THE INTEGRATION OF ALL SCIENCES

The need for integrating the vast body of knowledge that men have been able to accumulate into a coherent whole is a subject that has begun to engage the serious attention of educators. Practical aspects of knowledge are now being stressed at the expense of the purer branches. Advanced studies now refer mostly to technological subjects. Universities turn out more and more experts or specialists. As a result, those aspects of higher knowledge which were covered by the term 'humanities' have been by-passed and left behind.

Except in a few places such as the Collège de France, the Institute for Advanced Studies of Princeton, or perhaps also in the recently started Committee on Social Thought under the University of Chicago, attempts at any serious integration of courses seem inadequate and negligible.
  
There is, however, at the present time a growing feeling for a fresh synthesis of knowledge, so that the sterility of over-departmentalization and the consequent lack of the human touch in education may be effectively stemmed. Specialization at least must not be for its own sake, but must serve some tangible end to produce a better-educated man.
 
264                           
Besides the UNESCO, which may be looked upon as an expression of the desire for a revised impetus to culture and science on a world-wide scale, there are at present many private foundations, both in the East and the West, standing for the same ideal. They adhere to varied programmes, some being overly scientific and others relying more on esoteric cultural values. A particular cosmology or a tacit dogmatic theology can be seen to be implied in many of them. Even the theory of evolution itself is being treated by some of them as an article of faith. They often become thus open to the objection that they tend to be dogmatic, sentimental or religiously pre-disposed. They would fall short of the requirement that any modern attempt at an integration of knowledge should be conceived on more positive or scientific lines.
 
NO COMMON INTELLECTUAL FORMATION
Although senior professors of universities, who may be in charge of the admission of students for the higher courses, may be heard to refer to what they call 'intellectual formation' as a necessary prerequisite for following a certain specialized course, this expression remains still a very vague one. What precisely the expression is intended to convey may not be clear even as between one professor of a certain department and another who might belong to the same university. The expression as applied to inter-university standards generally becomes still more vague, because cultural backgrounds differ widely, not only between universities of the Old and the New Worlds, but even between universities of the same
continent or even country.
     
Eastern and Western cultural standards may be said to still lie poles apart. German universities each have an academic reputation and tradition all their own, and certain universities specialize only in select branches. Even in England, an Oxonian is expected to have a formation different from that of a graduate of Cambridge. In France, although the situation has been somewhat mitigated by the existence of the centuries-old foundation of the Collège de France, the 'intellectual

265
formation' demanded by a certain professor, even in the department of letters, may differ from the one required by another.
   
In India, which has no university tradition to call its own, but tries to graft Oriental culture on to the stem of Occidental classical tradition, the case for a preliminary intellectual formation for higher studies is in a sad state indeed. The influence, in itself not salubrious, of the non-idealistic and pragmatic tendency of the United States that prevails in the cultural world, as in many other departments of life at the present-day, is tending to further lower standards in cultural education. Measurement is being given primacy, and everything that does not lend itself to brass- or electronic-instrument experimentation or testing is tending to be discredited.
   
This influence, which is itself enough to dampen intellectual and moral enthusiasm for culture, works hand-in-hand at the present-day with that other tendency to be noticed in India, which gives primacy to localized cultural values. Linguistic preferences in the name of a pseudo-nationalism which encourages parochial loyalties and closed orthodoxies of different shades, are being allowed to compromise more or less completely the cause of the open and universal outlook necessary for any integrated education worth the name. In this connection it has been interesting to note that a group of Indian university vice-chancellors have recently been touring the United States of America seeking a formula for integrated education. From the report of their impressions, it would appear that nothing striking was discovered for adoption in India. In the United States themselves, we find a dissatisfaction which is expressing itself in the form of sporadic revolt by youth.

UNITIVE APPROACH NEEDED
Whether we are concerned with 'basic' or 'fundamental' education for the emancipation, social or cultural, of the masses of the world; or think in terms of higher cultural

266                         
values of an idealistic non-utilitarian programme in education for the select few; it is highly necessary at the present time to visualize the scope and methods of integrated education more clearly than hitherto. We have to be able to think of common human values in the global context of one solid humanity.
   
There should no longer be cultural preserves or prerogatives which try to divide humanity into sheep or goats. The myth of the primitive or inferior man has to be abandoned. The orthodox and heterodox, the conservative and the liberal, the rightist and the leftist, must be able to meet in the endeavour to preserve the best human heritage that belongs to all. A common cultural language which would enable these precious values to be referred to, irrespective of linguistic or traditional barriers, has to be evolved, Such a mathematically-precise language would pave the way for the formulation of a regular science. Values preserved through humanistic studies could then be effectively cultivated without the arbitrary and sentimental barriers that history or geography might interpose between people. An open,
dynamic and positive scientific attitude must invade the closed, static and private preserves in which higher human values have hitherto remained enclosed.
   
In other words, the challenge involved here is to bring the humanities and the human values involved therein back into line with the other scientific values which, for no just reason,have in recent years tended to be considered as if divorced or disjunct from the former.

THE SCIENCE OF SCIENCES
In the days of Aristotle all wisdom-disciplines were more unitively understood than at the present-day. The term 'science' covered equally the whole range of subjects, starting from physics and natural history (or rather, natural philosophy), to metaphysics, ethics, economics and politics. The doctrine of the Mean which was Aristotle's contribution to thought, was a subtle underlying unitive principle which strung together branches of knowledge that have now come to be considered as different or disjunct from one another.
 
267
From the time when writers like Mill began to arrange cultural or economic notions on a less idealistic and more 'utilitarian' basis, the firm hand of classical unitive thinking based on such bold dicta as "It is in ourselves that we are thus or thus", and the singleness of human end or purpose in life, gave way to the hesitant and wavering attitude implied in such expressions as "not expecting more from life than it is capable of bestowing". Unitive values began to be confused with non-unitive ones. The right regulative or normative principle that related ends with means through deliberation began to be compromised. Horizontal or "here-and-now" values of an ontological nature were stressed at the expense of idealistic, ideological or vertical ones. The intuitive understanding of the doctrine of the Mean was lost for ever, and thus cultural enthusiasm began to flag.
   
If we could again think of science as including both moral and physical sciences, the task of finding a basis for integrated education could be more easily accomplished. Knowledge can direct its search outward from the seat of the mind or soul within us. The "eye of the soul", to use Aristotle's expression, can look 'positively' and 'objectively' into the world of the 'knowables', or subjectively or introspectively into values or virtues within the personality of man.
   
The latter has been known as the negative way which, by the eye of the soul directed inwardly, can still conduct 'auto-experimentation' by comparing common human experience of the a priori order. While the positive sciences are a posteriori and actually objective, this negative science could still be 'objective' in discipline in a virtual or conceptual sense. The strictness of scientific exactitude in thinking need not necessarily suffer in the latter case. When proper terms have been fixed to refer to aspects of knowledge, the whole range of knowledge can be made to come under one science which could be called the Science of sciences. In fact this is what the Science of the Absolute (or brahma-vidya as such is called in India) claims to be. 'Knowledge' (jnanam) and "the knowable" (jneyam) are here to be distinguished, the first as negative and the second as positive. An epistemology and methodology based on a correct contemplative scale of values is here implied.

268                           
DESCENDING DIALECTICS
Some recent attempts at the integration of knowledge have proceeded from the variety of specialized analytic knowledge towards their synthesis. Thus there is the famous instance in which the top-ranking nuclear physicist Schroedinger makes a serious attempt to relate biology with chemistry and physics. In his booklet entitled "What is Life?" an attempt has been made to bridge the gap between inanimate and living matter. Later writers such as Andrew A. Cochran* have availed themselves of the quantum theory to establish a link between life and matter. Such attempts may be said to travel from the positive and overt aspects of reality towards the innate and subtle aspects, or from the positive pole to the negative.

DISTINCT VALUE-WORLDS
Even while we speak in terms of poles, we have to distinguish two sets of poles as belonging to two distinct aspects of values or interests in life.
   
Reality, it must be remembered, is to be studied for the human interest in it rather than just for its own sake, without reference to human interests or values. All attempts at integration are for man, and not for knowledge itself. When we visualize the world of values correctly, we will be able to see a vertical series of values in which the positive pole is the world of pure reason or that of the Platonic Intelligibles. The negative pole of vertical values will be  the prime means to the supreme end of attaining to the world of the Intelligibles, when understood unitively and synthetically. Thus there is a vertical world of pure values, and a horizontal world of material values.

*Mr. Cochran writes a very interesting and well-documented article on "The Quantum-Physical Basis of Life", postulating a basic hylozoism, with the 'wave' phenomena as the conscious aspect of matter, in the May 1957 issue of "Main Currents in Modern Thought".
(Journal of the Foundation for Integrated Education). Mr. Cochran is attached to the US. Bureau of Mines.
 
269
The building up of a cultural life in a person means the recognition of both these sets, while the doctrine of the Mean must constantly convert knowledge in favour of virtues. As we have elsewhere tried to develop, it is possible to bring Gold, Goodness and God to be comprised within the amplitude of a personal scale of values between the poles of which the life of man may be said to oscillate. The science of things taken in themselves, and considered without their fundamental value-import for man, is like a magnetic field, secondary to the main current along which life flows. This latter may be said to be along the vertical axis of pure deliberative values, by means of which man decides to affiliate himself to a good life. Actual physical life is of the nature merely of an epiphenomenon to the real-life interests normal and legitimate to man as Man.

THE KEY TO INTEGRATION
It is a recognized fact, tacitly understood already in the East as well as in the West, that man himself is the proper subject of study. Atmavidya (Self-knowledge) in India has been treated as the same as Brahma-vidya (the wisdom of the Absolute). Ananda (happiness), as a Supreme End or Value in life, has also been treated as in effect the same as the Self or the Absolute. Thus the key for integration of knowledge of wisdom is to be found in the human personality itself, where the subtlest aspects of wisdom find a natural home. The Self is the most precious of values for man, and the "mahavakyas" (Great Dicta) such as "Thou art That" signify this supreme point of culmination of all integrated wisdom.
   
With such as the target before them, it is encouraging to note that even physicists like Schroedinger have made some first efforts to bring these divergent aspects of human knowledge into integrated relationship. A contemplative Science of the Absolute, conceived in terms of Self-knowledge, could include the Chief End or the Final Good on the one hand, and the negative or prime counterparts of the same in actual life on theother, within the range of an integrated Science of sciences combining ontological and ideological values. Aristotle's doctrine of the Mean could then be understood in terms of "samya"
 
270
(sameness), which is the central doctrine of such Eastern texts as the Bhagavad Gita.When both are properly grasped without prejudice, culture would tend to be integrated and understood in unitive and universal terms.

271                           
18
       
THE INTEGRATION OF ELEMENTS OF THOUGHT IN VIEW OF A LANGUAGE OF UNIFIED SCIENCE

SECTION I: OBSERVATIONAL
This study is devoted to exploring the possibility of a scientific language. To think of the whole range of science as one integrated unity is itself a task that has engaged great minds from antiquity to recent times, without much definitive result. The approach so far has been more speculative than scientific in its full sense. A language that would have such a character as to serve effectively as a common basis for the whole range of sciences, experimental or normative, physical or 'metaphysical', as we ought to understand by the term 'Unified Science', is not easy to conceive. Of all the names of thinkers of old who had the ambition of accomplishing this impossible-seeming task, that of Leibniz stands out as one who came nearest to laying the philosophical, logical and mathematical foundations of a "universal language".(1)
This was to counteract the confusion of vernacular tongues.
 
272                           
Even he did not live to see the great ambition of his youthful days accomplished.
   
In spite of the apparent difficulty and enormity of the task, it is our contention in this study that a simple approach is still possible along the lines that Leibniz indicated. Here we are thinking in terms of normalisation and 're-normalisation' of what constitutes a 'unitive' approach to linguistic activity understood in the context to which it has properly to belong.
   
A scientific language that is all ready-made for use is not our aim in this study, nor even a scheme that has been worked out in detail to be considered as a blueprint for a universal language that could be adopted without further pains. This study is merely a contribution to a more fruitful discussion of this subject in which there is much interest shown, both by qualified and unqualified persons. Over-speculative, un-scientific and pseudo-scientific attitudes in this alluring field have to be discountenanced.
   
A scientific language, in order to be truly so, must firstly be one that itself can claim scientific validity. It must not disrespect the requirements of a correct epistemology and methodology. Both science and philosophy seek truth behind appearance: both aim at serving humanity by the serious pursuit of worthwhile interests. What gives unity to science in this inclusive sense is the common human purpose that runs through its methodology, epistemology and axiology.

Language lives and moves in that axis which is concerned with reasoning which links visible realities with the rational,intelligible or the calculable, or what lies beyond its scope, understood by such terms as the 'Absolute'. Although the absolutist way of thinking does not at present enjoy much recognition by strict scientific thinkers, an expression that has necessarily to depend on this notion is taking a large place in recent scientific literature, viz. Relativity. Side-by-side with those who denounce 'metaphysics' (whatever they understand by it) as 'non-sense', opposite trends are also becoming more and more evident. (2)
   
Secondly, a scientific language must be suitable for communicating to others, whether scientists or common men, truthful information about the problems, methods and 273 results of valid and precise knowledge of the required degree of certitude. It should not itself tend to become a closed and static jargon understood only by specialists of the same group. A certain public character and openness tend to make ordinary language more scientific. Universal communicability across geographic and linguistic frontiers is a necessary condition that should distinguish scientific language.
    
Thirdly, scientific language cannot afford to be merely a symbolic language of logical or mathematical abstractions. Unilaterally-applied symbolism makes language a puzzle to solve, as in the schoolboy riddle of A being the brother of B but B not being so. The fact that A and B are of two sexes is not revealed by symbolism as directly as in common language.
The 'meta-language' that some propose for a scientific language has innate defects of this kind. We shall examine the case of symbolic logic in this connection. Here we indicate in advance that, as when we name an object and call a spade a 'spade', there must be two sides that must come together and fuse before meaning can emerge. The actual thing, determined by its properties like form - and its name, which is a conceptual factor - come together to result in a meaningful event in consciousness. The elements of a symbolic meta-language have to be put in relationship with what we could with equal justice call a proto-language to result in a naturally meaningful language with validity and legitimacy.
The apodictic or other certitude on which scientific language has to be dependent, could result only when name meets form. The three desiderata of a scientific language are thus that it should be a language of science, for science and through science.

BROAD ASPECTS OF THOUGHT AND CORRESPONDING LANGUAGE
Language tallies with thought, and the requirements of thinking or reasoning in turn determine the nature of any language. Science and philosophy have much common ground between them. Instead of scientists trying in vain to

274                          
banish metaphysics as non-sense and philosophers excluding the matter-of-fact and considering science with mistrust, the language of unified science must try and adapt itself to the requirements of science and philosophy. There could be scientific philosophy as well as philosophical science, just as there could be psycho-physics and physiological psychology.
All science, being an experimental discipline, must have much of the matter-of-fact entering into its composition, while its inductive aspects may be said to be more philosophical in character. Thus we could think serially of three kinds of subject matter comprised within what is scientific; viz.: scientific philosophy, the science of science, and philosophical science. Linguistically speaking, the first-mentioned group relies on proto-scientific aspects which call for no proof; the second group hardly depends on inference, except for the mostdirect kind, as when we say the colours of the spectrum are due to the breaking up of white light; and in the third group its apodictic quality is derived from some meta-scientific theory such as that accepted for the purposes of quantum mechanics. We should thus be justified in referring to scientific language in a manner corresponding to its subject-matter, as either proto-linguistic, normal or formal, or meta-linguistic in character. That apodictic certitude with which a man calls a spade a 'spade', and that down-to-earth certitude with which human children take for granted (whether by a priori or a posteriori reasoning) that 2+2 = 4, come together in a certain manner of independence and interdependence to result in the meaning-certitude of scientific language. This subtle double, or as we shall clarity later, origin of language, forms the theoretical basis of this study it is our task to elaborate and clarify further in the pages that follow.

THE VALIDITY OF A LANGUAGE
Why a rose is called a 'rose', or by its corresponding term in any particular language, does not call for any proof. In like manner, the relation that is implied in the linguistic context between what we have tried to distinguish as the proto- and the meta- aspects of any language on which the structure of language itself is based, does not call for any proof in the

275
usual sense. Validity is not to be sought through inference as is usual in syllogistic reasoning. A certain non-arbitrariness and intrinsic compatibility, when respected, shows itself directly, and conviction is already there immediately before forms of mediate inference could operate. It is to the credit of L.Wittgenstein to have worked out the implications of this statement in recent years. What he states in the context of logic and philosophy becomes all the more true in the context of the structure of linguistic thought:

"4° 121. Propositions cannot represent the logical form: this mirrors itself in the propositions.
       That which mirrors itself in language, language cannot represent.
       That which expresses itself in language, we cannot express by language.
       The propositions show the logical form of reality.
       They exhibit it." (3)

Language must correspond to the form of the thought that is implied in its expression. (4) We suggest here that the validity of the impression-aspect of language, as distinct from its overt expression, lies deep in human consciousness where axiomatic laws of thought, on which all thinking itself has finally to rely without room for contradiction, but, as it were, tautologically and always with sufficient reason, are found.

THE ARCHETYPAL MODEL OF LINGUISTIC STRUCTURE
In the familiar linguistic context of the classroom the school-master might put a dot on the blackboard and represent it, with maximum non-arbitrariness and sense of correctness possible, by the letter "p" (or any other corresponding initial of the language he is employing). A student who would stand up and ask for the proof of it would be making a fool of himself.
Although the selection of the name is arbitrary, a maximum possible attempt has been made, without disrespecting any law of thought hitherto recognized, in the direction of non-arbitrariness. If he had used a letter of the Greek alphabet
 
276                           
instead of a vernacular one, it would perhaps have been more scientific in that there was a greater effort at de-Babelization. Sanskrit letters could have been used for indicating levels of contemplative consciousness with equal justice. Somehow a meta-linguistic aspect and a proto-linguistic aspect have to come together for a precise meaningful situation to emerge. What is important for us to note at this stage of our study is that, in the most primary of linguistic situations in view of a scientific language already in vogue in the scholastic world, we have a visible or perceptual aspect brought into contact with a conceptual aspect of the same reality. In the mathematics class the schoolboy might come to know, in a limited context, the meeting of algebra and geometry in the use of the language of Cartesian co-ordinates. School-room mathematics now comprises such notions as the group, the field, vector space, homomorphism, isomorphism etc.(5)

Starting from naming a point, to communication through vectors, scalars and tensors, the requirements of scientific language range between micro- and macrocosms, analytic and synthetic thought.

TWO SETS OF THOUGHT ELEMENTS ENTER INTO SCIENTIFIC LANGUAGE
Ordinary everyday language has to do mainly with observables. Linguists have used the expression 'thing-language' and the 'language of handling action' in referring to this ordinary workaday world in which linguistic intercourse among humans thrives. Then there is the world of the 'calculables', which has a more theoretical or a non-physical reference or status in reality. In the latest mathematical language these two aspects have been referred to as proper and improper elements. (6) Whatever be the full implications of this kind of mathematical language - which is still in the process of being perfected by those who want to use it for scientific purposes such as that of the relativity theory and of quantum mechanics - all we want to derive for the purposes of our study here is that science is the resultant of the summation or the multiplied product as between proper and improper elements, and that what emerges finally out of science
 
277
generally, is something that could be stated, either in correct ordinary language of everyday life or else in terms of a verticalized version of the same which refers to improper elements. Hume, as we shall see presently, would refer to these aspects as quantity and number. (7) Just as the sum and product of mathematical elements could be said to have independence and interdependence at the same time, the two aspects of thought enter into the composition of scientific language. Three kinds of connections between ideas have been recognised by Hume when he says:

"To me there appear to be only three principles of connection among ideas, namely: resemblance, contiguity in time or place and cause or effect" (8)

If we add to this analysis of association of ideas of Hume what is more fundamental, which as he himself said, pertains to either quantity or number, we shall be able, with these factors in mind, to reconstruct for ourselves a schematic and proto-linguistic pattern of the global unit of integrated thought. This we shall attempt to do progressively after other epistemological and methodological aspects have been discussed. Here we have to note in passing that out of the four relational factors above, two could apply to the proper and improper aspects of ideas. There could be innate causes and effects as well as causes and effects that belong to the existent experimental aspect. Scientific language in the meeting place of the experimental and the theoretical, corresponding to quantity and number respectively. Resemblance of past memory with future imagination would belong to contiguity of time rather than of place. The provability of the completeness
of this enumeration was doubted by Hume himself, but with the help of a schematic proto-language, the validity of the list of factors becomes at least more certain. (9)

A PRIMITIVE SCIENTIFIC ACTIVITY AND ITS LINGUISTIC SCHEME
Bertrand Russell, writing on the importance of logical form in "The Encyclopaedia of Unified Science" says: "The old view that measurement is of the essence of science would therefore seem to be erroneous." (10) This revision of an old view he
 
278                          
arrives at because, as he points out,

   
"It follows that the laws of macroscopic physics are topological laws, and that the introduction of number through co-ordinates is only a practical convenience."

What we should note here is that mathematics has arrived at  topology after many vertical stages of abstraction and generalisation and, just as the general theory of Einstein does not contradict but includes the special theory, so the idea of mathematical intrapolation and extrapolation could enable us to see that scientific activity could be understood schematically at different levels of abstraction or  generalization, or both, and that the old notion that science is measurement, is fundamentally not true when quantitative as well as qualitative aspects of number are admitted into the scheme.
   
The primitive pattern of a simple but typical scientific activity could be derived from a simple classroom example. The length, breadth and height of a table, determined with the help of an arbitrarily fixed unit of length, results in ordinary initial knowledge about it for practical purposes of classification or communication. Here the table itself is an 'observable' and the measurement, especially with arbitrary units, in spite of a rod of platinum existing in Paris or London, is a speculative, theoretical and non-empirical operation. Language may be said to participate on one side with brute actualities and on the other with elements opposed to perception diametrically, or at least by a vectorial angle of
90°. Whether with or without measurement or reliance on number quantitatively, the principle of what number represents as an 'improper' element and what in principle again the actual table represents more 'properly', yield that apodictic certitude that belongs intrinsically to scientific language. Between observables and calculables, conceived  as pure mathematical elements, all scientific activity is thus comprised.

THE LANGUAGES OF APODICTIC AND PROBABLE CERTITUDES IN SCIENCE
From the simple instance of measuring a table we could pass on to other examples of a graded order in which the two
 
279
elements that we have tried to distinguish enter into combinations of different degrees or proportions with modalities entering in as a distinct factor. If we should take the case of the spectrum, we know that it is, in the first instance, to be understood as equated to white light. It is as good for science to say that white light is formed from spectral colours as conversely to say that spectral colours form white light. As knowledge there is reversibility, but experimental reversal implies different experimental arrangements. Here the white light and the colours belong to the same grade of psycho-physical abstraction; while if we should say that each colour of the spectrum has its wave-length of radiation indicated by different numbers, the relation is between a set of observables and a set of calculables. There was no proof needed in the conviction that white light was the same as spectral colours and vice-versa, when stated in language; but the apodictic nature of this direct conviction becomes overlaid by more complicated experimental and inferential steps in order to be able to equate and understand each colour in relation to its wave-length. The inductive and deductive abstraction as between observables and calculables becomes more complex but retains its structural identity of form. In calculated predictions, later proved experimentally, we have probabilities that sometimes tally with possibilities. Except in axiomatically-valid laws, observables and calculables can enter into the fabric of the language of science, giving threadbare or one-sided theories or hypotheses which later get revised or revalued with more calculable or observable inventions or discoveries. The falling of an apple in the garden was the only observable element on which Newton erected the theory of Universal Gravitation with calculations derived from the writings of Kepler, Copernicus and Galileo. In Darwin's Theory of Evolution we do not know whether it is life or organism that evolves. He never claims to have observed a monkey changing into a man; nor has he been able to show the process experimentally with any direct evidence other than to give instances which resemble natural selection, the struggle for existence and the survival of the fittest under artificial conditions - and the rest of the evidence consists of

280
museum specimens studied in the light of the theory. As there are rival theories by scientific men like Lamarck and Russell, and rival philosophical versions of evolution in the "Creative Evolution" of Bergson, besides the parallel evolution theory - the scientific status of Darwinism is not on very firm ground at all. As it presents a picture of change on quite other lines than that contained in the scriptural version in Genesis, evolutionism has attained in the popular mind the status of an anti-religious doctrine of scientism. There is a just proportion in which observables could be mixed in science with calculables; and when the balance is lost one gets pseudo-scientific literature between whose nonsensical verbalisms and the verbalisms attributed to classical metaphysics there would not be much to choose. Promiscuous mixing of the observable and the calculable elements in scientific language leads to absurdities, of which Eddington
gives a striking example:
  
   "I am standing on a threshold about to enter a room.
    It is a complicated business. In the first place, I must
    shove against an atmosphere pressing with a force of
    fourteen pounds on every square inch of my body. I
    must make sure of landing on a plank travelling at
    twenty miles a second round the sun - a fraction of
    a second too early or too late, the plank would be
    miles away ... These are some of the minor
    difficulties. I ought really to look at the problem four-
    dimensionally as concerning the intersection of my
    world line with that of the plank. Then again it is
    necessary to determine in which direction the entropy
    of the world is increasing in order to make sure that
    my passage is an entrance, not an exit." (12)

It is easy to see from this extract that between the rival claims of science and common sense, instead of certitude of any kind, puzzlement results, which defeats the purpose of scientific language altogether. We have to beware as much of the false shadows of science, to use the expression of Dr.Holton cited above, as of the false doctrines of metaphysicians.
 
281
RENORMALISATION
The Pythagoras theorem could be proved either theoretically or practically. Mixed methods could perhaps be devised by those who know how to play with mathematical axioms and postulates and rules of inference, but the mixing of methods leads to various grades of pseudo- or non-science. In such matters as determining the specific gravity of bodies, it is a relation that is established in the form of an equation based on experimental data which gain primacy; while in formulating the law regulating the increase or decrease of the entropy of the universe, the languages of science and philosophy are indistinguishable. With the canons of Mill being based on agreements and differences; agreement and difference treated
together with residual and concomitant variations seem to refer to subtle laws of reasoning which give proportion, balance or harmony as between the two aspects of reality based on the observables and the calculables that we have distinguished. For the purposes of this study we prefer to think in terms of normalisation and re-normalisation (13), instead of thinking in terms of the canons of Mill which might be intended for the same purpose. Normalisation would presuppose the notion of a normative factor which it is the aim of this study to postulate in connection with a scientific language as we
understand it here.

A CENTRAL NORMATIVE NOTION NECESSARY FOR SCIENTIFIC LANGUAGE
Just as in biology plants or animals are classified and named by their characteristics that are primary or secondary with reference to some central representative of a family, genus or phylum; so scientific language would require that a central, neutral and normative principle or notion should be postulated, balancing justly the two factors that, we have seen, enter into the composition of scientific thinking. Language has to concern itself with the mind and matter with which science itself is concerned, and the normative principle has to be neutral as between the mental and the material, the 'psychic' or 'physical'.
 
282
We know in recent times of the school of scientific philosophers who called themselves Logical Atomists. Influenced perhaps by the monadology of Leibniz, atomism postulated a unit-entity as a basis for their discussions of questions of athematical, logical or philosophical import. Precise notions about it have to be derived from the "Principia Mathematica" of Russell and Whitehead, which deals with logic and mathematics as having the same principles. Logical atomism speaks of the distinction between 'atomic sentences' and 'molecular sentences' which result from the union of a unit atomic sentence. Earlier, Wittgenstein, while still under the influence of Russell, put more order into the concept of logical atomism when he said:

 "1°13   The facts in logical space are the world.
  2         What is the case, the fact, is the existence of atomic facts.
  2°01   An atomic fact is a combination of objects (entities, things)" (14)

The unit of logical thought is an atomic sentence round which philosophy and logic was built. James and Russell also agreed in calling themselves 'neutral monists', thus attempting to formulate a normative notion which was neither mental nor material for their philosophy. (15)
   
The very reference by Wittgenstein above to 'logical space' postulates a psycho-physical entity in which logical activity could have its being. That the concept is not totally without reference to the bodily aspect and the purely metaphysical, is clear from the fact that it belongs to the context of logical empiricism. This double expression is expressly meant to stand for that union of the two aspects which are the same as in the expression 'neutral monism' which we have just examined. The psycho-physical character of this entity is evident from Russell's own words when he writes:

   "Thus from both ends physics and psychology have
    been approaching each other and making more and
    more possible the doctrine of 'neutral monism'
    suggested by William James' criticism of consciousness."

283
He goes on to make the position of this school of thought clearer than ever when he adds in the same paragraph,

   "I think that both mind and matter are merely
    convenient ways of grouping events. Some single
    events, I should admit, belong only to material groups,
    but others belong to both kind of groups and are
    therefore at once mental and material. This doctrine
    effects a great simplification in our picture of the
    structure of the world." (16)

Although presented in the usual dogmatic form after the manner of older metaphysicians, without reference to any experimental evidence, it is possible for us to see that logical empiricists generally are already committed to the recognition of a neutral entity which is a kind of absolutist abstraction, neither belonging wholly to any one of the two rival worlds of physics or metaphysics. While this view simplifies matters, it is still open to the charges of a priorism, solipsism and arbitrariness, insofar that it is a doctrine that is asserted. Logical or linguistic structure generally could be examined more scientifically through observational situations of experimental status such as those we are outlining below.

INTROSPECTIVE OBSERVATIONS FOR THE STUDY OF LINGUISTIC STRUCTURE
If the indirect evidence of pointer-readings is acceptable in scientific experiments proper (which themselves depend on evidence many degrees removed from the direct observation of events), we may ask legitimately why introspective experimental situations could not be relied on to give us the same degree of scientific certitude that differentiates science from speculation. If a certain botanical specimen is available as a weed it is not necessary to grow it in a special herbarium. In common human life there are common human linguistic situations which have experimental value if the method of experimentation could be applied to them, even introspectively.
 
284
Scientific philosophers like Bergson have both relied on schematic proto-language, as understood in this study, and have also made use of the study of experimental situations to give validity to the discussion of factors of psycho-physical
import. He puts the question:

     "J'écoute deux  personnes converser dans une langue inconnue. Cela suffit-il pour que je les entende? Les vibrations qui m'arrivent sont les mêmes qui frappent leurs oreilles. Pourtant je ne perçois qu'un bruit confus ou tous les sons se ressemblent. Je ne distingue rien et ne pourrait rien répèter. Dans cette même masse sonore, au contraire, les deux interlocuteurs démèlent des consonnes, voyelles et syllabes qui ne se ressemblent guère, enfin des mots distincts.
Entre eux et moi, où est la difference?"

(Editor's Note: what follows, is a tentative translation by us, as are similar passages below.)

("I hear two people conversing in an unknown foreign language. Is that enough for me to understand them? The vibrations which come to me are the same as strike their ears. However, I only hear a confused noise which all sounds the same. I can distinguish nothing and could repeat nothing. The two people talking, on the contrary, can hear consonants, vowels and syllables which are not alike and which make up distinct words. What is the difference between them and me?")

After tracing minutely and in detail the insurmountable difficulties that intervene between the physical fact of sound-impressions and their understanding as language Bergson states:

"Ainsi se déroulerait dans notre conscience, sous forme de sensations musculaires naissantes, ce que nous appellerons le schéma moteur de la parole entendue." (17)

("This is how what we could call the "schéma moteur" for understanding words develops within our consciousness in the form of nascent muscular sensations".)

(Note that the term 'schéma moteur', roughly translated as 'motor scheme', which is used innumerable times throughout the Guru's works, was almost always left untranslated by him and so by us, the same applies to the term 'élan vital', more or less translatable as 'vital impulse'.cf. inf. ED)

Thus we see already strict scientific philosophers employing a new kind of introspective experimentation which must be considered at least as valid as the indirect evidence of pointer readings in physical laboratories.

INTROSPECTIVE PSYCHO-PHYSICAL OBSERVATIONS OF EXPERIMENTAL STATUS
Russell's norm of logical atomism, belonging to the philosophy of neutral monism, as he calls it, and Bergson's effort to
establish a 'schéma moteur' in the context of his philosophy of change and becoming of the 'élan vital', are recent attempts on the part of philosophers who are fully scientific in their outlook to arrive at a normative notion that would be free from the one-sided epistemological reference of classical speculations. Why should we not improve on this kind of approach by accentuating the experimental character more consciously and with greater scientific exactitude? By way of showing the possibilities that lie in this direction, and since language itself thrives where mind and matter meet, we shall give here an outline of experimental situations which would

285
yield us a greater degree of certitude than hitherto possible about the structure of linguistic consciousness. In doing so we shall try to keep as close to that fully scientific but as yet little-favoured branch of knowledge called psycho-physics, into whose domain both the logical atom and the élan vital should belong. We shall divide our experimental situation into two phases for making two sets of observations that properly belong to the observable and calculable worlds
which meet in a unitively-conceived psycho-physical event in terms of common human consciousness:

(I) FIRST PHASE
Think of two persons in a dark room. (18). Let us call them A and B. A says to B , 'Who is there?' B retorts with the same question, 'Who are you there?' The possible basic response of either or both of them would be contained in the common personal pronoun 'I', which could apply equally to anyone.
   
The important condition to note here is that all visual and other impressions are meant to be eliminated except the auditory linguistic link. The observables are eliminated here by the condition of darkness; and the calculables, which have their roots in the sense of hearing which leads to meanings of a conceptual order which refer to central as against peripheral objective realities, are isolated for epistemological analysis so as to arrive at a complete scheme of the structure of the thinking process that is to be understood as implied in language.
    
It is true that the voice of the two persons who communicate without visual impressions might contain certain physiological elements related to the past habits or tendencies of the person, giving him a certain individuality related to his memory aspect. The memory of the past might be said to determine in some indirect way the future conduct and the imaginative side of that person, giving him imaginative or futuristic orientation of the normative entity, whatever it might be called. This aspect could also give personality or individuality to A as distinct from B. But the intention of the

286
experiment is to give primacy to the central, invisible, subjective aspect of the personality. Peripheral or marginal factors which belong to the visible are meant to be eliminated in this phase of the experiment. Between the persons A and B, as they carry on a conversation, different grades of pure or practical memory or imaginative factors might enter into the common consciousness of both. The ideas may be said to move in a trans-subjective axis which for taxonomic purposes (which we shall justify more fully later), we shall call the vertical axis.

(II) SECOND PHASE
Now let us change the conditions of the experimental observational situation. A neutral observer or witness, 0, may be thought of as switching on a light in the same dark room. The visible aspect of the reality of the situation now becomes added to the auditory, which had a content belonging to the world of the calculables. The auditory content is not abolished, but a new dimension, depending on the perceptual, peripheral or more 'objective', is imposed on the original stem of the trans-subjective aspect, while the trans-subjective remains intact like stars during daytime. The physical peculiarities of A and B gain primacy and prominence, and sex, complexion, stature and other particularities that are specific and empirical in content emerge into the situation. One could examine the fingerprints of A or B to accentuate their individuality to its limits. Here the specific factors happen to be overt and not innate. They may in a sense be called outer ones as opposed to the innate or subjective ones of the first phase. This we shall refer to as the inter-physical. To put the line of demarcation between the two aspects would take much more discussion than what we might at first think. Wecould think of different grades of conceptual, perceptual or actual factors claiming primacy in consciousness at a given time. It would be impossible to isolate them and study their characteristics and modes of combination without going still one step further into the implications of this second phase of our experimental situation. Let us suppose now that A or B or both are using telescopes or microscopes to aid their vision
 
287
and are interested in the outer limits of space or the microscopic structure of matter as we can know it. They speak about what they are interested in to the neutral observer or witness 0. Now we are ready to extract the linguistic situation implied. In the consciousness of the neutral observer, language makes certain impressions which are events of a psycho-physical order of reality reduced into abstractions of a linguistic order. (19) It is not the actuality that matters any more but the conceptual aspect only. Between the trans-subjective concepts of the first phase and the inter-physical concepts of the second phase there is linguistic parity vertically and a 'strangeness' - if we may use a term borrowed from particle physics to express tentatively what we mean. Both these have the same status linguistically in the consciousness of the neutral observer. The inter-physical aspect thus isolated without full justification, which is to follow, we shall call the horizontal axis.

FURTHER IMPLICATIONS OF THE PSYCHO-PHYSICAL LINGUISTIC SITUATION
On the light being switched on, the specifically overt or the objectively perceptual aspects of A and B stand revealed. Their memories and imaginations give them a trans-subjective dimension; and their physical power of seeing objects as such, in true or false light, is an inter-physical or horizontal dimension, measuring along its axis tendencies to day-dreaming or eidetic peculiarities such as exaggerated colour vision, as when under the influence of drugs or colour blindness. The subjective 'I' may be said to converge into the common unity of the vertical self at its negative levels; while the arrow pointing horizontally and perceptively towards the object may be said to diverge into the plurality of conscious units, each with its specific characteristics, as against the  generic characteristics of the former.
   
If we now think that one of the persons A or B suffered from a tooth-ache or a stomach-ache - the facts could have been communicated in words with the lights out, and with  facial or other expressions or contortions of the body when the lights are on. 

288
If, as an alternative case, one of them said, "I have a heavy burden on my head which makes me groan under its weight", the linguistic link in a dark room would give less certitude than when the load is seen, and its weight, whether bearable or not, is appraised by the observer-witness. Between suffering from the weight of a load and that of a stomach-ache there is a change in the vertical scale as between the overt and the innate aspects. A sleepwalker or a daydreamer could have his mind at different points in the horizontal scale. When overt and innate factors enter into the situation, both vertically and horizontally, without any regulating principle involved, we have an absurd linguistic situation. All we have to note at this stage is that physical and mental factors could enter positively or negatively into the dimensions that we have distinguished.

NEUTRAL NORMATIVE APPRAISAL OF THE TWO MAIN TYPES OF LINGUISTIC EVENTS
If we think of the neutral 'observer-witness' of the above experimental situation that we have examined, and appraise the content of his consciousness with a view to arriving at primitive, atomic or elementary simple happenings therein, we could think of two typical movements which would act as references for all possible events in consciousness. The inter-physical reference may be said to move within the horizontal range of phenomenologically-represented objects or interests, whether subjective or objective in origin. An atomic sentence representing this horizontal movement in consciousness could be the thoughts implied in a sentence of the model, 'this is a pot': where the word 'this' would correspond to the negative horizontal aspect, tending to virtuality and to a general vagueness that is non-specific in character; while the word 'pot' would stand for a more specific actuality. Reversibility and irreversibility could both apply to the process or modality which depends on the degree of attention implied in each mode of thought. Likewise
in the sentence, 'this is reason', we have the typical case of a vertical movement in thought: the word 'this' standing for understandable items of thought in general, implicitly understood; and 'reason' representing an element in
 
289
thought which is more explicit in its content, though still of the order of pure thoughts. Much concentrated direction of the inner power of attention is needed before one could think of the specific content of reason. It could therefore be called a vertical-positive element in molecular thought consisting of atomic thought-events represented by the first instance.
   
The verb 'to be' is the link corresponding to the activity in consciousness which relates mental attention or relaxation in one sense or the other.
   
If we should now remember further that the neutral observer-witness in the imaginary situation does not enter into direct non-linguistic relation with either objects or with specific factors or elements of pure items in consciousness, we have within the schematically-conceived and globally- or unitively-understood personal consciousness, all the possible combinations, characteristics and modalities in which thoughts integrate themselves to form normative linguistic units. Based on such units an over-all norm is also possible to conceive.
 
SECTION II: EXPERIMENTAL
In the previous section we have confined our remarks to the study of the linguistic structure of thought from the point of view of what can be described as scientific philosophy. Intrinsic forms of thought, axiomatically given in the laws of thought, were taken to be our point of departure. Science is associated in the popular mind with a laboratory where brass instruments record pointer-readings to reveal verities that are unquestionable. Instead of theological belief we now have truth told to us by apparatus or appliances. These appliances verify equations experimentally. People are convinced more readily when we say that a cardiograph or encephalograph tells us the story directly or indirectly, through automatic recordings of some sort. The chain of inferences and the indirectness of the observations are easily excused. After what we have said in the previous section it is hardly necessary for us to look for further proof. Still, out

290                          
of respect for the popular temper of our times in such matters, we are going to examine in this section the merits of a certain number of evidences throwing light on the structure of thought, whether of direct value or only of indirect significance. If the normative notion of integrated thought that we have arrived at in the last part of the previous section is kept in mind; and if the experimental evidence presented in the present section is closely examined - the resulting validity of the structure of thought will surely be enhanced, though certitude may not be totally based on them. As we have to think about thought in this section, we can call this section one belonging to a science of sciences. Observables and calculables come very close together here, one lending certitude to the other. Negative evidence becomes as
significant as positive.

LIGHT ON THE INNATE STRUCTURE OF THOUGHT FROM THE EEG
That the activity called thinking has implied within it two different kinds of processes has been made amply evident by investigations conducted with the help of the recently invented Electro-Encephalograph (EEG). There is, in the first place, what is taken to be the normal activity of the brain which produces rhythmic oscillations which have been distinguished and named as alpha rhythms. The strange phenomenon noticed with regard to the activity of the brain is that these electric rhythms tend to disappear, instead of getting augmented, as we should expect, when we know by other evidences that the brain is engaged in thinking or is really active in respect of some problem to be solved. Relaxing and shutting the eyes normally brings alpha rhythms into evidence, but with certain other types of persons they continue when the eyes are open; and some persons are without these rhythms altogether. These paradoxical effects seem to depend on deep-seated factors independent of anything physiological. Changes in the degree of attention or relaxation contribute to the appearance or disappearance of alpha-rhythms, depending on the psycho-physical personality of the individual in question rather than on any physiological factor.
 
291
Prof. W. Grey Walter of the Burden Neurological Institute said recently in connection with the findings of the EEG as follows:

   "One of the most sobering, even humiliating facts of
    the whole of brain physiology is that scarcely a single
    phenomenon discovered by the study of electrical
    activity of the brain - the EEG - was foreseen or
    predicted by physiologists…" (20)

According to the same authority, not only are the evidences of brain activity independent of physiological foundations, as taken for granted hitherto by empirical scientists, but there are deep-seated factors contributing by their elusive paradoxical expression through the language of the EEG which are of such an indeterminate nature as to indicate what may be called personality traits. He continues in the same talk as follows:

   "The confusing thing is that even when the eyes are
    opened, or the person thinks hard, the (alpha) rhythms
    may disappear. Unfortunately for our understanding
    of this effect, not everyone shows alpha rhythms,
    even with the eyes shut, and in some people the
    rhythms persist even with the eyes open, so we are
    faced with an objective sign of a mystery that we
    accept and delight in in everyday life and find hard to
    fit into scientific analysis - that is, human personality."
    (21)

Thus for the first time the notion of a human personality, independently of physiological factors, enters into the experimental domain of science. This fact suffices to give to the normative notion that we have outlined in the previous section sufficient status as a scientific fact for the purposes of this study.
   
Prof. Grey Walter has approached the same problem from another end and, when his findings in respect of brain activity are put side-by-side with the story that the EEG has to tell, tends to make clear that there are two distinct kinds of thinking or brain activities going on alternately. Prof. Walter

292                           
points out firstly that the brain is essentially 'a problem-solving organ'. In solving problems a mental model that is either pictorial or verbal is involved. Actual seeing and visual imagination are activities that are different and even opposed in their effects. When mentally solving a problem - if the kind of model that the subject uses happens to be one of the usual variety of imagination (not vision) - the alpha rhythms, as seen through the EEG recordings, show a tendency to stop. The brain mechanism has thus two different reactions: the first is the kind that resembles the movement of the eyeballs when looking at an actual sight, and the second is when visual imagination operates at a deeper level of consciousness. The former tends to retain alpha-oscillations while the latter tends to suppress them. Looking at a whole page in reading a book is a visual activity in which "the sweep of electrical activity has implicit in it a sort of scanning process'', as Prof. Walter puts it. Scanning is different from looking at the whole page, in that one sees the words on it one after the other. One changes the steady shape of the printed lines into a series of visual signals spread out in time. In other words scanning means "turning spatial patterns into time ones''. Brain models have also been devised which have helped to reveal that they react as if they had the faculty of memory, where the time-factor rather than the space-factor counts. The relation between the scanning process of the brain and the stoppage of the alpha-rhythms which refer to the deeper or, as we might say, vertical activity of the brain as opposed to its mere spatial (horizontal) functioning, is sufficiently clear from what Prof. Walter has to say on the matter:

   "When one reads a page of print one's eyes scan it
    systematically line by line. The page is there all the
    time, but one sees the words on it one after the other.
    This means that one changes the steady shape of the
    printed lines into a series of visual signals spread out
    in time."

According to Prof. Walter again, scanning comes into evidence when a person looks for a word in the dictionary and finds it interesting. We can see his eyes stop moving. The Professor suggests his theory when he puts the question: "Is this the sort f thing that is going on in the brain when the alpha rhythm tops as a person thinks?" (22)

293
EEG and brain-model evidences put together thus lend uch experimental support to the space-time correlation of ental activities which fall into two interdependent though ndependent classes.

DIRECT EVIDENCE OF A PSYCHO-PHYSICAL AXIS FFORDED BETWEEN APHASIA AND APRAXIA
Various troubles connected with speech with which doctors ave had to deal, and which have been the subject of detailed experimental research in clinics and psycho-pathological aboratories in various progressive countries, have already a rich fund of accumulated data which afford us as conclusive vidence as possibly could be expected supporting the reality of a psycho-physical link along whose length various rades of speech-troubles could be located as between the psycho-physical function pertaining to one pole of linguistic abit or the other. The evidence, which is quite striking and conclusive, has been before the scientific world for more than alf a century now, but the inferences that could have been made for the service of scientific knowledge about human aculties in general have not, for some reason, received the
attention or been given the importance they deserve. It is to the credit of the intuitive intelligence of Bergson to have tried o enrich metaphysics with the minute details of speech-troubles and to have made valuable inferences based on the evidence they present.
    
It is not necessary for us to go into all the cases that have een passed in review by Bergson over several pages with full documentation in his fully-scientific study, "Matière et Mémoire: Essai sur la Relation du Corps à l'Esprit", but scientism has, as we have said, its own prejudices - imagining, so to say, that the soul, if real, should be found at the tip of the scalpel. Bergson's fully scientific inferences have been mixed up with other verbose speculations of no value, perhaps because of the lack of a fully-developed epistemology or methodology pertaining to science as such.
 
294                          
We need only two or three typical cases cited by Bergson (23) or the purposes of this study to see that - understood in terms f the schéma moteur (24) that Bergson has developed elsewhere in his studies of the élan vital, and provided that scientific physicalism is not an end in itself - there is sufficient vidence for inferring the reality of a schematically-conceived xis that is mathematically and logically valid and which ould help us to get a clear idea of the structure of thought hat must be at the basis of linguistic expression. Bergson rites:
   
    "Ainsi, dans un cas observé par Lichtheim lui-même, le
    sujet, à la suite d'un chute, avait perdu la mémoire de
    l'articulation des mots et par consequent la faculté de
    parler spontanément; il répètait pourtant avec la plus
    grande correction ce qu'on lui disait. D'autre part, òu
    la parole spontanée est intacte, mais òu la surdité verbale
    est absolue, le malade ne comprenant plus rien de ce
    qu'on lui dit, la faculté de répèter la parole d'autrui peut
    encore être entièrement conservée."

("Thus, in a case observed by Lichtheim himself, the subject had, after a fall, lost the memory of articulating words and consequently the ability to speak spontaneously. However, he could repeat what was said to him perfectly correctly.  Similarly, in cases of total verbal deafness where the ability to speak spontaneously is intact, the subject can still repeat what other people say to him")

After giving due consideration to all the theories that have een put forward by authorities like Bastian, Romberg, Bateman, Winslow, Kussmaul and Arnaud, besides considering the dozens of varieties of aphasia studied by Lichtheim himself ('Brain', Jan 1885, p. 447) and others, Bergson is able to reduce the phenomena in terms of the schéma moteur, with the help of which he is able to solve the mystery. He concludes by saying:

    "La vérité parait être intermédiaire entre ces deux
    hypothèses: il y a, dans ces divers phénomènes plus
    que des actions absolument mécaniques, mais moins
    qu'un appel à la mémoire voluntaire; ils témoignent
    d'une tendence des impressions verbales auditives à
    se prolonger en mouvements d'articulation, tendence
    qui n'échappe surement pas au contrôle habituel de
    notre volonté, qui implique même peut-être un
    discernement rudimentaire, et qui se traduit, à l'état
    normal par une répètition intérieure des traits saillants
    de la parole entendue. Or, notre schéma moteur n'est
    autre chose." (25)

("The truth appears to lie in an intermediate position between these two hypotheses: these various phenomena are made up of more than purely mechanical actions, but of less than a conscious calling upon memory: they signal  tendency of auditory verbal impressions to prolong themselves into articulation; a tendency which surely does not escape from the usual control of our will, and which may even imply a rudimentary discernment. In the normal state it gives rise to an internal rpetition of the main points of speech as it is heard - our schéma moteur is no other than this.")

(EDITORIAL NOTE - we are well aware that these translations are not particularly clear, but Bergson is well-known for the complexity of his thought and style of writing; the original French is difficult even for an educated native speaker, and opaque to most others. We are doing our best.)
 
295
Bergson's schematic representation of a psycho-physical unit of consciousness involved in language function is seen to emerge in clear outline in his analysis of verbalistic troubles known to medical science. That he has kept it strictly within the pragmatic frame does not affect the intrinsic and valid character of the scheme, which we can take as applicable to a more general philosophical context by extrapolation. Other cases of a related psycho-pathological order have also been studied and recorded - such as the case of a virtuoso who had lost in some way his material technique of external expression in music while his thoughts and understanding of music remained intact; as opposed to that of an eminent medical man who had retained all his knowledge about anatomy and pathology but had lost his power of fixing
his will on one act that was pertinent to a situation, and instead found himself for some days helplessly cutting paper into bits, punching holes or tearing up books. (26) As between neurological and psychiatric troubles there is a psycho-physical polarity which would justify our suggestion just made that the whole series of troubles, whether strictly related to aphasia or apraxia or even dyslexia (27), can be fitted into a common scheme with the help of intrapolation or extrapolation, as known to mathematical thinking.

EVIDENCE OF PSYCHO-PATHOLOGY
That a psycho-physical normative unit, whether called by the names of libido, persona, psyche or self, has a distinct and non-metaphysical reality is brought out strikingly by a case that Prof. Pierre Janet of the Collège de France has recorded in his lectures on "La Force et Faiblesse Psychologiques". He refers to a surprising instance of loss of speech. This loss of speech was due to a certain degree of negative withdrawal into oneself rather than the result of anything that had a physical cause in the physico-pathological sense. As one whose authority is high in such matters and one fully appraised of the latest development of this subject, both practical and theoretical, his estimate of the above case would help us to clarify the scientifically valid normative notion for the purposes of our study. We shall quote from

296
Janet a case in which it is neither a case of aphasia, apraxia nor dyslexia, but one of general mutism and functional hybernation or inactivity:

    "Je racontais autrefois l'histoire d'une étrange malade,
    soignée dans une maison de santé, qui pendant trois
    ans entiers était restée sans consentir à manger un
    aliment et sans prononcer un seul mot. . . Après
    trois ans, un printemps cette malade se dresse sur
    son lit et se met à dire à la garde la phrase suivante:
    "Ah ça, on ne déjeune pas ici?" (28)

("I used to describe the strange case of a patient in a nursing home who did not eat or speak a single word for three whole years…After three years, one spring day the patient sat up in bed and said the following to the nurse: 'For goodness sake! Don't we get any breakfast here?'")

One would be fully justified in inferring from such cases that there is at least a real psychophysical entity, understandable as a mathematical unity at least, which is neither body nor mind but something intermediate between the two. When psycho-pathologists say that a certain state is opposed to certain others, as they often do in the case of the troubles connected with the will, as above; or when they oppose or contrast cases of neurasthenia and psychasthesia or reduce both more simply into asthenia, as Pierre Janet prefers to do (29), there is in their minds a vaguely-conceived scheme of interrelation of psycho-pathological conditions.
   
Pierre Janet further suggests that mental cases which he classifies under 'les délires' (deliria) could all be thought of as pertaining to degrees in a hierarchic scale of over-estimation and under-estimation of the self with reference to speech. He says:

   "Examinez les délires et même tous les troubles de la
    croyance, quels qu'ils soient, vous pourrez toujours
    les résumer par l'une de ces formules: le délirant est
    un individu qui place mal sa parole dans la hiérarchie
    des degrés de réalité." (30)

("Examine delirium and even all problems of belief, whatever they may be, and you could always sum them up by a formula such as: 'the delirious person is an individual who has problems in placing his discourse correctly in the hierarchy of degrees of reality' ")

Certain other writers on personality problems, like F.Achelle-Delmas and Marcel Boll, go as far as to suggest the methods of interpolation and its inverse procedure of extrapolation, which latter he considers misleading in cases of dementia.
He also says:

297
     "D'une manière générale, nous nous efforcerons
      d'appliquer ce qu'on nomme après Stuart Mill, la
      méthode des variations concomitantes, qui est le
      véritable centre de tout raisonnement inductif." (31)

("Generally speaking, we shall try to apply what Stuart Mill would call the method of concomitant variations, which is the true centre of inductive reasoning")
 
The systematic classification and nomenclature according to a correct taxonomy becomes full of problems in this domain of psycho-pathology. If a central normative notion is supplied, we could imagine how at present the vast amount of literature of a pseudo-scientific or even non-scientific status could be normalized so as to standardise language generally. What the difference between the libido and the subliminal self amounts to in precise terms, cannot even be discussed at present without taking sides with one school of thought as against another. The classification of mental troubles is at present a fecund field of unscientific statements which, however, pass for science. Normalisation with reference to a norm conceived synthetically, and re-normalisation of terms that have tended to diverge into too many specific analytic sub-divisions of the same fundamental phenomenon, with which they may happen to be basically related, could be accomplished for the language of science only when the neutral norm has been given an integrated status in respect of possible modalities, combinations and characteristics of thought and corresponding language-elements.

NORMALISATION OF PEDAGOGIC THOUGHT
Psycho-pedagogy, as it is practised experimentally in modern times, is another department of knowledge from which we could derive some useful directives in regard to the normalisation of scientific language. Teaching and learning involve that bipolar relationship in which a constant interchange of thought is taking place, like a subtle process of osmosis. 'Education' itself is an expression that is full of ambiguity and vagueness. Personal relations between the pupil and teacher are becoming recognized more and more as desirable in the process. The philosophical basis of education could be negatively conceived as with Rousseau; naturalistically conceived as with Spencer; pragmatically

298                           
conceived as with Dewey and also idealistically or dialectically conceived as with Pythagoreans, Platonists, Neo-Platonists or their continuators in modern times like Whitehead or Royce. Whether a stimulus-response psychology, behaviourism or adjustments to the needs of man-making or character-building are to be given primacy as against adjustment to social or citizenship needs, are all questions on which educational literature can differ widely. Normalisation in this domain, so full of possible differences of attitude, can only be expected when the norm of the persons involved in the bi-polar process is postulated scientifically, mathematically, logically, biologically or psycho-physically as the common personal factor at the basis of the process that is to take place. There are at present extant verbose volumes which are a hot-bed of confusion, and this must be reflected in the language used. We cannot do better here than to quote from the writings of one whose scientific training and acquaintance with scientific problems cannot be questioned. Dr. Alexis Carrel writes:

   "The tests applied to school-children and students by
    inexperienced psychologists have no great
    significance. They give an illusive confidence to those
    unacquainted with psychology. In fact, they should
    be accorded less importance. Psychology is not yet a
    science. Today individuality and its potentialities are
    not measurable. But a wise observer, trained in the
    study of human beings, is sometimes capable of
    discovering the future in the present characteristics
    of the given individual." (32)

Having in the year 1932 myself submitted a thesis to the University of Paris entitled "Le Facteur Personnel dans le Processus Educatif", and in view of the fact that my work fully answers the question of how normalisation of personal relations takes place, with a central notion of the persons involved in an educational situation as between teacher and pupil, it might be permissible in this section to pass over aspects of educational problems covered in detail and with ample documentation in that study. Since those days, however, some interesting developments have taken place in the

299
educational world which deserve to be noticed here, especially as they tend to confirm the schematic norm that we have in mind in the present study. On page 25 of that thesis I had given a schematic representation, combining and correlating scientifically certain of the important aspects of educational psychology that have direct bearing on the development of the personality of the child. As most of what is represented there already is still to be considered valid and as by no means out-dated; and encouraged by the fact that it has already passed through the scrutiny of an academic body, the schema has been reproduced on page 193 above (fig. 14.3), and when examined and read side by side with the
concluding findings in the thesis, also given as the footnote below, it would give us here, for the present, a rough idea of what we mean by normalisation in the domain of psycho-pedagogics. (33)

RECENT PSYCHO-PEDAGOGIC EVIDENCE
Of the names that have made outstanding contributions of an experimental nature to the most recent developments in pedagogics, that of Prof. Jean Piaget may be mentioned as perhaps the most significant for us in this study. From the year 1921 he has been contributing serious works on such subjects, supported by experiments in every case, beginning with 'Une Forme Verbale de la Comparison chez l'Enfant' (1921) through one concerning 'Le Langage et la Pensée chez l'Enfant' (1928), and leading up to 'La Naissance de l'Intelligence (1932) and 'La Formation du Symbole' (1945). His latest publication, in collaboration with Inhelder, is devoted to the "development of two kinds of operational behaviour,
which are classification and seriation, which intervene in the formation of a large number of psychological and pedagogical notions". (34) Running through the whole series of works is his most important contribution of a vertical series of stages which he calls "paliers"*, described by him as a special type of thinking pertaining to child psychology. In the last of his works there is a reference to "the development of classification and that of seriation" which constitute "two unified and synchronous processes". Further there are said to be two factors whose co-ordination assures the reversibility of the

*(A "palier" is literally a "landing", as in a flight of stairs. Perhaps the closest English translation, following Roget and the OED, would be "plateau", but with the implication of being a temporary resting place in the course of an ascent. ED)

300                          
operations which are called retroaction and anticipation. The overall explanation is based on the notion of equilibrium. (35) It is not possible nor necessary for us to discuss here the merits of these findings. All we have to note is that they do fit into the scheme that we have so far outlined in which mental activity takes two different directions: one that could be called spatial, and the other connected with the time-axis in which anticipation and retroaction occur - with an overall notion of equilibrium marking the centre of the scheme. Expressions such as 'correspondence topologique bi-univoque et bi-continue' (36) ("bi-univocal and bi-continuous topological correspondance") which Piaget uses, make it unmistakably evident that a mathematical structure is to be understood in the scientific nature of his writings. The new kind of language with the latest terms, with a schematic pattern underlying it, can be discerned from the following summary of the import of Piaget's contributions, from the pen of another contemporary authority in scientific pedagogy. Dr. H. Wallon of the Collège de France:

     "Les expériences ingénieuses de Piaget pour connaître
      comment l'enfant acquiert les notions de nombre et de
      quantité montrent en détail à quelles contradictions il    
      peut se heurter dans son cheminement pour se débarasser
      des apparences purement sensibles, elles-mêmes
      contradictoires, et pour les résoudre en invariants auxquels
      il faudra que se superpose une vision opératoire . . .
      C'est par une suite d'echelons progressifs que le dynamisme
      des impressions et des réactions concrètes se fige en
      invariants auxquels doit se superposer un acte unificateur
      qui lui-même se fige en système stable de symboles. Et
      les symboles, prenant graduellement la place des éléments
      perceptifs auxquels ils se substituent dans la mesure òu ils
      en expriment mieux qu'eux-mêmes les rapports de co-
      existence et de devenir, deviennent chacun à son tour les   
      elements d'une progression nouvelle dans la réduction de
      l'être à la connaissance." (37)

("Piaget's ingenious experiments, intended to discover how children acquire notions of number and quantity, show in detail what contradictions the child comes up against in the process of discarding purely sensory appearances - which are themselves contradictory - and resolving them into invariables upon which he has to superpose an operational vision…
It is through a series of progressive stages that the dynamism of impressions and concrete reactions is resolved into invariables that have themselves to be submitted to an act of unification, which in turn resolves itself into a stable system of symbols. These symbols, as they gradually take the place of the perceptual elements which they supplant to the extent that they can express, better than they can themselves, their relations of co-existence and becoming, become in turn elements in a new progression of the reduction of being into knowledge")

Elsewhere in the same work Prof. Wallon speaks of three 'moments' which come into opposition in knowledge. The \first he describes as having

301
'irreversibilité absolue de l'empiricisme brut' (absolute irreversibility of basic empiricism); the second 'reversibilité totale de l'acte intellectuel (total reversibility of the intellectual act) and thirdly, 'réduction d'un irreversible en reversible.' (reduction of an irreversible into a reversible).
   
The number of scientific terms that have been used in the above paragraphs to represent something that could be immediately intuitively understood with the help of a schematic representation, and the difficulty for the reader to follow the trend of the transformation that takes place in the child-mind through such words as belong to a sort of meta-language of science, should be sufficient recommendation or us to think of something simpler and of the nature of a proto- rather than a meta-language, which would show these thoughts more directly. Such a language could be no other than the one that can establish a direct link between these two aspects of language. How such a relation could be established in a valid and workable manner is what we have still to make clear in the remainder of this study.

THOUGHT STRUCTURE EXAMINED FROM THE PSYCHO-PHYSICAL STANDPOINT
That branch of science known as psycho-physics may be said to take its position between what is called physiological  psychology and psycho-physiology. Physiological psychology and psycho-pathology as practised in clinics may be said to be on the side of physiology rather than on that of psychology. As our purpose is to discover the structure of thought just at the point where it gets inserted into matter, psycho-physics and its findings have special interest for us in this study. We shall therefore fix our attention on certain aspects of this branch of science which is based on simple stimuli and responses. Besides the study of relations which might be greater, equal or less than either stimulus or response, we have to have in this branch of knowledge what is called the threshold or "limen". Subliminal responses, both positive and negative, and threshold or liminal ones, are likely to give different laws, such as the different laws of psycho-physics attributed to different experimenters like Weber, Fechner, Delboeuf, Breton and others. Each of them had his own mathematical formula expressing the relation between

302                          
stimulus and response, by which the body was to be understood in terms of mind and the mind in terms of the body. Some used logarithmic language while others used the idea of geometric or arithmetic progression to relate the bodily and mental factors. Merkel's law was seen to go against the validity of the Weber formulation of the relation. It states that within the limits of the threshold, there is a simple equality of proportion between stimulus and response. If we should think of the human organism as a whole in the light of these rival and different theories called laws it would not be difficult for us to see that the innate global structure of the psycho-physical entity involved is what is at the origin of the different partial experimental findings. The limen is a notion that touches that zone of the psycho-physical entity which is nearest to the null or zero-point. Stimulus must be said to be quantitative as it is actually physical and measurable as such; and response, which varies geometrically or logarithmically, or according to more complicated mathematical laws, may be more simply looked upon by us as a qualitative factor. It is because even such terms as 'qualitative' are used in different contexts by different philosophers, and thus tend to produce ambiguities, that the need for a schematic language such as we are proposing in this study becomes a necessity. According to what we propose, the outline of which has already emerged from our discussion so far, we could call the response aspects, which are of the order of calculables rather than observables, as pertaining to the qualitative or vertical axis of reference. The stimulus aspects would legitimately belong to the quantitative or horizontal axis of reference. By using these vectorial terms of projective geometry in a certain sense that is to be understood as belonging to the context of analytical geometry and topology at once, as Spearman has already begun to discern, and as known to what is called vectorial psychology, we have the unique advantage of a language for which the languages of the various particular branches of science become merely particular instances. It is in this sense that semiotics could be made a veritable organon for all sciences. (39) Sir Russell Brain, President of the Royal College of Physicians, London, author of "Perception and Science", in a recent pronouncement pertinently puts the question:

303

"If we become aware of the colour solely as a result of changes occurring in the brain, which is inside the skull, how do we come to locate the red in the book which is lying on the table?" (40)

If this book gets its colour from inside the skull and not from any primary quality in the book itself, we are witnessing in such a question put by a scientific authority a complete change of reference for science as a whole, which, from the days of Heisenberg's Uncertainty and the Relativism of Einstein, has been shifting its accent from the observed to the observer. While we are still on the subject of the light psycho-physics could shed on the schema we are developing, we could also refer to certain findings that have had a well-recognized place in science for many years, such as the phenomenon called 'retinal rivalry', which records the peculiarity of the effect of colour or form on vision by which, if the two eyes are stimulated by different colours or forms at the same time, there is an element of intelligence that enters the situation, by which both eyes together alternately see only one colour after another.

The spatial rivalry is replaced by the mind, or by some inner factor which insists on seeing one colour or form at a time without rivalry.

The very term 'retinal rivalry' retains the old prejudice in favour of physiology as against psychology within psycho-physics, which ought strictly to give equal importance to both aspects. A more correct description of the phenomenon would be to ask how the conceptual factor solves the duality  of perceptions.

Sir Russell Brain refers to the phenomenon of 'referred pain', which is not actually in the part of the body to which it is attributed by the sufferer. He explains: 'many people who have had a limb amputated say that for a time it feels as though it were still there'.(41) Examples of this kind could be multiplied to show that even experimentally, mind and matter meet neutrally in psycho-physics.
   
The sensation of pain depends on its continuity or intensity; while that of a 'just noticeable difference' of colouris more related to space than to duration. The saturation, hues and the brilliance or darkness of colour-shades and their 'just noticeability', resemble modes of intensity characteristic of elements of thought. If we should add to these the notion of the peculiarities of combinations in which

304                        
elements of colour integrate themselves, we arrive at the well-known 'colour-solid'. The taxonomy derived from this is now adopted by the American Standards Association and is the accepted language of colour for use by many manufacturers of paints and other products demanding a simple and accurate method of referring to colour and its innumerable shades.(42)
Vectorial space and Cartesian correlation, put together into the idea of the colour-solid, with whose help scientific precision is given to the confusion of the names of colours and their possible varieties, introduces for the first time a public and universally-understandable language - at least with respect to one domain of language where ambiguity is most possible - whether between one vernacular and another or even between those who happen to be using the same language. The vertical axis is here represented by the central achromatic scale ranging from black through grey to white at the top. The spectral colours are related according to hue, light and shade, or degree of saturation, with three distinct integrating, characteristic, combinatorial or modal dimensions or factors which, though understood at present only in the psycho-physical context, could well apply to the integration of thought and language in general, in an extended or extrapolated
sense.

THE VALIDITY OF PSYCHO-PHYSICAL SPACE
If in logical atomism it is permitted for us to think of logical space as a distinct entity, the non-arbitrary status of the colour-solid must be considered to be beyond any question in respect of its validity, even by those who call  themselves 'logical empiricists'. Even when a modern physicist refers to space, there are two aspects of the notion of space that meet in it which have to be distinguished. Conceptual and perceptual spaces are put together by him, consciously or unconsciously. It is a sort of neutral space that is involved, as between actual space enclosed in a bell-jar in the laboratory (if a perfect vacuum is possible), and a space conceived by the mind as a metaphysical abstraction that has been defined by Aristotle as: 'That without which bodies could not exist, but itself continuing to exist when bodies cease to exist".

305
Space possesses magnitude or extension, though it is itself not a body for "in case it were a body then two bodies would exist in the same place" (Aristotle, Physics, Book IV). Colours looked at in the light of Sir Russell Brain's recent words would themselves be within the skull rather than in the object.

Putting this fact together with the structure of the colour-solid - with a vectorial psycho-physics to support it, and understood as having dimensions which schematically represent tendencies in consciousness treated topologically - we have arrived for our purposes at a rough idea of a unit-integrated norm of thought-elements. In order that the full implications of the structure of thought revealed by this analogy may be clear, we are reproducing it below with a full discussion of its possible grades of meaning. By the method of intrapolation and extrapolation we are expected to carry the pure schematic content revealed here to other departments of thought, with the confidence that not only is this method non-arbitrary and justified, but that it could claim to have that degree of apodictic or actual certitude which, as we said, is the criterion of science in general.
   
In passing it might be permitted to note here the slight difference that exists between this and the idea postulated by Ludwig Wittgenstein in his "Tractatus Logico-Philosophicus". (43) The following is characteristic of his normative notion of logical space:

"1°13       The facts in logical space are the world.
 2°01231  In order to know an object, I must know not its
                external but its internal qualities.
 2°0232    Roughly speaking, objects are colourless."

The logico-philosophic world of Wittgenstein, like the Monad of Leibniz, suffers from a slight accentuation of the vertical as opposed to horizontal aspect of the global totality of reality with which a scientific language has to cope with. Colour is not to be excluded by us from our world of scientific language - for otherwise it should become suitable merely for equations.

306 
INTEGRATED NORM OF THOUGHT VIEWED SCHEMATICALLY
At this stage we are almost in a position to outline some of the more important ideas of this study, ideas which we were unable to clarify at the beginning. We used the expressions 'proto-language' and 'meta-language' and said that these have to come together to result in a 'scientific language' of universal understandability, utility and validity. We have also used the expression 'normalisation' and 're-normalisation', which require to be clarified. These three types of language and the important concept of normalisation have to be conceived in terms of a normative notion which must be sufficiently easy for the human mind to grasp intellectually.

What is more, it must have the advantage of easy communicability, whether through speech or writing. It has to be proof against the gradual encroachment of vernacularisms or patois which may be called broad, low or parochial. It must have an innate stability, depending on its  intrinsic character. The very validity of the normative notion must be its recommendation, and the spread and acceptance of this norm must not call for any movement to propagate it, as with closed religious groups. Its open scientific status  must be the basis of whatever utility or interest it might have.

As its soundness shows itself, it must get a reputation depending on its own merits, private or public. To have all these conditions fulfilled naturally it is best that it agree with nature, both human and what belongs to the environment.
Physics and psychology, as Bertrand Russell (44) said, have been approaching from both sides to meet in what he called 'neutral monism'. This process of mutual rapprochement of two natural aspects of human thinking, as represented respectively by what we call physics and metaphysics, if it has been taking place, must be intelligently promoted  until these aspects of thought fuse into a normative basis, both physical and metaphysical. Mind and matter, spirit and body, physics and psychology, geometry and algebra - and many other pairs of words - refer to the same schematically-understandable aspects of human thinking. In the world of science we have already referred to them tentatively as the observables and the calculables. The distinction itself is a vertical rather than a horizontal one, to use here in advance the terminology we are still in the process of justifying. Language itself can emerge only where it could be meaningful.

307
If observables refer backwards to an archetypal pattern of language within the mind of man, naturally resembling geometry - as Pascal and Bergson (45), not to speak of Descartes and later Cartesians have intuitively known and have pointed out in their writings - the calculables would also be symbolic in the sense that algebra is. Algebra by its symbolism refers to the Platonic world of the intelligibles, which are like numbers as opposed to quantity. It may be said to be a language that refers forwards and upwards to abstraction of ideas. Symbolic logic, which depends on algebra, has already been named a meta-language. By this very token it is that we have here referred to the other anterior aspect of the structure of linguistic thought as referring to a proto-language. We have to visualize the whole matter schematically in order to follow the stages by which we could pass on from what we have called the normalisation of scientific thought to what we are going to clarify as the re-normalisation of the same.

THE COLOUR-SOLID OF PSYCHO-PHYSICS AS MODEL OF PROTO-LANGUAGE
The blue of the sky, the mirage, the sky-blossom and the gleaming sky-reflection of the mirage surface, have been used by Sanskrit philosophers in speaking of the phenomenal aspect of reality as superimposed as a passing show or appearance hiding the reality which is behind. Without lapsing into oriental contemplative ways of philosophising or promoting wisdom through mere a priori solipsism, pantheism or syncretism, we could in a very matter-of-fact sense still assert with justice here that the colour-solid could be availed of, as a model at least, for representing in tangible form what we have called the proto-linguistic pattern of archetypal thinking.
    
If the question is put: 'What is colour?', it could be answered in different languages in the same tongue:

1)
We could say, as the dictionary first puts it: "the red of  blood, the blue of the sky, the green of grass are colours". Here definition is by mere arbitrary juxtaposition of name and form or colour-aspects and nothing more. The helplessness of the lexicographer is evident. Ordinary expression in any tongue has to have this form for the sake of the apodictic certitude of the resulting knowledge, and no one says 'prove it!'.

308
2 )
The second definition of the term goes further than just juxtaposing the observable or the nameable, thinkable or calculable, which are, in principle, the same as that number which Pythagoras said was the secret of the universe.
We have distinguished it as the vertical. When the vertical aspect of language is admitted into the meaning, a second degree of certitude results which is not derived from the horizontal axis of reference but from the vertical.  2 + 2 = 4 is an apodictic certitude that the normal human child learns and accepts quickly. As Piaget would say,

  "Seriation and classification spatially and in time
  are simultaneous operations the child is capable of through
  stages of its mental development".(46)
 
In a higher stage of the education of the child it will be able to grasp the second dictionary meaning of "what is colour?". This time it will be put, as in Webster's New International Dictionary under 'second meaning', as follows:

    "A sensation evoked as a specific response to stimulation
     of the eye and its attached nervous mechanisms by radiant
     energy of certain wavelengths and intensities."
 
We have already here two grades of language: one of the first-degree common-sense language belonging to what Carnap would call the "protocol language" level, and another which a secondary schoolboy is taught to understand in the classroom. Both of them are scientific.In fact the common-sense language, being the result of the closest union of the observables and the calculables, is valid without the intervention of syllogisms or pointer readings, which only make scientific knowledge less apodictic or certain.

The second meaning in the dictionary under the word 'colour' is less scientific in one sense and more scientific in the other. The common vernacular is easily understood by the closed group which pertains to the vernacular tongue and the certitude has that horizontal quality in which the thought moves between very real or certain factors, whether actual or virtual. In the statement 'the sky is red' the word 'sky' is an observable and 'red' is a name and thus of a conceptual order to be counted as belonging to the calculables. The mental status of the colour-sensation, which is becoming

309
more confirmed, as we have seen from the findings of Sir Russell Brain above, justifies our assigning a virtual status to it which could be described as eidetic in the terminology of Rorschach's psychology. Colour-vision has its cause within the skull and not in the object outside; but the name by which a certain colour is recognised through ordinary language in any vernacular belongs to the metaphysical context rather than the physical one. A concomitant correlation between two postulated points on the positive and the negative sides of the horizontal axis would thus characterise the nature of the common-sense language. In the terminology developed in the Carnap school (47) this would correspond to the axis in
which the pragmatic 'handling action' language (48), the semiotic dimension of 'thing-language', and the 'protocol language' may be said to move. We shall be considering these terms presently in their proper contexts. For the present it would suffice to recognize that within the amplitude of actuality and virtuality which the mind is capable of in its alternating perceptual or conceptual activity there is always a concomitant variation as between points that we could mark in the positive limb of the horizontal and its own negativelimb.
    
The second meaning is removed from the 'protocol language' by its participating in less actual and more calculable aspects of knowledge, which function simultaneously to create the phenomenon of meaning in consciousness. Since the vibrations that correspond to colour and sensations are both physical facts - one treated perceptually and not actually, and the other treated conceptually and not virtually - we have to select the points of concomitant variation involved here very cautiously, without violating methodological, epistemological or axiological factors which enter into the consideration of the particular language that science might employ systematically for some utilitarian or idealistic end - to which the science is said correctly to belong. The  person responsible for the discovery of the relation between  vibrations and colour may also have to be taken into consideration for determining precisely the points of concomitant variations, agreements, differences or both, that may belong to the four limbs of the vertico-horizontal frame

310                          
of reference that we have outlined. Experts of the department of knowledge concerned might have to have their say, to be finalized by an expert committee which understands what normalisation means. One thing can be said at once. While in the first common-sense meaning the two points were located apart in the total range of the amplitude, here they have to be brought together. If the knowledge is for merely serving curiosity about colours, the branch of science is to be placed neutrally, and instinctive dispositions involved in curiosity and its intellectual counterpart have to determine where two other points have to be placed in the vertical axis. Instincts are retrospective in reference and therefore negative; while the interests of scientific progress involved must find a degree marked on the positive side of the vertical axis. The relational picture involved here is quite different from that of the actual and virtual colours that were placed on the horizontal axis to begin with. The mystical joy, if any, involved in the first meaning must also be marked, if necessary on the vertical axis, to the extent that it is considered positive or negative in tone. The second case being relationally of another epistemological context, the curiosity satisfied is a more scientific one. Any number of other fractional or multiplied dimensions, qualitative or quantitative, could be added to analyse the proto-linguistic implications.

NORMALISATION OF SCIENTIFIC LANGUAGE
Out of the two ways of giving meaning to the question 'What is colour?' we have so far discussed two varieties: one conforming to common-sense requirements, and the other with a more scientific purpose. The vertical component of the psycho-physical entity which gives us the satisfaction of knowing what colour is has been slightly accentuated in the second instance, when vibrations were equated with the name-symbols standing for the different colours of the spectrum. If a colour-manufacturer interested in actual colours and not in science for its own sake was thinking of vibrations with relation to colours, these two factors would have to be put in the horizontal axis. For a scientist in the class-room thinking of the subject for its pure knowledge-content,

311
a symbolic equation treating colour by letters in the abstract and vibration grades by number would bring them both into the vertical. When the relation is still of a hypothetical status, the vertical and horizontal may be put together tentatively in view of apodictic certitude, when it will be vertical, horizontal or both. What is positive-horizontal might have to be put on the negative side and primacy given to what appears otherwise. Normalisation thus has its rules derived from epistemology and methodology, with an axiological purpose as an over-all consideration. Symbolic logic can deal only with the verticalized aspects and can therefore have no utility except in the steps of mathematical inference involved. We shall be returning to this question later. All that we wish to stress at this stage is that normalisation is not easy and, as we have said already on page 280 above, promiscuous mixing-up of aspects in violation of the innate structure of thought makes the language absurd. If 'metaphysics is non-sense' we could retaliate and say pseudo-science tends to the point of
absurdity.

WHAT NORMALISATION CAN DO TO THE LANGUAGE OF SCIENCE
When the vertical and the horizontal aspects of language are juxtaposed, a certain system is put into language, and it gains an apodictic character without further demonstration or syllogistic steps of inference. No better example for this could ld be found than the case of the colour-solid. The colour-solid is able to circumvent the difficulties of vernacular confusions of tongues, and in one domain at least succeeds in creating the possibility of a standard universal language that is scientifically valid. From it we are able to derive the theoretical basis of a universal language for all sciences, if the integration of all branches of knowledge would be possible. The over-all integration of the whole range of sciences and philosophies could be undertaken with the same model of the structure of thought. In branches of study like sound, heat  or the sensation of taste we could adopt the same model so that the monadic units and the monad-of-monads unit, conceived on an absolute basis, could all adhere and organically cling together.

312                           
The rough possibility of a language for unified science based on a scheme of integration for each minute branch of science, each having the same proto-linguistic elements as the over-all scheme, thus comes into view.

HOW TO ADAPT THE STRUCTURE OF COLOURS TO LINGUISTIC PURPOSES
Again let us put to ourselves the question 'What is colour?' A complete scientific answer is found in the second half of its second meaning as given in Webster's New International Dictionary (49), which fortunately gives us within as short a span as possible the full psycho-physical and categorical implications. We shall take the liberty of extracting from it here while expressing our gratitude to the author of the same:

    "Colour may be regarded as a psychological category;
    it can be described and specified in terms derivable
    from introspective analysis, without any reference
    whatever to wavelengths, to energy or to any physical
    category; but it is also possible to state the physical
    correlates of the psychologically-determined
    attributes of colour and to draw up some psycho-
    physical relations between them. All colours are
    divisible into two classes, the chromatic colours, as
    reds, greens, purples, browns and pinks, and the
    achromatic or neutral colours, including black, white
    and the intermediate series of greys. The latter are
    found to differ from each other only in their degree of
    resemblance to, or difference from black (or white),
    and with each other grey differing from its intermediate
    neighbours by an equal sense of differences."

This series can be made into a scale by assigning an ordinal number to each grey, either ascending towards the lighter greys from black as zero; or ascending with positive numbers and descending with negative numbers from median grey as zero. That attribute which thus measures the variation of the
greys is called brilliance: dark greys have low; median grey has medium; and light greys have high brilliance.
 
313
Chromatic colours differ from each other not only in brilliance, but also in hue and saturation. Hue is that attribute in respect to which colours may be described as red, yellow, green or blue, or as intermediate between two of these. Hues form a natural cyclic series (hue cycle, colour cycle or colour gamut). Colours of the same hue and equal brilliance may differ from each other in saturation, that is, in vividness of hue or in degree of difference from grey.

In terms of these three attributes, colours may be arranged in a symbolic tri-dimensional space (the colour-solid) having the grey series as axis, with median grey at the centre and black and white at the extremities; (fig. 18.1).

Corresponding to each grey is a plane perpendicular to the axis, in which lie the points representing all colours of equal brilliance. In each plane hue is represented cyclically in the order of the hue cycle; and saturation is represented radially with the axial points (greys) as reference points of zero saturation. Thus any colour can be specified by giving three ordinal numbers (colour constants or dimensions) which are coordinates of the corresponding point in the colour-solid.
 
By establishing arbitrary division points on the scales of brilliance and saturation, any colour can be described as having very low, low, medium high or very high position in these scales.
 
By establishing arbitrary division points on the hue cycle, hues can be classified as e.g. yellowish-red, reddish-red-yellow, red-yellow, etc.

All principal definitions in this dictionary are in introspective terms like the following: "bay: a colour red-yellow in hue, of low saturation and of low brilliance"; "carmine: a colour red in hue, of high saturation and low brilliance".

We can see here that hue is a factor that could be correlated to the horizontal axis of the scheme we have been developing in this part and that brilliance belongs to the vertical axis.

Saturation is a third radial reference depending on the degree of centralisation. This last could be described as representing the combinatorial mode in terms of thought, while the other two dimensions determine the two main categories into which characteristics of thought could exist negatively or positively in the schematic linguistic space of human consciousness.
A normative proto-linguistic basis for the correlation of thought-characteristics and modes of combination has been outlined on an experimental basis so far, and now we pass on to the re-normalisation of meta-linguistic aspects in the next section of the study.

314

STRUCTURE Fig. 18.1: Figure of colour-solid treated as a non-arbitrary basis for thought integration.(50)
      

SECTION III : THEORETICAL CONSIDERATIONS
 
As we are leaving behind with the previous section our discussion of a language for unified science from a strictly experimental point of view; on commencing the present one, which relies on purer linguistics, logic, mathematics and more philosophical or metaphysical aspects of reality - it becomes necessary to preface it with certain preliminary remarks of methodological, epistemological and axiological import. Scientific validity depends on the apodictic certitude resulting from a methodic treatment of items of knowledge which have sufficient significance in human life. Far-off ends and means, dualistically conceived, would be less scientific to the extent that the verity in question is not certain. Too many indirect pointer-readings of observables, and too many steps of inference intervening in calculables, detract to that extent from the degree of certitude of scientific findings.

315
As we are here concerned not merely with scientific certitude, but also with the languag