameter [the square root of]1 – (v/c)^sup 2^. The value of localization A regulates the value of localization B. The field’s time is regulated by the parameter 1/[the square root of]1 – (v/c)^sup 2^. The field’s time A regulates the field’s time B. This relation for resting and moving systems can also be considered in reverse: seen from the moving system B we can say that system A at rest is in a relative condition of motion.24
To explain these typical phenomena, namely time’s dilatation and the proportional contraction of a measuring bar, we see that a turning point in our thought was necessary. In the Theory of Relativity it is postulated that various physical systems are in a relation regulated by the speed of light as a natural constant, (c).
At this point, it is important to note in caution that time’s dilatation and the proportional contraction of a physical measuring bar should not be hastily connected to the basic principles of Nishida’s Logic of Field. For Einstein’s principles are presented as rules of physics in a rigid science of nature. The contraction of a bar is related to a physical localization. Time’s dilatation is related to a physical reality that has been proved by stopwatches. Questions of our self-consciousness and how we receive and interpret these physical phenomena are problems excluded from Einstein’s physical research. Nishida took up these questions directly as themes in his Logic of Field: the significance of Relativity Theory to self-consciousness now becomes a topic of anthropological philosophy. Philosophical aspects in interpretations of Relativity Theory are not considered by Einstein. As a physicist he could complete his physical theory without having to deal with anthropological problems, because as a physical theorem the Theory of Relativity fulfilled the requirement that it be consistent, and completely disproved Galileo’s old principles.
Kant’s Analogy of Experience and the Theory of Relativity
Some scholars of natural science hold the opinion that Kant’s doctrine of space and time lost its validity at the beginning of the twentieth century, when the New Physics was established. To substantiate this, it is said that Kant depended on the physical theses of Newton and Galileo, the contemporary physicists of his time. Einstein was also of this opinion and explained his position in the following way:
Kant’s attempt to dispose of the difficulty of the objective existence of space can hardly be taken seriously. The potentialities of inclusion, embodied in the interior of a box, are objective in the same sense as the box itself and as in the included objects.25
As an interpretation of Kant’s work we have to say that Einstein’s opinion is absolutely incorrect. Einstein’s important mistake is found in his confusion of space in the philosophical sense of Kant with physical volume as objective physical existence. For Kant, space is a pure insight a priori not bound to empirical data. Space is constructed as a form of a priori pure insight, which can only be projected abstractly in our self-consciousness. In this sense space is not identified with a concrete physical volume. Without giving the matter much consideration, some believe that Kant depended on the old theses of Newton’s classical physics. It is necessary to comment on this error:
It is well known that Kant quoted fragments of thought from contemporary physicists in his Critique of Pure Reason.26 But this fact alone does not permit us to main- tain that there is a historical relation between Kant’s teachings and the opinions of contemporary physicists. The contents of Kant’s Critique of Pure Reason are separate from the cognitions of physics. Kant did not take physical materials as his theme. He was concentrating on how to explain the systematic construction of our Pure Reason. In his doctrine of time and space he also treated the problem of how we can grasp the contents of both categories (time and space) and how they can be utilized as cognitions in the architectural construction of our Pure Reason. Drawing up a transcendental apperception, we must treat various empirical facts. This is a central theme of the “transcendentality” (Transzendentalitat) from empiricism, which constructs the system of cognitions of our Pure Reason. This problem is connected directly to philosophical reflection. Nishida might say that this treatment leads us to establish a comprehensive system of cognitive knowledge. In Nishida’s position, this way of reflection leads to the horizon of constructing subjectivist cognitions, because reflections and judgments are constructed by our self as a thinking subject. In contrast, physics constructs a field for objective reference to arrive at objectivist cognitions.
The general problem of research is to find a universal and general cognition of truth. This problem is the same for physics and philosophy. Different ways of thinking result from different methods of thinking. Physics strives to find out how we recognize being as a material factor. The problem is researched from the standpoint of existing objects. Objective observation is connected to deductive discussion to construct a cognitive theory. If physical cognition goes beyond the limits of objectivism and touches on the problem of consciousness, it must be said that it is no longer physics.27 The establishment of the Theory of Relativity brings us to a turning point in our basic knowledge, for example how simultaneous events may not be valid as such. In examining this point it is helpful to reflect on the “Analogy of Experience” in Kant’s Critique of Pure Reason.28
It is well known that in this Analogy, Kant borrowed the model of thought and principle from Newton’s Philosophiae naturalis principia mathematica:
First principle: Every body continues in a state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.
Second principle: The change of motion (linear momentum) is proportional to the force impressed and is made in the direction of the straight line in which that force is impressed.
Third principle: To every action there is always an equal and opposite reaction; or, the mutual actions of two bodies upon each other are always equal, and act in opposite directions.29
It is obvious that the meaning of time and space is fundamentally different for Kant and Newton. We have to remark that Kant took only a formal construction from Newton’s theory, which concentrated on pure physical principles. The contents of Kant’s explanations are transformed into a purely philosophical topic: transcendental cognition (which is independent of various empirical facts) forms the most important part of his pure reason. In any case, Kant’s “Analogy of Experience” is well known to philosophers and describes a “consistency of the substance of being, its simultaneity and interaction.”30
This form of description is completely different from Newton’s third principle. The exact description of mechanical motion is out of the scope of Kant’s Analogy. Kant was concerned with the problem of how our transcendental-logical thought recognizes being in space and time in the transcendental schematism of Pure Reason.
“Consistency of substance” is interpreted in physics as the principle for conserving energy and is found in the continuity of space and time. The continuity of time is represented in physics as the parameter calculated by the natural constant c. Relativity Theory’s dilatation of time can disturb the idea of simultaneity. To account for this, a modification of the model of physical principles is permitted. But it must be noted that this modification can only be presented as an extended interpretation from the standpoint of modern twentieth- and twenty-first century physics, which has no direct historical connection to the work of Kant.
The following scheme is representative of the Theory of Relativity: each physical body can be represented with its own system of coordinates. Seen from a resting system (x, t), a moving system is present as another system of coordinates consisting of a horizontal axis calculated by Lorentz’ Transformation (x’) and a second axis for time, which is also calculated by Lorentz’ Transformation (t’). Here, we concentrate on the axes of time, t and t 0. If the axis t of a resting system forms an orthogonal coordinate of x and t, the time axis t 0 of a moving system must be modified by a proportional change of basic measure: 1 : 1/[the square root of]1 – (v/c)^sup 2^. We can refrain here from a discussion of the physical details of modifying the (t’) axis through geometrical proportions. (See figure 3.)31
The simultaneity observed from a body (coordinate system x, t) consists of itself and the relatively moving body (coordinate system x’, t’). Seen from (x, t), [tau] and [tau'] occur at the same time. Seen from the other system (x’, t’) [tau'] coincides with a further point: [tau'']. The physical occasion of simultaneity in an inertial system is shown in both pairs of values: “[tau] with [tau']” and “[tau'] with [tau''].”32 Depending on what kind of field is recognized as being a resting system, the field’s time can be determined, as calculated by the proportional Lorentz’ Transformation from (x, t) to (x’, t’).
Kant’s Third Analogy is an interaction between simultaneously existing substances. If one accepts the relativist pair-relation, it is possible to explain this simultaneous interaction between physical bodies consisting of the related coordinate systems: (x, t) and (x’, t’).
“Absolute Contradictory Self-Identity”: The Turning Point in Nishida’s Logic
Nishida’s reflections on the Theory of Relativity went beyond the limits of pure physical knowledge and entered the problem of consciousness. Nishida treated an anthropological problem: how does a relativistic conception of space and time affect the cognition of our physical existence? Nishida commentated on Minkowski’s theory of space and time as follows:
Conventional classical physics held to a dogmatic position of logic in which objects are separated from the existence of our thinking self. This position lacks a self-recognizingcognition of our active body and thought. The new physics brings back our selfconsciousness to the starting point at which we can reflect carefully about what our self as body and consciousness means. With the knowledge of Relativity Theory we reach an understanding of how the relation of space and time is cleared up through our autonomous activity of self-thinking. Relativity Theory succeeded in drawing up the construction of the new physical world. With the knowledge of Relativity Theory it is possible to recognize what kind of relations there are between physical knowledge and the existence of our body and consciousness. Our body and self-consciousness form an existing Field which takes part in history as a continuum of being mankind.33
Relativity Theory does not generally treat the self- consciousness problem. Nevertheless it contains the basic knowledge for anthropological reflection, namely that a value of physical measure is decided through the relation between the conditions of motion of an observer and an observed thing. In classical physics there is no such rule. A measuring and observing self is presented as an absolute objective unit. The measured value of a physical object is independent of any conditions of a measuring self. We can recall the basic principles of classical physics, which are abandoned in the Theory of Relativity:
1. The time interval between two physical events is not dependent on the state of motion of the reference body.
2. The spatial distance between two points on a hard object is not dependent on the state of motion of the reference body.34
Nishida sees in the difference between the old and new physics that Relativity Theory returns us to the original position of metaphysics or philosophia prima in the sense of Aristotle, namely in the relation between the observing subject and the observed object. By thinking in this way, Nishida felt that, parallel to Quantum Theory, the Theory of Relativity brought us to reflect on the subject-object relation and the relation between observer and the observed. In this context Quantum Theory and Relativity Theory presented a corresponding problem of physics and philosophy in the twentieth century.
At the same time, Nishida showed, in a few scant comments, the important difference between the Theory of Relativity and Quantum Theory: he pointed to the fact that, despite having a common basis in the relation of measuring and being measured, Relativity Theory shows a complete model of thinking that is similar to classical physics, because the act of measuring in Relativity Theory cannot have any effect of uncertainty on the measured object. In contrast to the uncertainty principle (Unscharferelation, Unbestimmtheitsrelation) of Quantum Theory there is a basic part of Relativity Theory that displays the character of classical physics.35
Nishida’s insight is extrapolated in the following opinion:
Some people condemn Minkowski’s Theory of space-time as abstract and difficult to imagine. But I am not of this opinion. . . . In conventional physics the act of measuring was understood as an absolutely objective and substantial position for physical thinking. The thinking self in physics takes a physical action for measuring and calculating physical objects and hence definitively and doctrinally renders itself as an absolute substantial subject for objective judgments. The new physics of the twentieth century left these old principles behind by returning to the original insight of our existing, bodily consciousness of our self. Our self exists as an inseparable unit from body and consciousness and it is present as a field of our self-being as itself.36
Studying the basic insights of Relativity Theory, Nishida found the following relation between the new physics and his own philosophy: Everything in the world exists as its own physical system. Every physical body shows its own Field’s measure and its own Field’s time. These systems are related to each other. This field is connected to the other field, so that a universal construction of all being is formed in the Theory of Relativity. Time-and-space and form-and-contents are distinguished as the categories. But Nishida unifies these classifications as the recognition of self-activity. This point represents a great difference between Kant’s cognition of pure reason and Nishida’s recognition of acting self. Our self-being exists as a unity of body and consciousness. This self-being presents its own Field as itself. Our self-being reflects the existing relation from one field to the other. During this action our self-being is present as a human being, which forms an interaction between our existing field and others. The Twin Brothers Paradox: Viewed from the Perspective of “Logic of Field”
Physicists are familiar with the “Twin Brothers Paradox.” Of the various interpretations of this paradox I have chosen the following version.
One of the twin brothers A flies with a rocket to the moon. The other brother B observes this from the earth. Observed by B, the rocket carrying A reaches a high speed that approaches the speed of light (c). According to the Special Theory of Relativity the clock on the rocket will begin to experience a proportional deceleration. When approaching the speed of light the rocket’s clock will slow down to an extreme degree.37
From the standpoint of observer B on earth, his brother A will become younger during his trip to the moon because of the retardation of time. Now, to see this fact in relativistic terms, we can turn this version around as follows. Observed by brother A on board the rocket, the other brother B on earth is in relativistic motion, which is able to change the positions in the inertial system: looking at the scene from the rocket, A is physically in a resting position. Bother B is moving relativistically to A. His clock will slow down to an extreme degree if he is observed by brother A in the rocket. The paradoxical question is: which brother will become older during the flight?
In figure 4, taken from Eriguchi,38 clock C0 is in the resting system on earth. The rocket R^sub 1^ is flying near the earth with clock C^sub 1^. We allow the two clocks to determine when R^sub 1^ nears the earth. R^sub 1^ continues to fly. Now, another rocket R^sub 2^ flies to R^sub 1^ from the opposite direction. At the moment that both rockets pass each other, let us set their clocks C^sub 1^ (at R^sub 1^) and C^sub 2^ (at R^sub 2^). The second rocket R^sub 2^ flies further and approaches the earth. When rocket R^sub 2^ comes near the earth, we set the clock for R^sub 2^ (C^sub 2^) and the clock for the observer on the earth (C^sub 0^). What is the result, if we present the line of motion of both rockets in relativistic space-time? I quote a further figure, from Eriguchi (see figure 5), to exhibit a relation of physical systems.39
In figure 5 there are three physical systems: the observer on the earth as a resting system and the two rockets, which are the physical moving systems. The observer as a resting system on earth does not move along the horizontal axis (x); its value is 0. Rocket 1 moves and arrives at place P. This is a position where both rockets set their clocks. It is possible to describe the first rocket’s movement with the Weltlinie R^sub 1^. The second rocket makes its own movement in space-time with the Weltlinie R^sub 2^. If we look at the moment at which both rockets set their clocks, we observe a fact that cannot be explained without contradiction: at the moment P both rockets check their clocks; this time should coincide with the other clock of the observer on earth, P^sub 0^. This hypothesis is self-contradictory if considered from the standpoint of Relativity Theory. The observer’s clock must be slower, according to the theorem of Time’s Dilatation (Zeitdilatation). Let us look at Weltlinie R^sub 1^; the moment P coincides with the further moment P^sub 1^. If we recognize Weltlinie R^sub 2^, P must coincide with the third moment, P^sub 2^.
Eriguchi notes this with a shaded triangle and presents the contradiction as follows: If the clocks on both rockets are set at 0 o’clock, in the fifth year after the start of the first rocket (R^sub 1^), we must accept the following reality: Rocket 2 needs the same time as Rocket 1 to arrive at the earth. Weltlinie R^sub 2^ shows the same time as Weltlinie R1, five years after the rendezvous with Rocket 1. If the speed of each rocket is 0.9 c, we must acknowledge a further reality: it is proved by the fourth formula of Lorentz’ Transformation that the clock on the earth would have to date twenty-three years, whereas the clocks in the rockets would date only ten years. The space in the coordinates noted in the shaded area in the figure by Eriguchi shows a forgotten Space- Time in Relativity Theory.40
This paradox appears because the coordinate time axis is different according to each physical system. Each system shows a different degree in its time axis and therefore has to issue its own time value. If we use only one system as a reference for the rest of the time axis, we will commit an error. Insofar as we don’t recognize the plurality of systems, this contradiction is unavoidable.41
Nishida did not explain the exact details of the physical analysis in his works. At least in his original works, it is unknown whether Nishida was familiar with the Twin Brothers Paradox. He did, however, refer concisely and exactly to the fact that every physical body is in a relativistic relation to the other with its own measure and its own time. With clear insight Nishida took this principle and associated it with his Logic of Field and its anthropological and ontological aspects. The type of association of the physical and ontological Fields was worked out in broad strokes, so there are some parts not sufficiently treated according to their interdisciplinary aspects. Nevertheless, it is possible to say that Nishida had a keen vision of the potential relation between the new physics and the new ontology. The key point is that our selfbeing is grasped as a Field that is seen from three dynamic dimensions: (1) the Field of physical localization and interaction, (2) the ontological Field, in which being is developed and fulfilled as itself, and (3) the Field as topos, in which various cognitions are reflected and predicated.
Our thinking self at the absolute contemporary point of here and now forms a Field of existing being as itself. With our self- consciousness it constructs a part of the whole world and is valid as a Field of physical and anthropological being. With its physical body it regulates the system of other physical bodies. This action is accompanied by the self-recognition of our self-consciousness. Beyond the limits of physical knowledge, Nishida ventures into the field of anthropological and ontological topos.
The unity of space-time and self-cognition forms a self- recognition for the comprehensive cognition of the whole world. This position was explained above in the second section of this essay. Space-time, self-cognition, and the self-recognition of the unity of the whole world as a dimension of oneness-these basic factors are the elements of Nishida’s Logic of Field. Each factor of this comprehensive cognition is found in a relation to the others and forms part of an associative interaction.42
The problem of different points of simultaneity in the new physics, as presented in the Twin Brothers Paradox, is unsurprisingly acceptable in Nishida’s ontological position: the different time-points for a simultaneous event (e.g., P – P^sub 1^ – P^sub 2^ in this section, or [t], [tau'], and [tau''] in the previous section) can be explained by the basic principle of the Logic of Field, that is, “Absolute Contradictory Self-Identity,” which can include different time-points from every Field.43
In classical physics it is the rule that a physical body falls according to the Law of Gravitation. But this principle is not valid according to the Theory of Relativity. It has already been explained that a physical body is recognized as having its own measure and its own time in Relativity Theory. The physical value changes relativistically according to the moving conditions of an observer and an observed thing. A physical body A does not fall because of gravitation. It falls because the space of A is bent due to its physical substance.44 In the classical theory, there is a rule that a light spreads in all directions in straight lines. This is not valid according to the Theory of Relativity. The cosmic ray is bent not only in astrophysical space, but also near the earth. This phenomenon occurs according to what kind of physical body is found in the way of the emitted light.
Nishida did not extrapolate on the details of physical cognition. With sharp insight he announced that every entity in the Theory of Relativity forms its own Field with its own physical localization. Each physical body is present as a physical system. Each of the systems is connected to the others. The own-being of a physical body A defines its existence with physical parameters, when A is in a relativistic proportion to another body (non-A). The definition of the entity A follows if it exists in a relation to non-A (e.g., B). From a philosophical standpoint we can say that entity A and entity B are in a regulative relation.
In contrast to Quantum Physics there is no problem of the uncertainly principle (Unscharferelation) in the Theory of Relativity. If a physical body A is in an inertial system in a state of rest, the relation of A to the moving system B is defined according to Lorentz’ Transformation. Without a description of the detailed physics involved, Nishida intuitively focused on the common ground as well as the difference between Relativity Theory and Quantum Physics: “Independent of the facts of the uncertainly principle (Unscharferelation), the Theory of Relativity represents the end of the excellent system of classical physics.”45
In my opinion, one of the most important principles of the Logic of Field corresponds to that of the Theory of Relativity, in the following way: The localization of every physical body forms its own time and its own measure. In Relativity Theory this modification appears according to the condition of its proportional motion. Nishida reflected on this reality and developed it as an anthropological ontology. The Field includes not only physical data but also the self-cognition of our existing and acting self- consciousness. This Field of our self-cognition is flexible and movable within space-time. As exhibited by Nishida’s scheme of the “Absolute Contradictory Self-Identity of Space and Time,” the focal point F forms the center of self-consciousness of our thinking and acting Self. I have remarked already that this aspect of self- consciousness is out of the scope of Relativity Theory. Nishida stressed the new aspects of Relativity Theory that departed from the doctrine of classical physics. Space and Time can no longer be defined with a single measure, but are bound to proportional modification. The modification depends on the relation between a physical observer (measuring self in a resting system) and an observed thing (measured object). Nishida interprets this relation anthropo-ontologically, where the system of entity A regulates the other entity B. Vice versa, it is possible to say that system A is regulated by B, especially in the case where B is a resting system and A is considered a relativistic moving system. It must be repeated that Nishida’s Logic of Field was not directly derived from the Theory of Relativity. A concrete and detailed description of physical knowledge is missing in Nishida’s work. But in interdisciplinary terms we can say that Nishida drew attention to the results of the latest research by contemporary scholars and physicists. Yet a prototype of the Logic of Field was found in the earliest works of Nishida, independently of research in physics or the other natural sciences.46
Although we cannot expand our topic to cover Nishida’s pure ontolgy and special epistemology in this essay, I would like briefly to describe the essentials of the “Logic of Field” as a pure ontological term.47 It is well known that Nishida’s basic epistemological principle is the “Field of absolute mu” (zettai-mu no basho …). In considering a word-for-word translation, this term should not be identified with “absolute nothingness connoting an absolutely negative ‘nihil non’ or ‘nihil negativum.’ ” Mu is, rather, a dynamic conception of unlimited oneness. Various contradictory concepts of being and nonbeing, absolute being and its absence, et cetera, are enveloped in mu. These aspects of mu are actually found in the terminology of original Zen Buddhism. The contents of Nishida’s mu cannot be identified with every detail of Zen terminology, but in their basic meaning they have common characteristics: mu is a common ground for being and nonbeing. Mu is present everywhere in the world of experience. Mu is represented by particular things in the empirical and metaphysical dimensions. In his Logic of Field (Complete Works, vol. 11) Nishida deployed absolute mu as a dynamic concept to mediate contradictory factors and categories such as being and nonbeing, absolute being and its absence. Mu brings contradictions to unlimited unity. Mu is grasped as a limitless dimension of our ego-less self-activity. In one dimension of mu our old knowledge is examined, modified, and reconstructed to form a new epistemology.
One main theme in Nishida’s philosophy is the idea that truth can be unfolded and developed in experience and in the consciousness of a thinking and acting Self. For Nishida, cognition is self- recognition, where the thinking self cannot be separated from the objects of its experience and reference. In the stream of multicultural ideas Nishida concentrated on the new knowledge from science of every type. As I mentioned previously, the Logic of Field has the following three central axes: (1) the Field as physical localization (hedra), (2) the Field as a potentially unlimited possibility for the development of the principles of being (xora), and (3) the Field as a basic position from which to construct predicative logic (topos). Nishida thought highly of the absolute objective (objectivist) knowledge of physics, but did not simply associate his position with physical knowledge. Nishida’s thought held that philosophy demonstrates its own excellence in a position opposite that of physics.
For Kant the significance of philosophy is as the transcendental apperception of an autonomous thinking and reflecting self. Nishida sees the significance of his philosophy in a self-recognition (jikaku …) that our self as body and consciousness is existing in the field of absolute mu (…). This recognition of mu is actual as a dynamic conception to mediate contradictory factors and categories. Nishida called Kant’s way of thinking the “subjectivist reference for cognition” (see endnote 8).
In Nishida’s opinion, ideal knowledge should include both types of cognition, subjectivist and objectivist. In combining subjectivist and objectivist knowledge universal philosophy presents a comprehensive world of truth. It is valid as a reflective science of all sciences in the sense of Fichte’s “Science of Knowledge.”48
To understand Nishida’s philosophy of nature we must remark on mu (…) as a key terminological point. In a word-for-word translation from the modern languages of East Asia, mu must be presented as “nothingness.” In the field of philosophy and thought in East Asia this term has further meanings. In Nishida’s philosophy mu is a conception that mediates contradictory factors and categories accompanied with its limitless flexibility. Bringing factual and categorical contradiction into oneness, the thinking and acting self is modified by unlimited mu activity. Through the unlimited flexibility of mu, an old way of thinking is modified from a dimension of old knowledge to reconstruct a new epistemology. In the background of this dynamic change mu is actual as a dimensional world for an unlimited activity of our ego-less selfrecognition. 49
To conclude our discourse we can say that Nishida’s term “Absolute Contradictory Self-Identity” is the result of the mediation and unification of contradictory factors and categories including a dynamic modification of our thinking selfactivity. 50
1 – Nishida, “An Inquiry into the Good” and “The Logic of Field and the Religious View of the World.”
2 – Nishida, “Basic Principle of Mathematical Ontology,”"The World of Physics,”"Logic and Mathematics,” et cetera.
3 – For the definition of “Physicalism,” compare Heintel, “Metabiologie und Wirklichkeitsphilosophie”; Klein, Geschichtsphilosophie, chap. 1; Klein, Metaphysik, chap. 1.
4 – Compare Heintel, “Metabiologie und Wirklichkeitsphilosophie”; Klein, Geschichtsphilosophie, chap. 1; Klein, Metaphysik, chap. 1; Pietschmann, Phanomenologie der Naturwissenschaft, chap. 5.
5 – Nishida, Complete Works, vol. 11, p. 73.
6 – Russell, Probleme der Philosophie (Problems of philosophy), chaps. 5, 2, 3.
7 – Russell, Introduction to Mathematical Philosophy, chap. 13.
8 – Compare Nishida, Complete Works, 1 : 78, 94.
9 – Compare Klein, Metaphysik, chap. 1, and Geschichtsphilosophie, chap. 1.3.
10 – Nishida, Complete Works, 11 : 254, 348.
11 – Compare Hegel, Enzyklopadie der philosophischen Wissenschaften, [section] 261, [section] 254, [section] 348.
12 – Nishida, “Basic Principles of Mathematical Philosophy,” and “The World of Physics”; Hashi, Die Aktualitat der Philosophie, chap. 7.
13 – See Nishida, Complete Works, 11 : 254-255, 348-349; Hashi, Die Aktualitat der Philosophie, p. 64; Hashi, Die Dynamik von Sein und Nichts: Dimensionen der Vergleichenden Philosophie, vol. 1, fifth main section, chap. 3.6.2.C.
14 – Minkowski, “Raum und Zeit,” p. 66. Compare Einstein, Uber die spezielle und die allgemeine Relativitatstheorie, [section] 17, Appendix 2.
15 – Einstein, ibid., [section] 6.
16 – Kline, Mathematics and the Search for Knowledge, chap. 9; Einstein, Uber die spezielle und die allgemeine Relativitatstheorie, [section] 16; Lorentz, “Der Interferenzversuch Michelsons,” pp. 2 ff.
17 – See the illustration constructed by Wada, in Important Aspects of Relativity Theory, p. 3.
18 – Compare Kline, Mathematics and the Search for Knowledge; Einstein, Uber die spezielle und die allgemeine Relativitatstheorie, [section] 16; Eriguchi and Fujii, The Actuality of Relativity Theory, chap. 1, pp. 4-7.
19 – Lorentz, Das Relativitatsprinzip, pp. 78-79; “Das Relativitatsprinzip und seine Anwendung auf einige besondere physikalische Erscheinungen”; Uchiyama, The Theory of Relativity: An Introduction, p. 23.
20 – Einstein, Uber die spezielle und die allgemeine Relativitatsttheorie, [section] 11, [section] 12; Hashi, “Vernunfttheoretische Bedeutung der Relativitatstheorie bei Philosophen des 20. Jhdts.”
21 – Einstein, Uber die spezielle und die allgemeine Relativitatsttheorie, [section] 11, p. 19.
22 – The simultaneous occurrence of the dissemination of light receives different values according to Relativity Theory. Various values result from where an observer is and what kind of physical status of motion he has. See Einstein, Uber die spezielle und die allgemeine Relativitatsttheorie, [section] 9; Kline, Mathematics and the Search for Knowledge.
23 – In other words, according to a receptor’s field and according to the condition of motion of a physical body there appear different measures of length (x) and time (t). Ernst Cassirer named these changeable values Zeitmass (Time’s Measure) and Ortsmass (Field’s Measure). Both of these might be issued as a physical Erfahrungsbegriff (Experiential Idea). See Cassirer, “Zur Einsteinschen Relativitatstheorie,” pp. 83, 73; compare p. 26.
24 – To simplify, we can imagine the following scheme: Someone is sitting in a train while the landscape is dashing past. If we determine the train as a physically resting system, the landscape is described as a physical moving body in an inertial system.
25 – Einstein, Uber die spezielle und die allgemeine Relativitatsttheorie, appendix, section 5, 1997, p. 93: “KANTs Versuch, das Unbehagen der Objektivitat des Raumes abzuschaffen, kann doch kaum ernst genommen werden. Die Lagerungsmo glichkeiten, verkorpert durch den Innenraum einer Schachtel, sind in demselben Sinne objektiv wie die Schachtel selbst und die in demselben lagerbaren Objekte.”
26 – Kant, Kritik der reinen Vernunft, B XII ff., B 40 f., B 218 ff., A 176 ff. 27 – Compare Hashi, “Vernunfttheoretische Bedeutung der Relativitatstheorie bei Philosophen des 20. Jhdts,” chap. III.3., IV.1.
28 – Kant, Kritik der reinen Vernunft, B 218-B 265, A 176-A 218.
29 – Newton, Mathematisch Prinzipien der Naturlehre, p. 32: “1. Gesetz. Jeder Korper beharrt in seinem Zustande der Ruhe oder der gleichformigen geradlinigen Bewegung, wenn er nicht durch einwirkende Krafte gezwungen wird, seinen Zustand zu andern. 2. Gesetz. Die Anderung der Bewegung ist der Einwirkung der bewegenden Kraft proportional und geschieht nach der Richtung derjenigen geraden Linie, nach welcher jene Kraft wirkt. 3. Gesetz. Die Wirkung ist stets der Gegenwirkung gleich, oder die Wirkungen zweier Korper auf einander sind stets gleich und von entgegengesetzter Richtung.”
30 – Kant, Kritik der reinen Vernunft, B 224-B 265, A 182-A 218: “1. Beharrlichkeit von Substanz, 2. ihre Zeitfolge und 3. ihr Zugleichsein.”"Erste Analogie. Grundsatz der Beharrlichkeit der Substanz. Bei allem Wechsel der Erscheinungen beharrt die Substanz, und das Quantum derselben wird in der Natur weder vermehrt noch vermindert. Zweite Analogie. Grundsatz der Zeitfolge nach dem Gesetze der Kausalitat. Alle Veranderungen geschehen nach dem Gesetze der Verknupfung der Ursache und Wirkung. Dritte Analogie. Grundsatz des Zugleichseins, Nach dem Gesetze der Wechselwirkung, oder Gemeinschaft. Alle Substanzen, insofern sie im Raume als zugleich wahrgenommen werden konnen, sind in durchgangiger Wechselwirkung.”
31 – Figure by Wada Sumio; see Important Aspects of Relativity Theory, I.5., p. 11. Compare Herbert Pietschmann, printed script for lecture on theoretical physics at the University of Vienna, 1999, p. 10.
32 – See note 31 above.
33 – Translated and summarized by Hashi Hisaki. See Nishida, “The World of Physics,” p. 50. Compare Hashi, “Vernunfttheoretische Bedeutung der Relativitatstheorie bei Philosophen des 20. Jhdts,” chap. 5, pp. 272, 273.
34 – See section 2; Einstein, Uber die spezielle und die allgemeine Relativitatsttheorie, [section] 11, p. 19.
35 – Nishida, “The World of Physics,” p. 50. On principles of Quantum Theory (Unscharferelation, Unbestimmtheitsrelation) see Heisenberg, Quantentheorie und Philosophie; Physik und Philosophie; Bohr, Heisenberg, and Hermann, Die Kopenhagener Deutung der Quantentheorie.
36 – Nishida, “The World of Physics,” pp. 49-50 (translated and summarized here by Hashi).
37 – See the fourth transformation of Lorentz: t’ = (t – vx/ c^sup 2^)/[the square root of]1 – (v/c)^sup 2^. Compare Einstein, Uber die spezielle und die allgemeine Relativitatstheorie, [section]11, p. 21; Hashi, “Vernunfttheoretische Bedeutung der Relativitatstheorie bei Philosophen des 20. Jhdts,” chap. III.2.
38 – Eriguchi and Fujii, The Actuality of Relativity Theory, p. 23.
39 – Ibid., p. 28.
40 – Ibid., pp. 29 ff.
41 – Eriguchi remarks on this question that independent of which brother might be younger during the moon trip, we have to know that the forgotten space-time causes a causal connection to form a self- contradiction. The physical brother A in the flying rocket must be younger, because his physical system makes a realistic move. See Eriguchi and Fujii, The Actuality of Relativity Theory, p. 29.
42 – See note 13 above.
43 – For a general interpretation of this term see Nishida, Complete Works, vols. 9 and 11; Hashi, Die Aktualitat der Philosophie.
44 – Eriguchi and Fujii, The Actuality of Relativity Theory, chap. 10.
45 – Nishida, Complete Works, 11 : 50-51; compare p. 41.
46 – Ueda Shizuteru commented that a starting position for the development of the later work, Logic of Field, is noticeable in the early work “An Inquiry into the Good.” See Ueda, “Experience and Language in the Thinking of Nishida,” and “Pure Experience, Self- Recognition, and the Field of Universal Truth.”
47 – See Nishida, Complete Works, 11 : 5-59. Nishida developed his theory of systems of the physical and ontological world using a key term, “the world as the field of mu” (ibid., pp. 9 ff.). On the term mu, or absolute mu, see Nishida, ibid. 11 : 395 ff., 398 ff.; Nishida, “Mu as a Dimension of Self-Recognition”; Complete Works, vol. 6; and Hashi, “The Topic of Self in the Field of Absolute Mu.” On mu as a Zen term, see Hisamatsu, “Mu in East Asian Philosophy” and “Existence via Mu.” On the terminology of “Field” (basho …) and “Logic of Field” (basho no ronri …), see Nishida, “Basic Principles of Mathematical Ontology” in Complete Works, 11 : 238 ff., 254 ff., 272 ff.; Nishida, “The Logic of Field and the Religious View of the World,” in Complete Works, 11 : 371 ff., 415 ff.; and Hashi, “The Topic of the Self in the Field of Absolute Mu.” On the system of Nishida’s terminology see Hashi, Die Aktualitat der Philosophie: Grundriss des Denkweges der Kyoto-Schule. On Nishida’s complete system of philosophy with comparative philosophical aspects, compare Hashi, Die Dynamik von Sein und Nichts: Dimensionen der Vergleichenden Philosophie.
48 – Fichte, Uber den Begriff der Wissenschaftslehre, p. 18 (page number in original 1794 edition).
49 – See note 47 above.
50 – On absolute contradictory self-identity, see Nishida, “Absolute Contradictory Self-Identity.” This term is presented in Nishida’s physical ontology in Nishida, “The World of Physics,” pp. 7, 9 ff., 20, 23-24, 28 ff., 31 ff. Compare Hashi, “Vernunfttheoretische Bedeutung der Relativitatstheorie bei Philosophen des 20. Jhdts”; “Die Bedeutung der Relativitatstheorie Einsteins bei Cassirer und Tanabe.”
Bohr, Niels, Werner Heisenberg, and Armin Hermann. Die Kopenhagener Deutung der Quantentheorie. Dokumente der Naturwissenschaft. Abt. Physik series, edited by A. Hermann, vol. 4 Stuttgart: S. Hirzel, 1963.
Cassirer, Ernst. “Zur Einsteinschen Relati