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Epistemology, methodology and axiology presuppose one another in the total sense of the term "Methodology". As applicable to this chapter this term requires some explanation. Each discipline or branch of scientific thinking aiming at certainty presupposes a methodology. There should be an agreement between the object of research and the subject who conducts the enquiry along the most fruitful and significant channels of research. There is a subject-matter and an object-matter which have to be put into a direct bipolar relation if the methodology is to be correct.

In the present work we are concerned with a Science of the Absolute and the wholesale methods of attaining the truth of the Absolute. The modern tendency is not to stress this wholesale aspect but to be less ambitious and to seek truth by piecemeal methods of trial and error. Logical positivists prefer to look upon scientific method in this fashion. As each discipline must have a proper method for attaining the knowledge which is its object, it is fully scientific even in a modern sense, to think of a wholesale approach to the study of the Absolute. Therefore we shall dispense here with the usual inductive and deductive approaches proper only to specific branches of knowledge. The detailed subdivisions of method, such as the inductivo-hypothetical, the historical or genetic, the descriptive or the analytic approaches, when unilaterally understood need not concern us here. The bilateral dialectical and axiological approach agrees with the methodology of this chapter, where a negative or descending reduction or cancellation of counterparts, tending to abolish plurality and relativity in favour of a unity and an absolute resultant certitude or validity are to be kept in mind.

In the first chapter it was supposed that the outer world, as given to the senses, was real. Here the relation between subject and object tends to become more subjectively verticalized. The two counterparts belong more closely to each other, as the Absolute can neither be conceived pluralistically nor dualistically because of the tautology or contradiction that would then result.

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The first task that we have to undertake in the present chapter is to reduce relativity and multiplicity so as to abolish them in the name of the One Absolute. The relativistic features seemingly tolerated in the first chapter have now to be revised into unitive and absolutist terms. This task is mainly one of reduction by the well-known method of the Upanishads called neti-neti (not this, not this) or Nivritti Marga. This is known in the West as the negative way and is very often used by the mystics. When the process of reduction has been fully accomplished, there is an element of reconstruction of the finalized position in respect of the central subject-matter of the work. Such is, in broad outline, the scope and content of the present chapter. The methodology belonging to such a context has not only to be wholesale and subjective in approach, but also one that belongs to the context of directing human understanding along lines that yield the greatest clarity and certitude in respect of the totality of truth and reality.

The definition of methodology found in Rune's Dictionary of Philosophy is as follows:

"The systematic analysis and organization of the rational and experimental principles and processes which must guide a scientific inquiry, or which constitute the structure of the special sciences more particularly"¹

Further on we read:

"Thus, methodology is a generic term exemplified in the specific method of each science .... In the last resort, methodology results from the adjustment of our mental powers to the love and pursuit of truth."²

From a perusal of this apparently sinuous definition it is evident that the clarification itself needs further explanation. Besides being related to epistemology, there is the question of structure, a term which is becoming popular in the West at present.

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This reference to structure is made in more than one context in the definition of methodology. The final summing up of the position unmistakably points to the necessity of relating the subject and object as counterparts that belong together to one and the same total knowledge-situation. We shall not be too far removed from the correct meaning of methodology when we state here that there is both an objective structuralism implied in positive truth as well as a corresponding negative structuralism in the mind of the person who seeks to find the truth. Methodology is concerned with the correct way of research in making the Self relate itself to its own counterpart, the non-Self. It is in the overall context of the central, neutral and normative Self always acting as a reference that a correct methodology, as understood in the above manner, attains its purpose, which is that of a certitude given at one and the same time to intuition as well as to reason or common sense.

Before passing on to other philosophers we shall devote some more space to a closer examination of the implications of Cartesian methodology. We shall not enter into an enumeration of all the aspects of method indicated in Descartes' "Discourse on Method and Meditations on First Philosophy". Descartes was an expert in optics, mathematics and logic. As the father of modern philosophy, all his elaborations follow an overall vision of reality, revealing the same structural implications, whatever might be the particular discipline by which he proposes to examine the absolute substance he is always concerned with. The two broad divisions of Cartesianism are known as res cogitans (thinking substance) and res extensa (extended substance). They belong to one and the same substance having its own structure represented by the same correlates.
Whether Descartes had the intention of applying a more general and extrapolated version of this structural plan of correlates to the larger domains of philosophical speculation has not been sufficiently clarified in his writings. Yet the so-called rationalist philosophers like Spinoza, Leibniz and others can easily be recognized as continuators of the Cartesian tradition, at least in the matter of postulating something like a thinking substance or monad. The schematismus of Kant can be traced back to the correlates when it is more mathematically and statically understood, and forwards to Bergson's notion of the élan vital which submits to a schéma moteur serving as the basis of his creative evolution. The schematismus attains finality in. the hands of Eddington where the new epistemological structuralism of the philosophy of science is introduced. We have examined elsewhere this movement underlying modern thought.³

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It was Cartesianism that set the ball rolling in this direction. Descarte´s method is misunderstood as accepting rather arbitrarily and artificially a form of dualism between the mechanistic and the living aspects. This was because he did not properly explain how they could belong together. A more careful study of his writings reveals that the main implications of his philosophy have always remained the same fundamental features of the structuralism originally implied in his correlates. Spinoza also defined absolute substance treated with its accidents or attributes on similar lines. This in turn gave place to the Monad of monads of Leibniz. Kant's ding-an-sich is not different from Descartes' absolute susbstance and could be taken to refer to the same.

The broad features of this structuralism are however, sufficiently evident in Descartes' writings. Besides these notions of substance there is also the tabula rasa of Locke and Hume's phenomenological reality. All these are meant to be normative notions of the Absolute viewed from possible cosmological, psychological or philosophical angles. The particular point of view of Descartes in respect of this normative notion is such that his epistemology and axiology provide a clear-cut methodology with its structural outlines fully in evidence. It is time that this particular structural methodology was more fully used.

It will be convenient for us to start with the notion of animal spirits, which Descartes recognized as a kind of mental substance or emanation wherein psychological and cosmological factors co-exist. This makes for the interaction of the body and the mind. In his cosmology the same absolute substance is the basis for what he called vortices which express their divisibility, figurability or mobility so as to bring into existence various objective entities. A kind of thinking substance similar to Spinoza's is implied here, although Descartes works out the cosmological implications in greater detail so as to make his position a continental rival to the more rigidly or radically conceived cosmology of Newton.

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Instead of straight lines and laws of motions, we have in Descartes' view curvatures of space without which his vortices could not be thought of. These vortices have at least the curvature in common with what other philosophers, like Bergson, have referred to in terms of a vermicular spiral which shares the features of a logarithmic spiral. Bergson also refers to a helicoidal movement involving space and time. Whatever the shape involved, the cosmology of Descartes lays the foundation of the notion of an absolute substance which could be referred to in terms of his two correlates These correlates have unmistakable structural implications whose epoch making significance is proved by their growing use in every department of modern science.

Whether Descartes himself established a direct relation between these correlates belonging to the context of his analytical geometry and his two famous divisions of reality (i.e. res cogitans and res extensa) or not, it is nonetheless quite legitimate for us to recommend their extrapolated use in the manner we have outlined.
The thinking of the Absolute substance is referable to the vertical axis which answers to all possible cogitations of the mind, while the other correlate refers to pure a priori space schematically understood, as with the philosophy of Kant where extension constitutes a self-evident or a priori essence of reality where extension has a horizontal reference. Thus res extensa refers to the horizontal spatialized essence while res cogitans refers to its verticalized counterpart, combining mind and matter into one absolute reality. This would not have been possible if Cartesianism implied a merely dualistic philosophy which did not postulate such an absolute thinking substance.

Descartes is content to call this substance a form of animal spirit and in doing this his position is not radically different from that of Bergson who insists on the fluid character of the substance in his notion of the ' élan vital '. The process of creative becoming is more important for Bergson, but the status of the animal spirit of Descartes remains, in principle at least, the same as his own ' élan vital '. Descartes was more of a mathematician whereas Bergson was more of a biologist. Such differences of bias however, are not important for us in our present task of extracting the broad features of structuralism common to the methodology of both these philosophers. For both of them there is a neutral and monistic substance which can be submitted to the two basic references of the cartesian correlates. The process involved in the participation of space and time, or extension and thought, reveals the same kind of vermicular spiral or figure-of-eight, not unlike the vortices mentioned by Descartes.

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Overlooking the details that such a structure represents, we can, even at this stage, see the broad outlines of the structuralism anticipated and presupposed by Descartes.

If we keep these features in mind, it will be easy for us to fit into the same picture the three basic types of ideas implied in Cartesianism which are: the innate, the adventitious and the factitious. The first mentioned class of all self-evident ideas belongs naturally to the bottom of the vertical axis, and the last one to the top of the same axis, because facts must also have a horizontal reference because they constitute what is called sensa or sensible realities "out there" with a spatial rather than a pure inner reference.

The status of the second type of idea (i.e. the adventitious) has been questioned or doubted by the critics of Descartes who thought there was something ambiguous or uncertain implied in it. An uncertainty principle is in fact inevitable even in modern scientific thinking. Therefore the questionability of the adventitious ideas of Descartes can no longer be considered a weak point in Cartesian epistemology. Uncertainty is an. admissible form of scientific certitude at present. When we admit into our logic the principle of non-contradiction, without the principle of the excluded middle, we make room for entities that are not definable from one point of view or its opposite. Vedanta recognizes this as the principle of non-predictability (anirvacaniya). Non-predicability is therefore a strong point rather than a weak one in Cartesian methodology.

When Descartes says that his three categories of ideas are self-evident he merely underlines their a priori status, just as Kant does in his notion of schematized space. It is a conceptualized version which. counts here, and Eddington readily recognized this when he said it was concepts rather than percepts that matter.

The animal spirit as an absolute substance is where innate a priori ideas belong. It has a schematic status which alone is capable of abolishing the paradoxical element of duality. Descartes' critics think that by comparing the body to a machine and the mind to some kind of superior soul-substance he committed the philosophical error of admitting a duality between mind and matter. This charge altogether fails when we see that the absolute animal-spirit-substance is the common basis both of thought and extension which are the two main expressions of life referable to the two intersecting coordinates which have to be treated together as belonging to the same structurally conceived substance.

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Coming now to questions more directly related to method, there is the notion of methodic doubt. Descartes recommends this for the correct guidance of human understanding in its search for truth and certitude in clear apodictic terms. This clarity is not necessarily experimental, yet it shares with science the spirit of scepticism which refuses to believe before sufficient clarity for belief has first been guaranteed by proper methods of investigation. Certitude according to Descartes lies within oneself. It is neither to be one-sidedly attributed to a posteriori thinking nor to the conceptual a priori side.

The understanding has to be guided properly along lines of maximum certitude, starting from the core of the total knowledge-situation which necessarily lies in human consciousness and not anywhere outside. The famous Cartesian dictum, cogito ergo sum (I think therefore I am) puts its finger on this central and neutral meeting point of all certitudes. Superficial critics have fallen into the error of treating this dictum as a compressed form of syllogism and some of them have tried to extract the converse of it so as to prove its absurdity. In whatever familiar logical form this dictum might be stated, it is meant merely to refer to the structural zero point of the knowledge-situation which any systematic philosophy must postulate if it is to follow some definitely conscious method. On the plus side of the vertical axis, cogitations lead us to factual ideas, and innate ideas constitute a kind of rearguard in consciousness. Adventitious ideas necessarily bring up the flanks and imply an element of strangeness and accident, lacking full reality.

Descartes believed in God as a guiding factor for his moral conscience but this belief did not exclude his correct scientific attitude which depended on the right to doubt one's thoughts when they were not sufficiently clear. He accepted, side by side with a God, the Aristotelian notion of an 'unmoved mover,' and his scepticism started with methodically graded doubts in order to guide his instinctive dispositions and save himself from the pitfalls of error.
He was thus a true believer and a sceptic at one and the same time. This made him a puzzle to the Roman Catholic Church authorities who suspected him of heresy even though he openly avowed his belief in Catholic doctrine. Although not condemned as a heretic there is still a touch of martyrdom involved in his fears of Papal persecution which lent itself to be thought of as being both for and against the Church authorities.

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Cartesian methodology consists of directing human understanding by intuition along what Descartes calls "right lines". How is it possible by instinct or intuition to attain a knowledge of discriminating between what is right and what is wrong? Here we have not only matters of logical judgment but also the entering into the picture of value appreciation. Morality involves an axiological certitude where the notion of God, the Good, the Ultimate Goal etc., are the final causes for guiding conduct. It is here that the conscience comes in, and a moderated conscience characterized by wholehearted affiliation to the Good through a passionate love of truth has to correctly help in guiding human understanding.

The general idea of Goodness, Truth, Reality or God must descend to confirm the ascending reasonings built up by methodic doubt, starting with the legitimate scepticism that we have already referred to. Thus there is an ascending and a descending dialectic moving on a vertical parameter among higher spiritual or lower moral values. Existence, subsistence and value blend and neutralize one another yielding that whole-hearted and passionate search for truth which is the motive for the right conduct or human understanding. Words like whole-heartedness and "passion for truth" are meant to underline the absolutist nature of the complete morality of Cartesian philosophy. While remaining a priori and conceptual and even schematic in his approach, Descartes has a fully scientific methodology in its demand for certitude at every stage of its progress. Adventitious self-evident ideas pertaining to the matrix of the absolute substance called animal spirit, are first to be reduced and referred to in pure unitive terms, bringing them under the purview of res cogitans by an ascending or a descending process of methodic doubt or possible degrees of value certitudes.

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In the domain of res cogitans with its origin implied in the dictum cogito ergo sum Cartesian methodology reduces and constructs its speculative findings freely and methodically, complying always with the requirements of mathematics, logic and experience. The rightness or wrongness of a certain line of thought or action is determined always by the self-evident truth-quality given to the intuitive mind at every stage of the double dialectical process. There is an orthogonal principle involved and necessarily implied here in the correlates which intersect at right angles. A right angle is so because it is more "right" than any other angle. Human intelligence relies on this primary orthogonal justification even in measuring simple lengths and breadths of objects.

Descartes is aware of such a rightness given to intuition for the guidance of human understanding, not only within the limits of the visible sciences, but also for guidance in choosing between alternative courses of conduct and value appreciation. There is a subtle interdependence between perceptual and conceptual rightness.

We read the following in his "A Discourse on Method" (Part III Maxim II):

"My second maxim was to be as firm and resolute in my actions as I was able, and not to adhere less steadfastly to the most doubtful opinions, when once adopted, than if they had been highly certain; imitating in this the example of travelers who, when they have lost their way in a forest, ought not to wander from side to side, far less remain in one place, but proceed constantly towards the same side in as straight a line as possible, without changing their direction for slight reasons, although perhaps it might be chance alone which at first determined the selection; for in this way, if they do not exactly reach the point they desire, they will come at least in the end to some place that will probably be preferable to the middle of a forest. In the same way, since in action it frequently happens that no delay is permissible, it is very certain that, when it is not in our power to determine what is true, we ought to act according to what is most probable; and even although we should not remark a greater probability in one opinion than in another, we ought notwithstanding to choose one or the other, and afterwards consider it, in so far as it relates to practice, as no longer dubious, but manifestly true and certain, since the reason by which our choice has been determined is itself possessed of these qualities. This principle was sufficient thenceforward to rid me of all those repentings and pangs of remorse that usually disturb the consciences of such feeble and uncertain minds as, destitute of any clear and determinate principle of choice, allow themselves one day to adopt a course of action as the best, which they abandon the next, as the opposite."⁴

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Put in common-sense language, the above maxim can be looked upon as tantamount to asking a person to follow the dictates of his conscience through his intuitive understanding. It is also capable of being understood in the light of Cartesian analytical geometry where a vertical parameter implies an orthogonal reference to possible horizontal errors of judgment. Doubt and indecision are great enemies to a whole-hearted pursuit of truth as understood in Cartesianism.

Absence of doubt does not necessarily mean belief in a hypostatic God, but rather combines with the scepticism that is its natural and necessary counterpart. Certitude thus is a point that moves up or down along the vertical parameter given to intuition. Even in cybernetics an orthogonal matrix is involved for the thinking machine to arrive at a stability of output having a maximum truth value. Thus the Cartesian method fully respects the logical structure that science is coming to recognize more and more in all precisely understood disciplines, hitherto divided and relegated into the distinct compartments of physics or metaphysics. It is now possible to treat them both as belonging to one and same integral structural context.

After roughly understanding the implications of the vertical reference of res cogitans it is not impossible to recognize its own horizontal correlate. Here it is the attitude of the subject, when interested in outward objects, persons or personified ideas understood in the axiological context, which become correctly referable to this horizontal axis. The emotional states of man arise from his love or hatred of things. This results in happiness, suffering or morrow.

Descartes enumerates such states as passions and lists them as wonder, love hatred, desire, joy, and sorrow. There is a circulation of interest here beginning with wonder and ending with Sorrow.

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This alternating process tends to repeat itself in a cyclic figure-of-eight, referable to the plus and minus sides of the horizontal correlate in pure self-evident conceptual and a priori terms and always having a schematic status. The methodology comes in when we understand the process as operating alternately in a necessary order of succession natural to normal man. Passions can be discarded when, by long repetitions of this alternating process, a point of surfeit or saturation has been attained by the person wholeheartedly seeking truth. In principle, however, the horizontal axis is never totally abolished as long as its use for guiding understanding is present.

The contemplative methodology in the context of a passionate search for absolute truth is seen to follow the broad lines of our structuralism. The essence of this methodology consists of a schematic reduction and verticalization of the self-evident factors involved under the overall categories of existence, subsistence and value. This essential feature is also adopted by Narayana Guru in this chapter. The negative movement of speculation started in this chapter is maintained up to the end of the Fifth Chapter. Thereafter what follows is not a reduction but a construction, still retaining however, its unitive and more positive tendency. In the last Chapter this tendency is finalized in the perfection of the man of nirvana.

We have just seen how Cartesianism implies the beginnings of a structuralism which affords us a means by which not only can time and space be treated as correlates, but also one which can act as an instrument of research extended into the whole range of philosophy. A total philosophy, structurally conceived, will include rationalist and even value-factors, ethics, and aesthetics. All can be discussed in a structurally unified and integrated fashion. The barriers that have kept physics and metaphysics apart can now be treated in a unitive fashion. Physics and metaphysics have been enabled now, by the common structure underlying both, to be treated as one and the same integrated whole in the context of a total truth.

The most epoch-making event that has taken place in our time is the formulation by Einstein of his Relativity theory. No other theory in modern times is so much talked about. Although Einstein took particular care not to erect a philosophy by characterizing the world of physics as a reality based on a sufficiently radical concept of relativity, still his theory has not failed to shock common sense.

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Relativity as first formulated by Einstein within the scope of the Restricted Theory does not admit of any unique or universal Time which common sense tacitly assumes and which absolutist philosophy always presupposes. There are many frames of reference possible to a relativist and pluralism, as one of them, goes better with relativity than any unified notions of an absolutist nature.

The plurality of times is thus a corollary directly derivable from Relativity Theory. When the plurality of the reality of time is conceded philosophical pluralism is tacitly assumed. In spite of the care that Einstein took to keep his theory within the bounds of physics, we now find that it has become the fashion among modern thinkers to put pluralistic or relativistic notions on the pedestal as a sort of article of faith in order to uphold such a theory before the public eye in the name of progress, technocracy or civilization.

The spectacular triumphs in modern science have added their large volume of support to this technocratic attitude. As a result there is now a serious disruption of the sense of right values. It is therefore highly desirable that this lopsided approach to truth be rectified by a full formulation of the Science of the Absolute where both physics and metaphysics can coexist without conflict. The epoch-making step taken by Einstein in formulating his Theory of Relativity is not however a step taken in the wrong direction. On the other hand, Einstein started a new tradition in physics, implying a revised epistemology and methodology that no more emphasizes experiment and observation as unilaterally understood, but instead relies on the observer and the observed as correlated counterparts. The new physics relies more on mathematics than on mere observable laboratory experiments. It represents an attempt to bridge the gap between axiomatic and experimental thinking. The Cartesian correlates play an important part in relativity theory where they are treated as time and space belonging together to one and same continuum. Whatever the term "continuum" might mean, we enter here into a new kind of physics where time, that is not visible, and space, that is evident only through visible objects, are treated together as belonging to one and same knowledge-situation, whether that of physics or metaphysics. Thus physics and metaphysics come together and overlap in the post-Einsteinian version of the expanding or contracting universe with its red or violet shifts.

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The more radical mathematical view of the universe of cosmologists like Kepler, Galileo and Copernicus has also been found inadequate by Einstein, although it is not very easy to determine at present where exactly we stand in respect of the physical world presented to us by modern physicists. One thing is certain however; that many conventional notions have been put into the melting pot. The physical world that we are now asked to accept for the common purpose of intelligently guiding human life is full of inconsistencies, improbabilities and impossibilities. The way out of this impasse consists, not in retracing our steps from the point to which relativity theory has taken us, but in going forward boldly to face the fullest implications and consequences of relativity. It goes without saying that relativity as a guiding characteristic of all physics must necessarily presuppose its opposite of absolutism so as to have any linguistic validity at all. Thus we are faced with the problem of putting relativity and absolutism together in the name of an integrated Science of the Absolute.

When one says that there are absolute and relative truths, one unconsciously creates in the mind two rival entities answering to the requirement of what is called truth. These two rival truths are two limiting instances of a more neutral and central notion which combines in its scope these two possible variations. Thus we have, in the context of the two antinomies referring to the absolute as plus or minus limiting notions, one which can be pluralistic and another which will not admit of any pluralism. What admits of pluralism can be placed subjectively, for purposes of linguistic clarity, at the bottom of the vertical axis. What does not admit of pluralism as a concept more positively understood finds its place as a limiting case on the plus side of the vertical axis. The normative Absolute will have its structural position at the very centre of the total knowledge-situation. This means we have a relative of an absolutist context and an Absolute of an absolutist context. They are positive and negative limiting cases of a normative Absolute which implies normalizing with reference to the two others.

Such are some of the semantic and epistemological implications which we have to keep in mind in. order to avoid confusion in the matter of understanding all things sub specie aeternitatis.

The methodology and structuralism tacitly presupposed in the Darsana Mala imply both a reduction and a construction by which multiplicity is first reduced to negative unity in the first five chapters. Both plurality and duality get abolished by a method of elimination of what is doubtful and unessential.

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Having touched the rock bottom of ontology by this negative reduction, the last five chapters aim at a more positive construction, implying the normalizing of existence with its own rational subsistence. There is a construction implied in the method here by which ontology gets transformed into a value world where teleological first and final causes gain gradual primacy. Even at this stage of reconstruction there are always the Self and the non-Self involved as irreducible counterparts related by complementarity, reciprocity and cancellability. We shall explain these later on. Here we have only to remember that the methodology of this work has to be treated together with its own epistemology and axiology.

The methods of mathematics and the rules of logistics or semiotics could be looked upon as operating from one limb of an equation, and the resultant understanding could mean the same truth seen from opposite sides of a total knowledge-situation. These methods and rules are not outside the world of discourse proper to an integrated Science of the Absolute. They have to be thought of as legitimate features of the methodology which we are here concerned with. Pluralism might be admissible in a merely utilitarian philosophy. Axiomatic certitudes of mere idealism might support only one Truth. The modern scientific tendency which gives to percepts and perceivable realities a place more important than concepts and conceivable realities takes a one-sided position. It goes without saying that such preference for the perceived is a partiality of the scientist which cannot be admitted in a normalized integrated Science of the Absolute, where all realities are to be viewed in an impartial and neutral light. No philosopher should have any "private axe to grind" as Bertrand Russell rightly asserts. Bergson puts the same requirement in better form when he says he proposes to follow the rule as one "of not accepting anything which cannot be accepted by any philosopher or scientist, nor accept anything that is not already implied in all philosophy and science". (D & S, pp.87-88).

Even Eddington revised scientific epistemology for his Philosophy of science, as we have already pointed out. He wants to give concepts a more important place than scientists have hitherto given them. He takes his position as a non-experimentalist and categorically asserts that it is concepts that matter.

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Concepts and percepts belong to the same total knowledge-situation when they are accommodated under one and the same schema. Bergson does not find any objection to such an inclusion of conceptual and perceptual factors, and says: "they could be represented by the same schema". (D & S, p.84)
We also read the following from Bergson:

"I can also conceive that all the points of the universe that are mathematically related to the present and to the past - that is to say, the future unraveling of the inorganic world can be represented by the same schema." (D & S, p.84)

We have here to remember that the actual time that passes has a perceptual status and future time has a conceptual or metaphysical one. Our inclusion of both these aspects in one and the same schema is justified by thinkers like Bergson, who have improved on the schematismus of Kant on lines we have already explained. The two correlates schematically referring to the time and space of Einstein, the res cogitans and res extensa of Descartes, and the natura naturans and natura naturata of Spinoza can all be fitted into one schema.

We can even extend the application of these same correlates into the domain of Vedantic thought where reference to the horizontal as the world of effects and to the vertical as the world of causes is found. In the language of the Bhagavad Gita one can think of the same correlates as representing the field (kshetra) and the knower of the field (kshetrajna). The latter is the vertical because of its attenuated or refined status, referring to the same universe of Einstein wherein the observer and the observed have to belong together to a context common to the liquidity of matter and the fluidity of mind.

Newtonian physics is a limiting instance of modern post- Einsteinian Physics which insists on characterizing itself in its own deliberate way as relativistic in outlook.

Absolutism thus implies relativism and it is by giving to these terms their proper places in a normalized schematic totality that ambiguities and confusions can be avoided. Such a schema is what we have suggested all along.

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In this present chapter it will be seen that Narayana Guru relates the world of effects to the world of causes. This implies a negative reduction of horizontal factors into vertical terms. This gives a mathematical or dialectical reduction of counterparts wherein the visible world is absorbed by gradual steps through reasoning into its existential or ontological residue of absolute reality. Even when reduced in terms of existence it continues to be characterized by subsistence. Its rationalist status and value belong to the world of aesthetic or ethical significance pertaining to axiology. Finally characterized by existence, subsistence and value, this Absolute as seen from a total philosophical or scientific standpoint. We have thus to first arrive at the ontological Absolute by the method of reduction. A positive mathematical construction would then yield place to this negative methodic reduction. The present Chapter is meant to explain in broad outline the implications of this negative methodology.

Common sense takes it for granted that there is a unique and universal time having its reality in the minds of animals and man. Whether this duration is precisely measurable with the help of clocks or only understood in reference to sunrise, sunset etc. such a common experience of time is a matter that is not usually put into question. Even in such matters vouched for by common sense there is a possibility at present of two rival positions between sceptics and believers.

Modern scientists or empirical and positivist philosophers prefer to call themselves sceptics who have no use for any unique or universal notion of time. Such a time according to them would have an absolutist status. Because relativism and pluralism are now in fashion, in the name of a scientific tendency treating all metaphysics as nonsense and excluding belief in any God or even in a godlike entity, it is only to be expected that the relativistic outlook does not tolerate the unique time of common sense. Relativity puts the observer and the observed together at various points of universal space and every observer relates himself to the observed belonging to his particular pluralistic frame of reference. Time is thus measured preferably in piecemeal fashion rather than in any wholesale manner by relativists. Relativity results from the interaction of many possible observers placed at various points in space, each with a corresponding event in the universe he is observing , with or without the help of instruments.

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When the counterparts of the observer and the observed are brought into interrelation, participation or interaction, the resulting relativist universe does not admit of one time but only of a time that is multiple. Light being independent of both space and time and of any movement of its source can, in principle, yield simultaneity and not duration.

Even such a natural position is not presupposed, at least by the "restricted" theory of Relativity. It is easy to see how this theory recognizes and gives primacy to spatialized factors, referring to the horizontal axis, in the structure of the Absolute.

In the General Theory of Relativity time and space enter together to be treated as a continuum. Here we begin to have the vertical correlate representing time coming into the picture side by side with space. The fragmented time implied in the Restricted Theory of Relativity is one that has shocked both common sense and ruled out the philosophers´ belief in absolute time. Sceptical philosophers favour this kind of time as against the absolutist a priori time which metaphysicians glorify sometimes, putting it on a pedestal and giving it equal footing with a theological God. Descartes could be cited as representing such a philosopher who speaks of pure duration as given to intuition as a divine factor. He did this in order that his occasionalism could operate.

Time could either be related to mechanistic or to creative evolution, and there are philosophers like Julian Huxley who admit time into their metaphysics, yet claim to remain empirical scientists. There are, however, various brands of evolutionism, some mechanistically biased and others conceived on a more fluid basis and called 'creative.' To the extent that time is included as a pure duration given to intuition, strict scepticism may be said to yield place to some sort of belief.

Between scepticism and belief history has produced many instances of martyrs who have suffered the highest penalty for believing truths unacceptable to orthodoxy. Even Descartes had to withdraw his book on cosmology which was being printed at the time when Galileo was being condemned for heresy. Bruno was executed for not believing what the authorities wanted him to believe about the universe. Some of those who first suffered because of the Church have later become acceptable and some, like St. Joan, have even been canonized. A Science of the Absolute has to recognize both kinds of martyrdom with equal fear or favour as the case may be. It cannot take sides. The same applies to the question of accepting or rejecting the claims of a unique or universal time.

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This means that the Science of the Absolute cannot altogether refuse to give due importance to the practical reality of time or duration. To do so would be to take the side of those who deliberately wish to do violence to common sense. The question of duration which is so directly within the scope of human experience can be scientific even when we decide to take the side of believers as against sceptics. It is a neutral and normalized position that is proper to any correct Science of the Absolute. In the light of the prevailing vogue in the scientific world of not recognizing universal time or the duration that presupposes it, what is the position that we should take? Is there a correct scientific methodology whereby we can arrive at a unique and universal time while starting from the relativistic position in respect of time implied in the limited theory of Relativity?

Does such a methodology take account of the modern scientific equations and experiments? It is these alone which give strict scientific status to the reasonings and calculations of this new methodology required to admit a unique and universal time on a par with its own relativistic counterpart belonging to the same total knowledge-situation? If they are put together under the same schema combining physics and metaphysics are we able to attribute a homogeneous epistemological status to both of them together? What is the nature of this neutral monistic substance or stuff in which time and space exist without contradiction, participating in matter and mind at one and the same time? Does this neutral substance resemble the animal spirit of Descartes or does it rather answer to the structure of non-Euclidean geometry where, losing its radical rigidity of uniform motion in straight lines as in classical physics, this neutral stuff accommodates the notion of a space-time continuum. When treated as neither mind nor matter , irrespective of the observer or the thing observed, do we not attain to the position of postulating what Narayana Guru in this chapter calls chaitanya, or vital consciousness?

Such are some of the questions that we might be called upon to answer when we are concerned with a methodology for the Science of the Absolute. In the present chapter moreover we are concerned with effecting a transition from the world seen as an effect or a presentiment, to one where causes and effects can be treated together on a more neutral and homogeneous ground.

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A Science of the Absolute cannot tolerate an inner tautology or an outer contradiction. Besides methodology, as we have already said, such a science must have its own epistemological and axiological presuppositions or implications consistently belonging to it. We have to avoid at any cost being merely conventional in such matters, whether in the name of traditionalism or of progress. When we keep all these questions together in our mind it will be seen that there is hardly any literature available at present which takes the correct impartial position between the two disciplines of physics and metaphysics. Starting from what is known through the senses and thus naturally with realities that depend on space, we can travel step by step to attain a notion of pure time that is not directly given to the senses. Thus we have to travel from rigid objects in space to the pure flux presupposed by absolute time. The limiting instances in such a journey that we can understand mentally are precisely those of classical and modern physics. The steps of such a transition from a rigid or radical universe to a universe that is recognized as affiné or refined, together with a notion of time proper to each of them, have been worked out in great detail, without omitting any experimental or mathematical details, by Henri Bergson in his Durée et Simultanéite.

Strangely enough, Bergson withdrew this work in the year 1922, Even though he pleaded for a time that is given to the common sense of all men irrespective of scepticism or belief, Bergson had to be cautious and circumspect. It was not however in the name of the prevailing values of any orthodox religion, but strangely in the name of scientific scepticism that he acted. Concerned as we are with the methodology proper to the reduction of the relativistic or horizontal multiplicity of pluralistic factors or elements into unitive terms, we are also interested in supporting our arguments fully with experimental and mathematical notions of modern science. Bergson's work comes admirably to our rescue here. We cannot enter into minute examination of all the implications found in Bergson's suppressed work, but we will rather only concern ourselves with those parts of the book which directly support our own arguments. Bergson says he wrote the book for the following reasons:

"We have undertaken this work exclusively for ourselves. We wish to know to what extent our conception of duration was compatible with Einstein's view on time." (D & S, p.v)

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Bergson was also interested in Einstein because, according to Einstein's way of thinking, "science and philosophy are different disciplines but are made so as to complete each other." (D & S,p.v). Thirdly, Bergson considers that there is a paradox that spoils the clarity of time as understood by Relativity. He explains its nature as follows:

"We have had to call special attention to the paradox of the theory of Relativity, to the multiple Times which flow with greater or lesser speed, and to the simultaneity which could become succession and the succession which could become simultaneity when one changed the point of view".(D&S,p.v)

He continues:

"The general theory of Relativity comes to place itself on the side of time when it wishes that one of its coordinates would effectively represent it." (D & S, p.viii)

These three features can. be understood with their various implications only when we keep in mind the questions we have suggested above (pp.298-299). It will be further helpful for the reader to begin to think in terms of the schematic language that we have developed, in order to follow more easily those preliminary remarks of Bergson.. Let us also say here in advance that we shall hereafter take the liberty of relying more and more on the structural language of our protolinguism. If such a linguistic device proves in any way helpful to the reader, that itself would amount to its justification and add to its validity because of the useful purpose it serves.

Bergson is interested in making philosophy a discipline that can be treated with physics in order that both physics and metaphysics could form one integrated or unified discipline. This can be called a science or a philosophy as one prefers. What results is a philosophy of science or a science of philosophy, or even a science of sciences. In our view this is no other than a Science of the Absolute.

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In India, brahma vidya is referred to as the science (vidya) which is the foundation of all sciences (vidyas). It deals not merely with "truth" but with the Truth of truths, the light of lights, or the Value of all values. The Absolute is the natural and normative notion around which this science was built. When stated in such a wholesale fashion the Science of the Absolute becomes repugnant to the spirit of modernism because it appears as a seemingly totalitarian discipline. Totalitarianism in politics and religion has left a bad taste in the mouth of most Europeans, who prefer a humbler piecemeal approach to truth. In spite of such an understandable objection, this is in itself another form of prejudice not necessarily justified with equal force in other contexts, outside religion or politics.

Bergson's hesitation to characterize his attempt to give time its legitimate importance and place in a more broadly conceived science than hitherto, is thus quite understandable. He has said openly in his Preface that he was interested in seeing how far the time of common sense corresponded to the time of Relativity. Each observer of a given system has his own time reference independent of his rival in another system. Such was the basic presupposition of Relativity, legitimate only in the context of physics as a discipline distinct from metaphysics. This kind of time shook commonsense as well as the philosophical notion of a unique and universal time that metaphysics always assumed.

Bergson is interested in showing that there should be a time that could be viewed as both perceptually and conceptually valid with equal force. In taking a central normalized position in respect of time, Bergson is in reality arguing the case for a Science of the Absolute. The time that interests Bergson is therefore a fully normalized version of absolute Reality, perceivable, and conceivable at one and the same time. He fits such a time into a common schema that is independent of relativistic physics and pluralistic philosophy.

It is therefore not wrong to assume that the unique and universal Time that Bergson is interested in is no other then the absolutist version of the pluralistic time of Relativity. We have already said that it is possible for the purposes of this Science of the Absolute to choose any one of the basic categories that find place in the totality of the structure of the Absolute so as to revise and restate its status and give it a neutral, central or normalized position for the clarification of the content of the Absolute.

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In this chapter Narayana Guru refers to the notion of cause rather than of time. Whether cause or time is used, for our purposes of clarifying methodological aspects here, the resulting steps of the argument involving the reduction that we have spoken of remain unaffected. It is therefore no less useful for us to follow the steps of the scientific reasonings of Bergson, even when we should be thinking of cause and effect rather than universal and unique Time. The first and final material cause of the universe must have an absolutist status in the same way as the multiple time of Einstein must presuppose more philosophically an absolutist concept of Time. It is in this light that it is interesting for us to pay some attention to the five main objections of Bergson to the pluralistic time of Einstein.

Bergson's five objections are as follows:

"It is because of not having defined with rigour the terms employed, it is because of not having been sufficiently habituated to see in relativity a reciprocity, it is for not having had constantly present before the mind the relation between radical relativity and attenuated relativity, for not having been cautioned against a confusion between the two, and finally for not having pressed sufficiently together the passage from physics to mathematics that one so seriously erred on the philosophical meaning of the considerations of time in the theory of Relativity." (D & S, p.52)

Even before formulating these charges so boldly and categorically, Bergson explains in the Preface that a major paradox is hiding at the core of the problem and is responsible for all these errors. In our own words we can say that this paradox consists of whether one should take a horizontalized and spatial view of the universe or a verticalized and temporal one.
In Bergson's own words:

"The confusion of this basic paradox is in the mind of those who erected this physics as such into a philosophy. Two different conceptions of Relativity, one that was abstracted and the other imaged, one that was incomplete and the other achieved, coexisted in their minds and interfered with each other. In dispelling this confusion one made the paradox fall."
(D & S, p.vii)

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The task of making the paradox fall as Bergson proposed to do is tantamount to the task of abolishing relativism altogether along with its implied pluralism. Whether such pluralism implies time, space or both, it is nonetheless understood that a non-pluralistic notion of the Absolute should be attained. Bergson as a philosopher who denounces conceptual or conventional metaphysics cannot be expected to say this as openly as we do here. An examination of his laborious work is sufficiently convincing on this point all the same.

A process of becoming or flux understood in terms of life is the ultimate absolute reality for Bergson.. In the present work, as in all his other works, he seeks to find support for this flux of the élan vital at the basis of creative evolution. Spatialized time is converted and understood in terms of a time that correctly represents this unique and universal Time for which Bergson's philosophy stands. The duality of time and space found in the Cartesian analysis of absolute substance is abolished by Bergson. He does this in terms of a dynamism that is ever in the process of a creative becoming. He however takes care to present a schéma moteur more dynamically conceived and without a Cartesian fixed frame of reference. The logical and semantic purpose or use of correlates is not discarded by Bergson. If we keep these features of Bergsonianism in mind it will be easier for us to follow clearly his own line of attack on relativity theory.

Bergson's main task is to give a unique and universal status to time by ridding it of its spatialized and pluralistic prejudices. In order to accomplish this difficult task he makes use of the same mathematical equations which Einstein used. The contraction of Lorentz supported by Fitzgerald depends upon a mathematical transformation taking place between the terms of an equation. We know elsewhere from analytical geometry that equations can answer to lines on a graph and vice versa. There is a rigour, adequacy and a possible homomorphism to be presupposed between them. The two proofs of the Pythagorean theorem refer to the same central truth which can be looked upon in a formalized and logical, or a structural and geometrical fashion. They belong together to one and the same mathematical entity.

The Lorentz equations answer to the correlates or vice-versa. Both obey the same relational laws in nature, logic and the propositional calculus. Schematism can be treated either protolinguistically or metalinguistically.

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We have explained these possibilities at length elsewhere. Bergson in following up his revaluation and restatement of the relativity theory without its paradox, next turns to the equations of Lorentz. When schematically understood they reveal the same structural pattern based on the reciprocity between timelike and spacelike factors in the physical universe which are both gross and subtle at once. The Lorentz equations apply to an attenuated and refined universe wherein contractions and expansions involve distances to be expressed by six decimal points, observable only indirectly through red and violet shifts or by the aid of a tentative mathematics based on a priori postulates and axioms. Strictly speaking these postulates and axioms have only a hypothetical and non-experimental status of their own. The validity of some of the remaining assumptions are left to be fully verified by future observations of the micro- and macrocosms.

Bergson however is on safe ground when he bases his objections on the very same equations that Einstein used in his theory of Relativity. In his work under reference here Bergson has used the same mathematics as Einstein and also the same frame of reference implied in the Michelson-Morley experiment. Light affords an absolute frame of reference and the failure of the Michelson-Morley experiment to show any fringe effect further proves the fixed, immobile and absolutist status of the space in which no ponderable ether in motion is found.

Both the equations of Lorentz and the observations made by modern physicists have, in the structure of space in terms of the velocity of light, an absolute frame of reference. Newtonian space and motion have a rigid status and are considered absolute by Einstein in the sense that they are treated as independent of the observer. Classical physics is not however altogether dispensed with by Einstein. It is often referred to as a limiting case for the world in which the relativity theory operates. We cannot enter into all these implications of absolutism or of relativism that enhance or detract from the value of the relativity theory. It is therefore safer for our purposes to follow the same line of reasoning as Bergson.

305

By doing so, as he says, the case for a unique and universal Time still remains valid and fully justified even according to the mathematical equations of modern physics.
He writes:

"To know this (that is to know what interests the philosophers rather than the physicist) we have taken the formula of Lorentz term by term and have searched for the concrete reality and the thing perceived or perceptible that each term corresponded to. This examination has given us an unexpected result. Not only did these arguments not contradict themselves, they also confirmed and accompanied the commencement of the proof of the natural belief of all men in respect of a Time that is unique and universal." (D & S, P.vi)

Bergson here is evidently interested in giving to time a universal and unique absolutist status. We have to remember in following his methodology that the same can be applied in an extrapolated manner to the question of a unique and universal principle of causation. The change from Time to Cause would change nothing in the methodology. It will only be an additional case where the Absolute would become once again reaffirmed.

In the enumeration of his five objections against relativity theory, Bergson puts the first one as, "not having defined with rigour the terms employed." In the first two chapters of his work he uses terms such as "demi-Relativity" and "unilateral Relativity". He also refers to reciprocity as a more suitable term than what he refers to as "incomplete Relativity". He also uses the phrase "complete Relativity" for his revised version. It is important to see how far he is justified in thus revising or applying his correction to the Theory of Relativity as presented by Einstein.

Einstein speaks in the name of physics and he is perfectly correct in doing so. Bergson on the other hand as a scientific, philosopher is speaking in the name of a unique and universal Time of common sense, free from the mere world of particular physical distances and events mechanistically understood in multiple time.

We are not merely interested in such a philosophical view of Time as a flux with an absolute Reality, but in the larger context where duration and distance are both included within an absolute principle of causality. We have elsewhere made some general remarks about such matters in order to clarify our position (see p.916 below).

306

In taking up one by one the five objections raised by Bergson, we are making an effort here to clarify the position afresh. Scientific truths can be stated in simplified fashion so that men of commonsense will feel their rightness even when they have no technical training. We are not against any notion that resembles the Absolute . We keep an open mind in this matter and understand why modern science finds it repugnant to think in terms of one absolute truth and avoids anything resembling the a priori approach. We have already explained elsewhere the origin of such prejudices which cannot be continued into our own attitude in respect of an integrated Science of the Absolute. Let us now try to restate the position of physics and Bergson's approach.

The Michelson-Morley experiment has given Physics a mathematical and structural frame of reference involving the Cartesian correlates and the equations of Lorentz. A new way in physics was thus opened up by Einstein. In this new physics the observer and the observed belong to the same spatio-temporal frame of reference. Distances in space are more easily perceivable than intervals in pure Time. Relativity must refer to both Time and Space as belonging to the same homogeneous matrix or basis. To make them belong together thus was a philosopher's task rather than that of a physicist.

Thus, when the Michelson-Morley experiment failed, the average undaunted physicist started to theorize about space-time relations within his own arbitrarily postulated closed systems where a physicist observer interested in perceivable realities was supposed to live within what he was observing. This was at first crudely accomplished either with mechanical clocks or by the measurable distances of the moving system. Refinements were introduced stage by stage resulting in the "restricted", "general" and "unified" views of Einstein. Such is the basis of the relativity theory erected by Einstein as a revaluation of Euclid and Newton. The ensuing convulsions and sensations in the world of general philosophical thought rudely shook all previously held notions about the physical universe. It was at last given to Bergson to bring forth his arguments in order to salvage at least the case for a unique and universal Time.

The denunciation of absolutism seemed to gain some unduly exaggerated initial momentum at the time when Bergson thought fit to intervene to save Time from the permanent damage of being forever discredited. His arguments seen in this light more clearly reveal their validity and force.

307

We are concerned here specially with his first objection which is that of not defining the terms with rigour. He means that the term "relativity" as used by Einstein only amounts to a demi-Relativity or an incomplete or unilateral Relativity. In justifying this charge Bergson points out certain innate inconsistencies presupposed especially by the restricted theory of Relativity where Space rather than Time is treated as more important. The familiar example that is given when one tries to explain the implications of this theory is that of a train moving at a speed approximating the speed of light. It moves in a direction that is horizontal and at right angles to a fixed source of light placed somewhere to serve as a reference. The length of such a train when travelling in the direction of light is supposed to shrink into nothingness when the speed corresponds to the velocity of light. Such is the theoretical assumption of the Lorentzian equation, implying a Fitzgerald contraction in the context proper at least to the Restricted Theory of Relativity.

If the common man should ask such a relativist whether this contraction is observed or observable he would say that such observation is only possible if the observer could be placed within an immobile and independent frame of reference. The possibility of such a perceivability in science together with the theoretical conventions proper to it is the basis of the validity of the contraction. These conventions are accepted only to the extent necessary to justify the truth of relativity as a physical and not a metaphysical reality.

The assumption of the physicist is that even though the Michelson-Morley experiment failed, the actual physical medium in which space and time are to be interrelated through velocities and intervals such as that of the motion of the earth around the sun, is still within the scope of a possible perceivable calculability. This is accomplished by the cooperation of postulates, axioms and conventions in modern mathematics on the one side, and on the other side by possible recorded observations or verifications. Many of the implications of the three tentative theories are still to be verified.

Such is the thin, attenuated and highly refined world situated at the point where rigid realities are made to melt and blend with a world to which the red shift legitimately belongs. The status of such a universe is at present exceedingly vague and questionable, even in the eyes of strictly trained physicists.

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Is it any wonder that the philosophical instinct is rudely offended by some of the easy assumptions of prevailing relativistic thought?

We do not feel competent to enter into the merits of this discussion which requires a more mathematically trained mind. Also we do not wish to part company, if we can at all help it, with the claims of physicists when they are found valid from the standpoint of a future Unified Philosophy of Science. We shall therefore rely on some direct quotations from Bergson to show how, without violating the requirements of a scientific methodology still based on acceptable mathematical conceptions of our time, he is able to reveal to us some of the errors and anomalies of relativity theory. The following quotation is from Bergson's first chapter, entitled "Demi-Relativity":

"We wish to manipulate all the transitions between the psychological and physical standpoints, and between the Time of commonsense and the Time of Einstein. For this we have to place ourselves in that state of mind where we one can find oneself at the original point when one believed in an immobile ether in absolute repose, while at the same time explain the Michelson-Morley experiment. We shall thus obtain a certain conception of Time which is half relativist by one side only and which is not yet that of Einstein, but which we think is essential for us to know. The theory of Relativity may not take any notice of it in its deductions which are scientific in their proper sense: we believe it is subjected all the same to its influence as long as it stops short of being a physics that wants to become a philosophy. The paradox that frightened some and reduced others so much, seems to us to come from this. It depends upon an equivocation. It is born from the fact that two representations of Relativity, one that is radical and conceptual and the other that is attenuated and imaged, accompany each other in our unconscious mind arising from the fact that the concept is subject to the contamination of the image." (D & S,pp.2-3)

On examination the above paragraph brings into relation two aspects of absolute Reality which Bergson has distinguished clearly. He has elsewhere tried to apply other predicative attributes to it. In doing this, Absolute Reality becomes a paradox both to the physical theorist and to the scientific philosopher.

309

In our structural language it is fully legitimate to refer to these aspects as the verticalized and horizontalized versions of the same absolute Reality which can be attained when the implicit paradox is dissolved. Bergson also clearly recognizes this.

Newtonian physics with its laws of motion is the horizontal version of spatialized reality, while time treated as a continuum with space as found in Einstein's General Theory is the vertical correlate belonging to the same paradoxical content. It is in this sense that Bergson, in the concluding sentence of his work, sums up the position of Einstein when he says that "Einstein is the continuator of Descartes." (D & S, p.241)

Descartes' two categories of res cogitans and res extensa correspond to his correlates. These correlates represent by their intersection space-like and time-like aspects of absolute substance and the principle of universal causality can also be located at the point of origin of the four-limbed quaternian structure. These are matters we have already elaborated sufficiently in their logical, semantical, structural and schematic implications. A logarithmic curvature of space and time can find its place at the same point in the vertical axis. We have already quoted (see pp.154-155 above) more than once from Bergson's "Durée et Simultanéite" where he graphically elaborates the structural implications of a complete theory of Relativity. As a result of all these discussion carried on term by term and stage by stage, Bergson is able to give to Time a unique and absolutist status.

There are two footnotes in Bergson's work which are of special interest to us, and since we are still concerned with demi-Relativity we shall quote them. The first footnote refers to the common sense question which is concerned with the contraction of the length of a body when it moves in the direction of light. The question can be asked, "What happens to the height or the breadth of a body, if any, which cannot shrink because of being at right angles to the direction of the propagation of light?" This objection is referred to by Bergson as follows:

"It seems, in the first place, that instead of a longitudinal contraction one could as well have supposed a transversal dilation, or one or other at one and the same time, in the correct proportions. On this point, as on many others we are obliged to leave aside the explanations given by the theory of Relativity. We limit ourselves to what interests our present research."
(D & S, p.8)

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Such incompatibilities arise from the violation of the basic laws of epistemology and methodology necessarily implied in mathematical equations and their corresponding visualized or structural versions, between which modern structuralists postulate a homomorphism. We shall now pass on to some other aspects of Relativity that reveal the incompleteness of the theory as pointed out by Bergson. In his second interesting footnote we read the following:

"It is important in effect to remark (one has often omitted to do this) that it is not enough that we take the contraction of Lorentz for establishing the point of view of the ether, the complete theory derived from the Michelson-Morley experiment performed on the surface of the earth. One has to join to it the lengthening of Time and the dislocation of simultaneity, all of which we shall come back to presently, after transposing them into the theory of Einstein. The point has been put into proper light in an interesting article of C.D. Broad called "Euclid, Newton and Einstein" (Hibbert Journal, April 1920)"
(D & S, pp.9-10)

It is evident from the above remarks that many aspects of relativity remain to be revised and completed in the light of a unified methodology and epistemology. Bergson takes the trouble of following up the broad assumptions on which the theory of Relativity is based so as to bring in, stage by stage, the corrections needed in the equations and the applied visible aspect belonging to the form of the equations. Here Bergson may be said to anticipate modern structuralists who see a common structure implied in all the laws of physics. When properly formalized or schematized they reveal a common homomorphism. At the time when Bergson wrote this the structural interpretation of the laws of physical nature had not yet become as acceptable or nearly accepted as it is at present.

Bergson is next seen to manipulate the Lorentzian equations conforming to the same axioms and conventions acceptable to the mathematicians of his time. In doing so he adopts the device of speaking of different time-space systems or schematized versions which represent the results of the Lorentz equations when applied to situations real or imaginary.

311

The first reference to such a rival system is to be found in the following quotation which is self explanatory. Moreover to speak of a proper frame or system of reference belonging to each observing physicist is not inconsistent with the overall position acceptable to the theory of Relativity. We read the following:

"Generally speaking, let us call S an immobile system and S' another sample of the same system, as its double, which in the beginning was one with it and which detached itself afterwards in a straight line and with a speed V. As soon as it departed S' contracts in the direction of its movement. All that is not perpendicular to the direction of the movement participates in the contraction. If S had been a sphere, S' would have the form of an ellipse. By this contraction the Michelson-Morley experiment is shown to give the same result as when light had a constant velocity and equal to C in all directions."
(D & S, p.8)

We are here concerned with three different aspects of reality. The first belongs to the immobile ether where the Michelson- Morley experiment reveals the velocity of light to be a constant. In the second we have a system S wherein an imaginary physicist named Peter is situated before any motion effects a contraction of space. Finally there is a system S' which is a double of the system S, subject to the contractions and dilations directly derivable from the Lorentzian equations. System S´ is occupied by an imaginary physicist, Paul. Both Peter and Paul have mechanistic clocks to refer to in each of their systems. When the implications of the equations are fully manipulated we get a more complete picture of Relativity than envisaged by Einstein. The manipulation of the equations and the visible implications of the same, (i.e. the mathematical and physical versions), are brought together by Bergson in the following way:

"In brief, the system S´ envisaged in Space and Time is a double of the system of S which is contracted in respect of space in the direction of its movement, which has dilated in respect of time in each one of its seconds, and which finally in time has dislocated in terms of succession all simultaneity between two events of which the distance is retracted in terms of space. But these changes escape the observer who is part of the mobile system. Only the fixed observer can see it."
(D & S, pp.20-21)

The incompleteness of the approach of Einstein is here initially exposed.

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Bergson's second objection arises because "of not having been sufficiently habituated to see in Relativity a reciprocity." He points out that the term "Relativity" only means a unilateral and incomplete demi-Relativity. This is because the full implications of the equations of Lorentz have not been taken into account by Relativity theory. Bergson passes on in the second chapter to a closer examination of what he calls "complete Relativity". His objection is more positive in so far as instead of merely correcting definitions and revising the terms of the equations, he rather proposes an alternative theory of his own. This theory is strictly based on the same equations and theoretical intentions of Einstein.

According to Bergson, relativity of movement implies a reciprocity when we think in terms of the distance between two points in the universe increasing or decreasing. One has no right to prefer to this two-sided standpoint a relation to motion which is taken only from any one of the points, because of the unilateral view of the distance involved. When we take a bilateral view we come closer to a complete theory of Relativity. Even Einstein as a physicist who is interested in measurements only because his theory claims to abolish the classical theory of physics and replace it with something applicable to the whole of the physical universe should, as Bergson thinks, agree to this. As soon as reciprocity is admitted by the physicist as the only legitimate point of view to take he will move from demi-Relativity to a complete Relativity theory. Ultimately he must do this because he already adopts and uses an axiomatic method when he manipulates mathematical equations.

Physicists who are content to verify their theories occasionally when some astronomical event or spectral shift is observed may not be interested in stating the theory in its correct and complete form. The practical laboratory physicist is content to travel from one working hypothesis to another. But a philosopher is interested in the status of Time in the theory of Relativity and his method is not limited to the experimental method. Bergson too fixed his vision. on visible and perceptual aspects of reality, as he is first a pragmatist and operationalist philosopher. It is possible for him to guide his own speculations along mathematically valid lines. This is exactly what he does when he boldly proceeds in his second chapter not only to reveal the position of radical Relativity known to Copernicus, Kepler, Galileo, and others, but also to reveal what he calls "attenuated Relativity".

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For the Newtonian scientist it was natural to think in terms of straight lines from some point of origin ending at some other point in infinite space. An outside force was needed to change the course of this straight line. Such a classical universe presupposed a Euclidean structure of space. Einstein's theory of Relativity put these classical or radical features into the melting pot and boldly started a new way in physics. Bergson's complaint now is that, even having discarded classical physics, the new way has not been completely or consistently developed. Interested as he is in the status of absolute Time given both to philosophy and common sense, he also refers to the question of absolute movement and puts the relative movement already envisaged by the classical astronomers side by side with absolute movement which is no other than the verticalized version of relative movement in practical horizontal space. Pure or absolute movement belongs to the context of an attenuated theory of the universe and is more timelike than spacelike. This is because of its a priori mathematical character. Thus we have two limiting cases to keep in mind when we try to follow closely and intelligently the arguments advanced. This builds up into a surprisingly realistic picture of a colourful universe as contained in pages 42-52 of Bergson´s work and which we have quoted previously

(see p.148-153 above).
It will be easier for the reader to familiarize himself with this completed version of Relativity as understood in the light of Bergsonian philosophy before trying to follow further the system S and S' into which he has been able to reduce the implications of relativity theory at the end of his first chapter. These independent and closed systems, each with a frame of reference of its own, need not be thought of as big or small. Furthermore, they are independent of each other and interchangeable in status, although still belonging to the world of observing physicists who can look at their own systems without inconvenience or contradiction Each closed system is not unlike a monad of Leibniz, and does not preclude the thought of a system of systems like a Monad of monads.

Keeping these remarks in mind, let us now proceed to examine a few selected passages from Bergson. The first one refers to reciprocity as against demi-relativity.

314

We read the following:

"The 'Reciprocity' of movement is therefore a fact of observation .... science refers to measurement and measurement applies to lengths, and when a length grows or decreases there is no reason to treat one extremity as privileged: all that can be asserted is that the gap becomes greater or diminishes between the two."
(D & S, pp 36-37)

Bergson continues:

"Thus the relation between the two systems already mentioned as doubles of each other is treated as reciprocal. Reciprocity also implies a subtle philosophical aspect which was first outlined by Descartes where internal (felt) and external (measured) reciprocities are brought together into the same picture."
(D & S, p.37)

Further alluding to such a reciprocity Bergson continues:

"Certainly it should be that all movements could be reduced in such a way as to be capable of being perceived in space. By the side of the movement that we can observe only from outside, there are those that we can also feel internally, as being produced. When Descartes spoke of the reciprocity of movement, it was not without reason that Morus replied: 'If I should be seated quietly and another on going away a thousand paces from me, should be red with fatigue, it is I who have been resting."
(D & S, p.37)

Here Bergson explains how it is possible for one or the other person involved in the situation described by Morus to decide to move, when we could even say that the ground moves away from the man or the man moves away from the ground. Animals and non-metaphysically minded men might treat the movement as unilateral. Movement thought of in itself has an absolutist character about which Bergson says later:

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"He (i.e. the metaphysician) should penetrate into the interior of things, and the time essence, the profound reality of movement could never be better revealed to him than when he accomplishes the movement himself, even when he perceives it from outside, as in the case of every other movement, but appraises it as an effort from inside, where the trace also was visible.

The metaphysician obtains this direct perception, which is both internal and certain, only for the movement that he accomplishes for himself. From this alone he can guarantee that they are real acts, constituting absolute movement. Already for the movement accomplished by other living beings, it is not by virtue of a direct perception, but by sympathy; it is for reasons of analogy that he would give them the status of independent realities."
(D & S, pp.38-39)

The passage from physics to metaphysics is here accomplished without violating the requirements of the absolute reality of movement. The position involved is summed up strikingly by Bergson:

"The movement that it (i.e. science) studies is therefore always relative and cannot consist of anything other than what is reciprocity of displacement .... Descartes marked with precision the point of view of science .... He went even beyond the science of his time, beyond Newtonian mechanics, beyond ours, formulating a principle to which Einstein gave a demonstration."
(D & S, pp.39-40)

In this last sentence of Bergson´s he is only reiterating what we have already quoted him as saying before about Einstein being the continuator of Descartes. The relation between space and movement is brought out by Bergson as follows:

"Descartes stated that everything relevant to physics was spread out in space. By this he gave the ideal formula of a universal mechanism."
(D&S, p41)

Thus placing the demi-Relativity of Einstein, Bergson is able to bring us to the point of accepting an idealist and universal mechanics which is basically the same as what modern physics could legitimately accept. Relative motion in the visible world and its inner and outer vibrations and movements when related to discrete bodies can be realistically visualized, irrespective of the requirements of physics or metaphysics. The structure of universal space when viewed as it were from inside can also be reconstructed by us without violating epistemological laws or norms.

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Whether we think of a universal observer with measuring instruments seated at the apex of a pyramid-like structure or situated at every point of space, the vision of relativistic space will be on the lines elaborated by Bergson, which we have already quoted on pp.148-153 above. This long quotation deserves examination once again so as to enable us to realize all its real and structural implications. Likewise reciprocity, when fully understood, does not reveal the same picture as unilateral Relativity. The reader could reread with profit here our quotation from Bergson .found on pages 148-153 above.

Bergson's third objection to Relativity theory is that the physicist does not have "Constantly present before the mind the relation between radical and attenuated Relativity." At the end of the previous section we have seen how Bergson was able to arrive at the notion of absolute movement in space as proper to a universal mechanics in terms of what is compatible with the philosophy of science. The res extensa of Descartes corresponds to the horizontal and is given recognition by Bergson. This correlate is a reference for all physical motion when understood in terms of the pure and universal mechanics implied here.

Having settled the question of space by bringing the discussion to the highest degree of abstraction and generalization, Bergson now proposes to give to time and its nature the same kind of philosophical and scientific treatment. He examines time from the two perspectives of what he calls "Spatialized Time" and "Pure Time". Spatialized Time has a horizontal reference and Pure Time a vertical one. Simultaneous instants of time do not refer to real time at all, but represent conceptualized ideas of time which are metaphysical rather than physical. Simultaneity of two instants when verticalized as two points in two distinct fluxes with a "before" and "after" can be represented as continuous lines. This represents time more in the light of a succession of juxtapositions of instants rather than as simultaneous points in time. Spatialized Time is not the same as Pure Time based on our inner sense of duration. This duration is one that is within the common experience of all human beings and is more directly given to perception than the conceptual points of spatialized time on which the theory of Relativity relies.

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The fourth dimension derived from such a time is, according to Bergson, nothing but a spatialized metaphysical and conceptual entity with no perceptual element implied in it. The fourth dimension borrowed from Minkowski by Einstein thus falls outside the scope of physics and the paradox which underlines the acceptance of such a space-time continuum is the result of a confusion between pure and specialized time.

Bergson's third objection is therefore to be understood by us as referring to the confusion between. what he calls radical and attenuated Relativity. Radical Relativity refers to the horizontal aspect and attenuated Relativity to the vertical version of the same. Simultaneous instants are proper to the radical view and succession based on continuity of duration, implying a "before" and "after" in a process of flux and involving memory or future virtual possibles is the verticalized version. Each person can privately feel time as a general murmur of an eternal duration within him in subjective and abstract psychological terms. He can represent it as a measurable positive content in a spatialized and schematic form. Both times can be included under one and the same schematic representation.

Pure Time can be represented as a vertical line in which the past, present and future organically belong together. Subjectivity and objectivity can be cancelled out into a sense of actual duration in which the experienced past and the virtual future have between them a complementarity and reciprocity. The pure Time of Bergson is an abstraction and generalization of spatialized time with its own horizontal counterpart. It is not necessary for us to bring out the subtleties of this analysis of the nature of pure Time where Bergson tries to abolish the paradox between the radical and attenuated viewpoints of Relativity theory. We cannot do better here than to give a string of striking quotations so as to confirm what we have just said.

Bergson wants to escape the charge of being called a metaphysician. To him reality is as important as it is to the physicist. He does not want to decide whether all reality is perceptible or not. He only wants to maintain that time as a reality is at least on par with what can be perceived. It is the Theory of Relativity that Bergson accuses of being metaphysical by its acceptance of a fourth dimension, which as he points out, has a conceptual rather than a perceptual status.

I

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As for his own position as a philosopher of science, he takes care to remark:

"We have besides to distinguish between the point of view of philosophy and of science: the former considers the concrete as real, as altogether charged with qualities; the latter extracts or abstracts a certain aspect of things and retains only what is size and what is in relation to size. Happily we have not ourselves to be concerned with anything in all that follows, except the one and only reality, namely time. In these conditions it will be easy for us to follow the rule that we had imposed on ourselves in the present study, which is not to accept anything which cannot be accepted by any philosopher or by any scientist, not even anything which is not already implied in all philosophy and in all science." (D & S, p.34)

Bergson takes a stand which is common to both physics and metaphysics. This is unequivocally clear in the above quotation. It is thus that his methodology fulfils the requirements of an integrated Science of the Absolute.

In the next quotation, Bergson seems to imply that the essence of time implies a "before" and "after" and not absolute simultaneity.

We read:

"To tell the truth, it is impossible to distinguish between duration, however short it may be, which separates two instants, and a memory that relates one to the other. For duration is essentially a continuation of what is no more into what is. This is the real time which I want to say is perceived and lived. Duration therefore implies consciousness and we place consciousness at the basis of things by the same reason that we attribute to it a time that endures." (D & 11, p.62)

Bergson here explains that a schematic representation of duration by a line has not the same reality as pure duration. He clarifies his position in the following way:

"Listening to a melody with the eyes shut, thinking of it only .... one finds it undivided, the melody or the portion of the melody which you would have replaced in pure duration. In other words, our interior duration, envisaged from the first to the last moment of our conscious life, is something similar to this melody. Our attention can turn away from it and as a result from its indivisibility; but as we try to cut it, it is as if we passed a blade across a flame we would be dividing space only." (D & S, p.62)

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We cannot examine in detail this minute analysis of Bergson on the question of the two ways of schematizing time as pure duration and as spatialized time. Instead we will give the most important quotations dealing with this subject.
We begin with the following:

"If I should pass my finger on a piece of paper without looking at it, the movement I accomplish, seen from inside, is a continuity in consciousness, and something of my own flux, that is to say, duration." (D & S, pp.63-64)

The flux is of four different grades. This is clearly seen in the example given below where simultaneity in the Einsteinian sense presupposes an absolute time, which is strictly speaking outside the scope of relativity theory. The fourfold structural pattern is reflected here where we read the following:

"When we are seated on the bank of a river the flow of the water, the gliding of a boat or the flight of a bird are three different things to the uninterrupted murmur of our deeper life, or (they can be) one alone according to our wish. We could interiorize everything, thus having to do with a unique perception in its courses which entrains or drags behind it in a confused fashion the three fluxes; or we could leave the first two outside and divide our attention between what is inside and what is outside: or better still, we could do one or the other at a time, our attention relating together or separating the three flowings, by virtue of the singular privilege which it possesses of being one or many. Such is our first idea of simultaneity. We call something simultaneous because the two external fluxes occupying this same duration where they belong, the one as well as the other, to the duration of an identical third one, which is ours: This duration is nothing but our own when our consciousness is directed only to ourselves, but it becomes equally theirs when our attention includes the three fluxes into one individual action."
(D & S, pp.67-68)

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Bergson now goes on to define real time and explains that it has no instants.
We read:

"The instant is that which terminates a duration if it should stop. But it does not stop. The real time cannot furnish us the instant; the latter results from a mathematical point, that is to say from space. But all the same without real time the point could not be anything but a point and there would not be any instant. Instantaneousness thus implies two things: a continuity of real time, that is to say, of duration, and of time spatialized, which described by a movement becomes a symbol of time: this spatialized time which consists of points rebounds on to real time and makes the instant jump out of it."
(D & S, p.69)

Bergson continues further on:

"Simultaneity in the instant and simultaneity of the flux, are things quite distinct, but they complete themselves reciprocally. Without the simultaneity of the flux, we should not be able to consider the one capable of being substituted for the other of the three terms: continuity of our interior life, continuity of a voluntary movement which our thought prolongs indefinitely, and continuity of any movement whatsoever traversing space. Real duration and time spatialized would not therefore be equivalent.
(D & S,p.79)

All these above quotations refer to the two perspectives. One of them is vertical and the other is horizontal. Time can therefore be viewed either as measurable or as something that is felt within. Bergson now arrives at the notion of time as a fourth dimension. He does this by mathematically schematizing it without a reality of content. The fourth dimension of Einstein comes to have a mathematical rather than a real status. We read the following

"Immanent to our measure of time there is the tendency of time emptying itself of its contents into a space of four dimensions where past, present and future are juxtaposed or superposed for all eternity." (D & S, p.79)

Bergson is full of hesitation. when it comes to speaking the proper language of an integrated Science of the Absolute. In company with thinkers of his own generation he avoids the a priori method as well as absolutism as starting points in his speculation. Much of the obscurantism that we find in his arguments arises from this desire to keep company with realistic pragmatists and operationalists.

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What is valuable to us however is the fully scientific methodology developed stage by stage in the chapters of his book. A vertical axis of reference implying past, present and future, and absorbing within its scope the possible dimensions of physics is what he is able to arrive at by the end of the third chapter. It is at this point that we are concerned with the correct relation between radical and attenuated time. Attenuated time has a vertical reference. The status of future time is a virtual and conceptual one. The world of objects and events implying a future that is still to unravel itself is thought of by Bergson as entering our consciousness backwards rather than forwards. Such delicate distinctions remain to be clarified in the Chapters to follow.

Bergson's fourth objection is that the relativity theory has not "prepared the mind against a confusion between the two" (i.e. between radical and attenuated relativity).

The interaction and interference of the two kinds of Relativity, described by Bergson as the radical and the attenuated, have to rely on the physics and philosophy of Galileo, Kepler and Newton, presupposing a Euclidean space and as well as a Cartesian cosmology and the mathematical space-time correlates. Bergson has to agree and differ alternately with each or both of them. The argument that he adopts becomes delicate and closely knit, replete with personal examples and equations, manipulated with expert ease. He brings in microbial and sub-microbial clocks and beings, and speaks of rival systems belonging to Peter and Paul who are physicists, the latter accepting philosophy only under the very special circumstances of being shot into outer space within a ball. There are also flat, one-dimensional beings who are used as literary devices by Bergson and who are represented as speaking to each other as "blood brothers." Besides Peter and Paul there are also John and Jack who belong to the horizontal structural poles of reciprocity in terms of spatial perspectives, while Peter and Paul belong to the context of expanding, contracting or multiple times acting as simultaneous instants or dislocated into successive continuities in more deeply perceived time.

322

All these difficulties presented by Bergson arise from the fact that he does not straightaway adopt the metaphysical notion of the Absolute substance as Descartes did. He is also not willing to accept the full implications of the static, formal and general structuralism of post-Hilbertian mathematics. The Bourbakians are still to be accepted in respect of their extreme structurally-minded predilections. It is therefore no wonder that Bergson relies on his own intuitive genius and originality in developing without a conventional a priori method the argument by which he comes to state finally at the end of his book that Einstein is a continuator of Descartes.

His closely knit arguments and equations are essentially inimitable and we cannot do better than attempt to give the gist of what he wishes to say. In doing so we have to rely on a series of quotations following the order of the book. We do this without trying to add more confusion to his delicate thought by rearranging them in any way ourselves. The reader is sure to find such an abridged text very hard going but in order to preserve these methodological and epistemological contributions of Bergson we feel justified in doing this.

The interference of classical physics with modern notions in physics is a question full of many assumptions and presupposition and Bergson's last three chapters are concerned with meeting this question. The reader has the task of seeing Bergson's own standpoint separately from all others that he incidentally discusses. The overall conclusion of an absolute time will then emerge.

With these remarks we shall now examine the contents of the fourth chapter called "The Plurality of Time." The famous episode used by relativity theorists of a man shot into outer space in a ball who on returning finds his counterpart on earth has aged by 200 years while he has aged only two years falls within the scope of this chapter. It is by replacing unilateral Relativity with a bilateral reciprocity that Bergson is able to restate and revise this famous and rather tall claim. He does this in order to abolish the paradox in favour of a fully common sense view acceptable to both philosophy and physics. We now present the important parts of Chapter four in summary fashion.

323

Bergson opens Chapter IV as follows:

"Let us finally arrive at the Time of Einstein and let us gather together all we have said by supposing in the first place an immobile ether. There is evidently the world moving in its orbit. The instrument of Michelson-Morley is there when one performs the experiment - one repeats it at different periods of the year and as a consequence for the variable speeds of our planet. Always the ray of light behaves as if the earth were immobile. Such is the fact. Where is the explanation?"
(D & S, P.91)

Continuing with this theme we read:

"In the first place what have they to say about the movement of our planet? Would the earth be, in an absolute sense, in movement across space? Evidently not; we are in the hypothesis of Relativity and there is no absolute movement in it. When you speak of the orbit described by the earth, you are placing yourself in a point of view chosen arbitrarily, which is that of the inhabitants of the sun (in a sun which has become inhabited). It is at your pleasure that you adopt this system of reference. But why should a ray of light thrown on the mirrors of the Michelson-Morley apparatus take any notice of your fantasy? If all that is produced in effect is the reciprocal displacement of the earth and the sun, we could take for a system of reference the sun or the earth or any other observatory. Let us take the earth. The problem disappears for it (the earth). There is no occasion to ask while the fringes of interference conserve the same aspect, why the same result is observed at whatever moment of the year. It is just simply because the earth
is immobile."
(D & S, p-92)

Bergson explains how between the observer on the sun and one placed on the earth there is a question of having somewhere a reference which is not his own. Each of these physicists would put the question of movement with reference to what he is not (The man on the sun chooses the earth as a reference and the man on the earth chooses the sun). Peter and Paul, when placed in two systems S and S´ as before, Bergson explains, would each have a reciprocal recognition of some system of reference:

"Now there is no more absolute movement, and as a consequence there is no absolute repose of the two systems which are in a state of reciprocal displacement. Each of them would be immobilized in turn by the degree which would raise it to the status of a system of reference." (D&S,p.93)

324

The two physicists in S and S' conduct the Michelson-Morley experiment and derive from it some information about light and its velocity representing only half its total reality. The paradoxical situation between the two physicists, each of them treating their own system as immobile and real and the other as a mere reference, is brought out by Bergson in the following way:

"But the physicist in the system S´ would proceed in exactly the same way. Declaring himself immobile he would repeat from S all that his fellow physicists placed in S would have said about S'. In the mathematical representation of the universe which he would construct, he would treat exact and definite the measurements he would have taken in the interior of his own system, but he would correct according to the formula of Lorentz all these measurements taken by the physicist attached to system S.
(D & S, p.95)

Bergson continues:

"Thus two mathematical representations of the universe would be obtained, totally different from each other, if one considered the numbers that figured in each but identical, if one should take account of the relations which are indicated by them as existing between the phenomena, - relations which we call the laws of nature. What is more, this difference is the very condition of their identity. When one takes diverse photographs of an object by turning round the object, the variability of the details does nothing more than translate the invariability of the relations which the details have between them, that is to say, the permanence of the object."
(D & S, p.95)

Bergson now sums up the definite implications of Relativity when reciprocity is fully recognized:

"We are thus brought back to a multiplicity of Times, to simultaneities which will be successions, and successions which will be simultaneities and to lengths that should be considered differently according to their being considered at rest or in movement. We are now facing the definitive form of the theory of Relativity." (D & S, pp.95-96)

Bergson now compares the status of the time taken by systems S and S' as understood by the respective physicists within each system. The reciprocal movement between the two systems can be thought of as taking place horizontally, while the measurement of time can be thought of as taking place vertically.

325

Bergson refers to this perpendicular reference (the vertical axis) as follows:

"We shall suppose therefore that the physicist is only interested in the line of light ....placed perpendicularly to the reciprocal movement of the two systems." (D & S, p.96)

He then goes on to say that both the physicists concerned belong to system of reference which have between them an interchangeable status:

"But if S' is a double of S, it is evident that the Time lived or acted by the second physicist during his experiment in system S', judged by him as immobile, is identical to the Time lived and acted by the first physicist in system S, equally considered immobile because S and S' once immobilized are interchangeable. Therefore the time lived and counted in the system, the time that is anterior and immanent to the system is the real time and is the same for S and S'." (D&S,pp.96-97)

Bergson further discusses time that is considered paradoxical and mathematical time. He compares and contrasts the times of both the "physicists":

"Thus, in summary, while the time attributed by Peter to his own system is the time lived by him, the time that Peter attributes to the system of Paul is neither the time lived by Peter nor the time lived by Paul, nor a time that Peter conceives as lived or one that could be lived by Paul as a conscious and living being. What would it be other than a simple mathematical expression, destined to mark that it is the system of Peter and not the system of Paul which was treated as a system of reference" (D&S, p.100)

Bergson now resorts to a striking and familiar example of two men painting a picture of two persons placed at a distance. The perspective in the painting corresponds to the distance. The person nearest to the painters appears bigger than the other person. The change of perspective by the painter and the consequent change of size will not really affect the size of the persons concerned. This is also true with the times recorded in their pure mathematical systems. Returning to the two systems, the one mobile and the other immobile, Bergson says:

"But by immobilizing my system I have mobilized the others; I have mobilized them diversely. They have acquired different speeds. The more the speed, the more it is distant from my immobility. It is this greater or lesser distance of their speed to my speed, which is zero, that I express in my mathematical representation of the other systems when I count their times as more or less slow which are always longer than mine, in the same way as it is the greater or lesser distance between Jack (the shorter subject of the painter) and myself which I express by reducing his height.

The multiplicity of times does not exclude the unity of real time; it would rather presuppose it, in the same way as the diminution of height with the distance of a series of canvases where I would represent Jack, more or less distant, would indicate that Jack conserves his own size.
(D&S, pp. 101-102)

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Bergson now examines the claim often put forward by followers of Einstein who say that a man shot from a cannon at a very high speed into space, on returning to Earth will find his friend to have aged by 200 years while he aged only two years. When the reciprocity between Peter and Paul is fully accorded, Bergson says such a claim is then untenable.
We read:

"The movement being reciprocal, the two personages are interchangeable. (D&S, P.103)

Bergson goes on to explain how physicists and philosophers are naturally obliged to take a differing point of view, even when faced with the same data. A physicist is more interested in the real rather than the theoretical aspect of the situation. He is obliged therefore to treat individually Peter and Paul as real and never theoretically. Bergson, speaking about the physicist says;

"If he is with Paul he will concede to him the time that Paul himself counts. That is to say, the time which Paul effectively lives; and to Peter the time that Paul would attribute to him. But once more he would necessarily choose for Peter or for Paul."
(D&S, p.104)

Bergson continues:

"In effect both Peter and Paul have to do with the same physics. They observe the same relations between phenomena and in nature they find the same laws. But the system of Peter is immobile while Paul's is mobile. As long as we have to do with phenomena attached in some manner to a system defined by physics in such a way that the system in motion is considered as having them as a consequence, the laws of these phenomena should evidently be the same for both Peter and Paul: the phenomena in motion being perceived by Paul are animated by the same movements as they are immobile to his eyes, and appear to him exactly as they would appear to Peter in the phenomena analogous to his own system. But the electromagnetic phenomena present themselves in such a manner that one can never, when the system where it is produced is considered to be moving, consider them as participating in the movement of the system. However the relations between these phenomena and their relations with the phenomena consequent on the movement of the system are still for Paul what they are for Peter.

327

If the speed of the ball (the man referred to earlier as being shot into outer space) is really what it is supposed to be, Peter could not express this persistence of relationships except by attributing to Paul a Time a hundred times longer than his own, as one could see according to the equations of Lorentz. If he counted otherwise, would he not be inscribing in his mathematical representations of the world that Paul in movement finds between all phenomena, including electromagnetic phenomena, in the same relations as that of Peter in repose would affirm implicitly that Paul as one referred to could become Paul referring; for why should relations be conserved for Paul, and why should they be marked by Peter or Paul in such a way as they appear to Peter, if it is not because Paul would describe himself as immobile by the same right as Peter? But this is a simple consequence of the reciprocity which he notes, but not reciprocity itself. Once more he makes of himself one who refers, and Paul is nothing but one who is referred to. In these conditions the time of Paul is a hundred times longer than that of Peter. But it is a time that is attributed and not a time that is lived. The time lived by Paul would be his Time as referring and not a time referred to: it would be exactly the time which Peter comes to find." (D&S, pp.105-107)

Bergson now shows how to distinguish real Time from fictitious Time:

"What in effect is a real Time if it is not a Time that is lived or which could be lived? What is an unreal, auxiliary and fictitious Time if it is not that which could not be effectively lived?" (D & S, p.107)

The origin of the confusion between these two Times is now explained by Bergson. Mathematically speaking there is a freedom of choice between two systems of axes by actually choosing one of them in preference to the other. What is chosen becomes a privileged system. Bergson explains:

"In the mathematical usage that one adopts, it is indiscernible in an absolutely immobile system. Thus we see why unilateral relativity and bilateral relativity are mathematically equivalent, at least in the case which concerns us. The difference exists here only for the philosopher, it reveals itself only if one should ask what reality, that is to say, what thing perceived or perceptible is implied in the two hypotheses. The older one is of a privileged system in a state of absolute repose, and will end in posing multiple and real Times.

328

Peter, who is really immobile, would live through a certain duration; Paul, who is really in movement, would live through a duration which is slower. But the other, which is that of reciprocity, implies that the slower duration should be attributed by Peter to Paul, or by Paul to Peter, according to whether Peter or Paul are referent or reference. Their situations are identical; they live one and the same Time, but they attribute reciprocally to each other a Time that is different to the former and they express in this manner, according to the rules of perspective, that the physics of an imaginary observer in motion should be the same to that of a real observer at rest. Therefore in the hypothesis of reciprocity, one has at least as much justification as commonsense in believing in a unique Time: the paradoxical idea of multiple Times imposes itself only in the hypothesis of a privileged system. But once more, one could not express oneself mathematically except in the hypothesis of a privileged system, even when one has commenced by proving reciprocity."
(D&S, p.107-109)

While the physicist Paul adhered to his own privileged point of view, Bergson remarks:

"Basing his belief on such a physics, Paul will enter into the ball. We will see while en route that philosophy was right. The hypothesis of the traveler enclosed in a ball who lived only two years while 200 years were passed on Earth, was put forward by M. Langevin in a communication to the Congress of Bologna in 1911. This hypothesis which is universally known and quoted everywhere is mentioned in particular in the important work of M. Jean Becquerel on page 52 of "Le Principe de la Relativité et la Théorie de la Gravitation". Even from the point of view of pure physics it is raising certain difficulties, for we are, in reality, no longer confronted with the theory of Restrict