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"Nature, by an absolute and uncontrollable necessity, has determined us to judge as well as to breathe and feel." "All our reasonings concerning causes and effects are derived from nothing but custom, and belief is more properly an act of the sensitive, than of the cogitative part of our nature."
"If we believe that water refreshes, and fire burns, 'tis because it costs us too much pains to think otherwise."
David Hume - A Treatise of Human Nature
These conclusions, the fruits of some of the most lucid and cogent reasoning in the whole of philosophy, appear to have been so unpalatable to their author that he resorted to the desperate policy of deliberately ignoring them. Later philosophers have been equally unable to accept them, although likewise unable to produce any convincing refutation of the reasoning which led to them.
To the best of my knowledge, nobody has ever seriously considered accepting Hume's conclusions and using them as the foundation for a coherent philosophy; this is what the present book sets out to accomplish.
No empiricist ought to have any objection to starting from the initially solipsist position which this involves; after all, every new-born infant inevitably starts life as a solipsist, and its experience, at the outset, consists of virtually nothing but visceral and tactile sensations. Nevertheless, in spite of this unpromising beginning,we all, as Hume himself emphasises, build up a picture of an external world which seems to be intelligible and provides us with satisfactory guidance for our activities.
The only faculty available for the purpose is the obligatory one of judgment. We take it for granted that the likes and dislikes of all new-born infants will be predictably the same. In this book I show that this initial identity of judgment, or æsthetic, is a necessary and sufficient hypothesis to account for the possibility of communication by word and symbol. This in turn makes possible the accumulation of a body of "public" knowledge, expressed in words and symbols. The concept of "truth" can hardly arise until this has been achieved.
Nevertheless, public knowledge is not the knowledge of "facts" lying outside experience. We all believe that such facts exist, even if they are no more than events in someone else's experience, but they are not knowable. Any conjectures that we make as to their nature, or as to the nature of processes linking them, can only be analogies based on events and processes with which we are directly acquainted.
These consist entirely of feelings - including memory, which, like feeling, comes unbidden - judgment, which follows necessarily upon feeling, and effort, a different kind of feelng, which follows necessarily upon judgment. This is our prototype of a causal sequence, and in postulating causal connections between the supposed external sources of our feelings, we are simply drawing an analogy from our own experience. Our habits spring from our judgments; persistent habits in the 'physical' world presumably spring from the operation of some kind of judgment there.
Linguistic communication depends on the presence of certain persistent elements of feeling which are common to the communicants, and which they judge in the same way; communication is only successful if the importance of these elements of feeling is identical for all of them. This result is vital, since it disposes of the notion that there can be any "truth", expressible in words or symbols, which lies outside experience and is independent of human judgment. This abominable superstition has plagued mankind ever since Plato's time. It teaches that words and symbols can somehow express "truths" which lie outside experience, and which are frequently referred to a 'divine' origin. In consequence, large sections of the human race are still engaged in killing one another in support of their own 'sacred' dogmas, derived from their different 'holy' books - or, perhaps even more frequently, from divergent interpretations of the same one.
Words and symbols have no intrinsic value whatsoever. They should be our useful and obedient servants, but we, by attaching quasi-magical values to them, have turned them into merciless and tyrannical masters.
There can be no truth that is independent of human judgment, and therefore no 'absolute' truth at all, except for certain unanimously accepted conventions internal to language and symbol-systems, and these are obviously not 'eternal'.
The general acceptance of mathematical and scientific truths, which provides a striking contrast to the state of affairs in metaphysics and religion, is due to the circumstance that they have their roots in early, pre-verbal experience, where there is a lowest denominator of judgment which is common to all mankind.
The "basic statements" descriptive of the experiments used to test a scientific hypothesis consist entirely of words and numbers which can be ostensively defined with the assurance that this will result in their uniform interpretation. Any hypothesis which cannot be tested in this way is metaphysical; it can only be "true" for that limited and indefinite sector of mankind which interprets the words in the same sense as their author.
Logical methods are also derived from certain relations and operations, to which importance is universally attached, in this primitive field of identical judgment. Nevertheless, dogmatism is out of place even here; there is no certainty, in mathematics or logic, that all practitioners are interpreting their symbol-patterns in exactly the same way, especially in the higher branches of the subject.
The more subtle the matter to be communicated, the less likelihood there will be of a uniform interpretation of the symbols, and the fewer there will be who claim to understand the language. Seeing that the value of "truth" depends on its quasi-universality, it is clear that the concept is barely applicable to attempts to communicate the higher subtleties of experience. Its applicability, however, decreases gradually, pari passu with the increase in subtlety of the material communicated.
This is where Kant's answer to Hume is unsatisfactory. He realised that the extreme subjectivism demanded by an empiricist philosophy might be made acceptably by postulating a common mode of judgment in all mankind - the 'Transcendental Aesthetic', which obliged us all to adopt the same spatio-temporal type of 'Anschauung' and the same categorical methods of reasoning. He was, however, unable to conceive of its operation beyond the realm of what he regarded as "absolute" truth, which included Euclidean geometry and Newtonian physics. He himself regarded the 'Critique of Pure Reason' as an answer to the question 'How, in the light of Hume's conclusions, are mathematics and physics possible?'
Since he regarded these "truths" as absolute within the sphere of phenomena, he had to consider them as independent of 'Practical Reason', i.e., the normal operation of the judgment. We now know that they are nothing of the kind, although our judgment generally leads us to prefer them to any possible alternative; thus we no longer share his need to divorce the "cogitative" and "sensitive" sides of human nature.
By asking the question "How is language possible?" I have, I hope, succeeded in showing that all "truth" is dependent on community of judgment. This is very nearly absolute in early childhood, and the habits of thought that we form at that stage and mostly retain, because of their customary utility, throughout our lives,1 constitute Kant's 'Transcendental Aesthetic'.
1. Is there any better reason for retaining a belief than that it "costs us too much pains to think otherwise"?
But the Aesthetic does not remain at this primitive level. It is a living thing, endowed with a natural tendency to development, especially in sensitivity. Assuming, however, that we all start level - perhaps at conception rather than at birth - the extent and nature of that development must be entirely conditioned by our environment, of which our bodies form persistent and extremely important elements.
What we normally think of as our 'æsthetic' faculty is the developed, possibly even 'evolved' form of the primitive 'transcendental' variety with which we started life. The determinism attributed by Kant to our 'pure' reasoning in the realm of phenomena is extended over the whole range of judgment, but is by no means the strait-jacket that Kant considered it to be. The developmental tendencies of the æsthetic may be the same for all mankind, but the nature and extent of its development in each individual will be entirely dependent upon the environment. Our behaviour, in turn, is completely dependent on this æsthetic, which represents the necessity of our own nature.
This conclusion involves a complete re-examination of ethics. Since all behaviour is regarded as determined - although not predetermined and, therefore, not entirely predictable - the concept of moral responsibility has to be discarded. We can still praise or deprecate behaviour, but cannot maintain that it deserves reward or punishment. It is simply an indication of the stage of ethical-æsthetic development that its perpetrator has attained. This, in turn, is entirely attributable to his past environment, which can only be regarded as initially a matter of pure luck. We are all familiar with the saying 'There, but for the grace of God, go I'. Substitute 'the luck of the draw' for 'the grace of God', and we have a concise expression of the ethical position advocated here, without any substantial alteration in the meaning of the saying.
I am completely in accord with the modern tendency to explain all behaviour-differences in terms of past and present environmental influences, provided that the body, with its genetic factors, is included as a necessary part of the environment which is not capable of radical modification.2
2. I may add that my ethical views have been strongly reinforced by ten years' experience as housemaster in a boys' comprehensive school.
This book consists of four essays. The first two are concerned with the transition from direct experience to word and symbol, and vice versâ. There is some repetition of material, but the first is mainly concerned with persistence, the second with common importance; these are the two conditions needed to ensure the success of the key process of ostensive definition.
The third essay deals briefly with causation and probability, and the fourth with the ethical system appropriate to an æsthetic determinism. This has obvious and far-reaching implications for sociology, which I hope to follow up later.
Editor's note: Nothing in the remaining content of J.D. Solomon's surviving papers that has so far come to light enables me to specify which four essays our author is here alluding to. Any relevant new 'find' will be communicated.
Introduction
The linguistic school of philosophy which is undoubtedly the most fashionable in England at the present time, holds that philosophical problems - by which I mean lines of thought which have gained general acceptance but which, when followed to their logical conclusion, lead to paradoxical inconsistencies which destroy their own foundations - result entirely from the uncritical use of language and can, therefore, be shown to be pseudo-problems and dissolved by the methods of linguistic analysis.
In many instances this is undoubtedly the case; nevertheless, I hope to show in the present essay that important sources of such problems - which naturally become linguistic when expressed in language - are to be found in the pre-verbal stages of thought and concept-formation.
It is generally agreed that our earliest language is what Russell1 has called the Object Language, which consists entirely of words representing concepts which can be ostensively defined. Ostensive definition is, in fact, the bridge between what is said and what can only be shown; nevertheless, in spite of its critical importance in this respect, it has generally been taken for granted and never, as far as I am aware, submitted to critical examination.
1. An Inquiry into Meaning and Truth, Ch.4. I do not entirely agree with his delimitation of this language, as will appear later.
In this essay I propose to examine the assumptions underlying our belief in the validity of the method itself. I believe that this examination can throw a good deal of light on the formation of pre-verbal concepts and on just what happens when they are replaced by words.
I begin with a simple and typical example of an early stage of the process, casting myself in the rôle of teacher.
I suppose myself to be pointing to a plain white cup (the reason for stipulating plainness and whiteness will soon be apparent) standing by itself on a table. Having ascertained that my pupil's gaze is directed towards the complex of my hand and the cup, I utter the sound 'cup', maybe repeating it once or twice.
Provided that my pupil has normal intelligence and vocal organs and is familiar with cups, I can be reasonably confident that the procedure will suffice to achieve my intentions.
The assumptions needed in order to justify my confidence appear to be as follows:-
The first two of these assumptions concern the conceptual construction of public space, and I will leave them aside for the present. The third, however, is absolutely fundamental.
For why should the child attach importance to the mere image of a plain white object, quite devoid of any æsthetic merit? No image can exert any causal influence on its beholder, apart from an æsthetic reaction of some kind or other.
The only possible answer to this question, and, indeed, the obvious one, is that the image is already familiar to the child as a sign for something else that is of intrinsic importance.
Following Peirce, I propose to regard the first recognition of a sign-situation as the beginning of conceptual thought, which, though naturally incapable of explicit expression at that stage, appears to be clearly present even in animal inference.
What is a Sign?
The following definition is a rather tight one which covers the uses of the word as applied to animal and infantile thought, but excludes part of the range of meaning included in its colloquial use.
"An observed sense-Gestalt become a sign when the observer takes it to indicate the possibility that if a certain familiar process occurs, another sense-Gestalt of expected type will appear. This latter will be the interpretant of the sign".
This definition rules out the retrospective use of the word, e.g., "there were signs of a struggle". In such cases it can be satisfactorily and more accurately replaced by 'trace' or 'evidence', both of which imply retrospection.2
2. Peirce's 'indices' are only to be regarded as signs when their interpretants, i.e. their presumed causes, are persistent.
The necessity for the intervention of a process between a sign and its interpretant, though obvious enough when you consider it, does not seem to have been generally realised. It is of great importance, because it implies that a word, taken out of context, is never a sign, since it cannot indicate any process which would lead to an interpretant sensum. It can conjure up a memory, but this is far too vague to serve as a satisfactory interpretant.
Used as an exclamation, ostensively, or as a label, an object word, as Russell observed,3 does become a sign; but this significance is not inherent in the word itself. It is the context which points to the process needed to arrive at an interpretant and turns what appears to be a single word into a proposition which can represent a sign-situation.4
3. Loc.cit., Ch.1.
4. Similar considerations apply to all signs classified as 'symbols' by Peirce. The confusion of signs and symbols is the root-cause of most human superstition.
The degree of possibility indicated by a sign can vary from slight to near-certainty. Take our road-signs, for instance. "Falling Rocks" and "School-children" will only occasionally provide interpretants, but "Road Narrows" or "Sharp Curves" will almost certainly do so, provided that the expected process occurs, namely, the continued progress of the car without any marked change of direction.
The immediate interpretant of these signs will itself be a visual image, of no intrinsic importance. This will, however, serve as a second-order sign for the possibility of an intrinsically important interpretant, namely an undesirable impact, should the process continue as before.
Some such SEMINAL INTERPRETANT is always needed to provide the motivation for the construction of any sign-system.
Peirce considerd that the seminal interpretant of a sign-system must be an object, but this, I think, is a mistake. Any sensum will serve, provided only that it is intrinsically pleasant or unpleasant enough to be of importance to the observer.
Objectivity or, as Price calls it, perceptual assurance,5 can, however, be defined as follows in terms of signs:-
5. Perception, Ch. VII et. seq.
The senses concerned are usually those of sight and touch. For example, if I look at a table, its image is a sign that if I move towards it (process) I shall contact it (interpretant). On the other hand, if I bump up against it in the dark, this is a sign that if a lamp is lit (process) I shall see it (interpretant). Its objectivity is assured when I see and feel it at the same time.
Perceptual assurance needs corroboration from every sense that is thought to be able to provide it, and is weakened whenever an expected interpretant is missing. For example, if I rap on the table with my knuckles, but fail to hear the sound, I shall be just a bit doubtful about the objectivity of the occurrence, which would become a little dream-like.
Perceptual assurance of a degree which merits the title of 'objectivity' is obtained by corroboration alone. Descartes' criterion of clarity and distinctness is not enough, although, as we shall see presently, clear and distinct images are of such importance as signs that they tend to compel perceptual acceptance, which is somewhat weaker.
Sign-Formation in Infancy
We will now consider the development of pre-verbal sign-systems. Since direct verbal information on the subject is obviously unavailable, we will have to rely on infant behaviour and on the inferences drawn from it and universally accepted by mothers and others responsible for looking after babies.
Two basic inferences are actually sufficient. They are as follows:-
Thus an infant's cry is a sign for the mother, having the alleviation of the assumed distress condition as its seminal interpretant. A variety of processes and intermediate interpretants may intervene, such as feeding, changing nappies, etc. etc., the process chosen being always designed to remedy what the mother herself would regard as a distress condition if she were in the baby's place. The discomforts are almost all visceral or tactile - a loud bang is the only exception which comes to mind - so that it is practically certain that the first seminal interpretants motivating the formation of a sign-system by the infant will be of this kind.
What appears to happen is that the baby recognises a certain complicated visual Gestalt - the image of Mummy or, significantly, of anybody who looks sufficiently like Mummy - as an integral part of every conscious episode. The appearance of this Gestalt is usually followed by the alleviation of the discomfort with which most conscious episodes begin in infancy, so that the image becomes a sign, with the relief from discomfort as its seminal interpretant. It is natural that the first pleasure-behaviour - the smile of recognition - should accompany this discovery of significance, which probably constitutes the beginning of conceptual thought.
The unpleasant nature of the start of most episodes of infantile consciousness, beginning with the slap administered at birth in order to set the baby crying - and therefore breathing - is of great importance. It ensures that the seminal interpretants giving rise to the earliest sign-systems are all, or nearly all, favourable, since the unpleasant beginnings of consciousness are never heralded by warning signs. An accident such as an over-hot bath may occasionally turn the image of the bath into a warning sign, but normally such signs do not develop until the baby becomes mobile, when they become common.
The favourable nature of most early seminal interpretants carries with it the corollary that most early disappointments are unpleasant; this has an important bearing on the fact that the general affective tone associated with negation is pejorative. We shall return to this point later on in this essay.
At this stage the baby also begins to realise that it can create signs. It may well arrive at the successful conjecture that its crying is a sign for maternal attention whether or not it is actually associated with a condition of physical distress. Once this has occurred, the original maternal assumption ceases to be valid, although most mothers will continue to act upon it on humanitarian grounds (Cf. Wittgenstein:- "my eyes are shut").
With mobility comes the ability to grasp and push; sign-sequences associated with these activities are the obvious origins of causal notions. Indeed, the rooted objection of the physicists to any suggestion of "action at a distance" would be senseless unless their basic notions of causation rested on that of forcible contact between adjacent objects.
The importance of solid objects and, to a lesser extent, of fluids, now becomes paramount, and this leads to the development of the most important and general sign-hypothesis employed by sighted human beings. It can be stated as follows:-
This conjecture is not felt to imply any causal relation. It remains the main guide throughout the whole of our lives for all action involving bodily movement. It is not completely reliable; a patch of sky viewed through a window frame is an obvious exception, which an infant soon grasps. Others such as mirages and hallucinations are discovered much later.
"Bodily motion in the direction of the image" is objective, since there is mutual significance between the increasing size of the image and the sense of forward bodily movement - the kinæsthetic sense, which has its sense-organ in the semicircular canals of the ear. Most philosophers have ignored this sense, which is the original source of our spatial 'intuitions'. Without it, it is clear that blind people would be completely unable to develop any sense of perceptual assurance.
Once the significance of visual images is grasped, their sign-function becomes overwhelmingly dominant. They provide a great abundance of detail; much of this, colour in particular, has little or no significant value, but becomes an object of interest and importance in its own right.
This has led to great confusion of thought, since our memories of objects have tended to become dominantly visual, so that the image, in thought and in word, has come to stand for the object of which it is no more than one constituent sign.
The result is a strong tendency to assume that an image - or even its verbal description - must be a sign for a corresponding object. To take a rather notorious example, it makes sense, when confronted with the appropriate picture, to say "That is a golden mountain".
Most erudite argument concerning the existential status of golden mountains has arisen from this kind of procedure. It can all be summarily dismissed provided that we insist that "existence" in the case of entities denoted by concrete nouns, must include objectivity, and therefore the mutual significance of data from more than one sense. In the case of the picture, the tactile interpretant of the image will be the feel of the paper on which it is drawn; this will certainly not have a "mountainous" image as its visual interpretant.
If a golden mountain existed, the visual shape serving as the interpretant of a tactile-kinæsthetic "mountainous" quality would be golden, and, simultaneously, the tactile-kinæsthetic interpretant of the golden shape would be "mountainous".
It cannot be too strongly emphasised that images, like words, are not signs for the objects they purport to depict. They only assume that status where the context provides a clear indication of some process which would yield that type of interpretant. Failure to realise this point has led to vast quantities both of superstition and of philosophical nonsense.
Images, of course, become important in their own right and can serve as seminal interpretants as soon as a visual æsthetic has developed.
Before returning to the actual process of ostensive definition, I will briefly sum up the foregoing discussion on sign-systems. Here are the main points:-
'Meaning' as Established by Ostensive Definition
We can now return to our original example of the plain white cup standing by itself on a table.
The image will certainly be regarded by the child as a sign of an object, but neither the image nor the tactile interpretant will have much intrinsic importance for the child. The implied object has, however, an important sign-function, since it indicates the possibility of a drink. This is the seminal interpretant which renders the image meaningful.
This example illustrates what seems to me to be a fundamental principle, which can be stated as follows:-
Looking around the room, with its table, chairs, desk, walls, carpet, etc., this seems to be a glimpse of the obvious. There are, however, many apparent exceptions to the principle, which arise from three main sources:-
Firstly, the necessity for referring to objects with nothing but their 'objective' character which is of any interest or importance.
Secondly, the abundance of objects whose importance is mainly or entirely visual; in this case their appearance is their function.
Thirdly, the slovenliness of ordinary language, which renders it incapable of accurate reference.
I will deal with these in turn.
Every clearly bounded visual sensum is interpreted as a sign for an object. Now 'being an object' is itself a function - we may call it "minimum function" - in that objects always constitute impediments to movement and may sometimes be manipulable. Every object, therefore, is a potential source of a seminal interpretant.
If it has no other function of importance, we can only denote it by words standing for its size, shape and weight, which will determine the manner in which it fulfils this minimum function. All these are adjectival qualities applicable to the signs for the object, which is itself taken for granted. This fact tends to be overlooked, and shape-words especially tend to assume the status of substantives.
Thus 'Pyramids' are really pyramidal objects. It should be obvious that the ostensive definition of shape would be impossible without shaped objects. If, however, the object has a familiar function, this will take precedence over shape as the meaning of an ostensive definition. For instance, if the words "sphere" and "cube" were used for the initial ostensive definition of a ball and brick respectively to a child familiar with them as playthings, "sphere" would denote "something used in throwing-games" and "brick" "something used in building-games".
An aboriginal child would stand a better chance of interpreting these words "correctly", since the shape of the objects would for him be the most important thing about them; as they are highly symmetrical, they might be striking enough, from the point of view of visual æsthetic, to be memorable.
The shape, size and inertial qualities of an object are themselves 'objective' in character, since sight, touch and the kinæsthetic sense provide mutually significant sensa regarding them; the feeling of effort is also involved in the case of inertial qualities. The indications provided by sight are far more detailed and accurate than those provided by the other senses.
Let us now consider objects whose useful function is purely decorative. In this case there is no sign-situation, since the image itself would also be the seminal interpretant.
Even these are objects, and their objectivity is important when it comes to handling them; but for most of the time they are there to be looked at, so that their non-visual properties play little or no part in their denotation, which is confined to their visual appearance. Where a picture counterfeits the visual appearance of objects, it is usual to name it after the objects counterfeited; the pretence is frequently indicated by the use of inverted commas, e.g. "Mona Lisa".
This precaution is generally omitted when ordinary objects are used for decorative purposes as, for example, in the case of cut flowers. This omission leads directly to loose thinking, as is shown by the admissibility of questions like "Are those flowers real?". This question yields, on analysis, "Have those 'flowers' (i.e. flower-like objects) ever fulfilled the (botanical) function of flowers as defined in the dictionary?"
It is in this type of context that ordinary language is seriously inaccurate. For example, an object should certainly not be denoted as an automobile unless it is auto-mobile, yet we happily perpetrate statements like 'This automobile won't go'. What we are actually denoting are the visual and tactile signs for an automobile, which in the present instance have proved misleading, since the appropriate processes have failed to yield the expected interpretant, so that the object is not at present an automobile!
I am not advocating any attempt at reform; it would be intolerably clumsy if we had to refer to a "quasi-automobile" or "automobile-like-object" every time that the plug-leads were damp! It is not even language that is basically at fault here; it simply reflects the tendency, established well before speech begins, of taking interpretants for granted, and jumping directly from the image-sign to the indicated object-function.
Our linguistic habits serve to reinforce this tendency, completely concealing the two stages of inference - from image to object, and from object to function - which are actually involved.
The denotation provided by an ostensive definition can generally be determined by consideration of the answer which would be expected to the question "what is that?"
The answer, according to the prevailing circumstances, will be either a name or a function, or both; the choice will depend on what is thought to be most interesting and important to the questioner. It is always an object which is denoted; the inference from image to object is assumed to be veridical.
If the object has only minimum function, as defined above, and no readily denotable shape, we will have to reply "I don't know", although the material of which it appears to be made may give a useful indication of its inertial qualities, leading to answers such as "a lump of stone".
If the function of the object is decorative, we may denote it, and reply "a picture", "a statue", etc. This is generally obvious, so that the question is really a request for the appropriate name, and perhaps also for that of the artist; the latter, from the point of view of interest, may be considered functional.
If the function of the object is thought to be unknown to the questioner, it will certainly be assumed to be the denotation required. The name alone would be quite useless, although if the responder knows it but is ignorant of the function he may give it, probably adding "I don't know what it is for".
A sensible answer to such a question will always atempt to fill any important gaps in the questioner's knowledge. For example, "what is that crop?" requires not only a name, but some account of the nature and use of the product, supplementing the "crop" function which is already known.
If the function of the object is believed to be well known by the questioner, the question will be simply a request for its name. It would be more accurately replaced by "What is that called?" This is the normal procedure in learning languages by the 'direct' method, and is clearly also the one that children use in learning their mother-tongue.
Ostensive definitions rarely include words describing sense-perceptions; visual descriptions would obviously be redundant, and such descriptive words as do occur denote qualities essential to the functioning of the object, as for example the "hard shoulder" of a motorway.
Descriptive adjectives in fact qualify the sign-sensa by means of which we recognise objects; but the objects are identified and named on account of their functional importance. This is why it is a mistake to regard an object simply as a bundle of qualities. Its constituent signs can be analysed in this fashion, but the "essence" of an object, i.e. what is denoted by its name, is its functional importance. It is precisely this element which escapes the net of any analysis based on methods such as those of physical science.
Proper Names
Similar considerations are applicable to proper names. These are attached to more or less persistent objects which possess functional uniqueness in several important contexts. Such objects are regarded as intensional unit classes, and this status is certified by their possession of a proper name.
This procedure is quite arbitrary, and a proper name could be attached to any persistent object. For obvious reasons of economy, it is only employed in the case of objects which are likely to be functionally unique in a great many different contexts.
It is especially suitable to human beings, who receive their names as a birthright in view of their unique functional importance to their mothers, and retain them so long as their possession of vital characteristics endows them with the probability of functional uniqueness in a variety of situations.
The denotation of a proper name is indicated by the answers expected to the question "Who is that?"
The presence of a human being is already implied by this question. The answer, if not simply a name, will be a function or position, i.e. a context in which the person in question is functionally unique.
"Who's Who" is in fact a summary of the most important contexts in which the persons whose names are included have been functionally unique up to the time of compilation, beginning with their parentage and date and place of birth. It makes no attempt to describe them; its value might indeed be increased if every entry were accompanied by an up-to-date photograph.
This functional theory of names confirms and greatly simplifies the Theory of Descriptions. "Scott is the author of Waverley" simply identifies the unit class which obtained the name "Scott" as a birthright with the one which was unique in respect of writing "Waverley". "Is", in this context, is not the usual copula linking subject and predicate, but is the equivalent of "=" in a mathematical equation.
An arithmetical equation such as "5 + 1 = 3 × 2" states that there is a certain numerical class - at present unnamed - which is of unique functional importance in the two contexts described on either side of the equation. It is analogous to "The author of Kenilworth is the author of Waverley". The number 6 would here be the analogue of "Scott". This use of the word "is" is logically preferable to its normal employment as the copula, because it unites entities of similar type. The copula, on the other hand, is most commonly used to unite an object-word, denoting a function, with a description word denoting its appearance. What it actually asserts is the spatio-temporal compresence of the two.
Take, for example, a statement like "This book is red". If "book" denotes a function, as indeed it does, this statement is, in a way, nonsensical, since the book cannot be read 'redly' - unless, perhaps, 'red' is used in the contemporary sense of 'inciting to revolution'.6
6. "The Little Red Book" of Chairman Mao is red in all respects!
Most subject-predicate constructions are logically analogous to statements such as 'This flavour is yellow', or 'This colour is slow'.
What can be properly described as red is 'This book-like object'. Even this is perhaps a little doubtful, since shape and not colour is the visual quality which contributes to the 'objectivity' of the object. Still, as the shape is partly defined by the boundary of the coloured patch in the visual field, such usage is logically acceptable.
The somewhat ridiculous use of the copulative 'is' provides a further example of the way in which language exploits the 'right to be sure' that the image-sign indicates an object, and that the appearance of the object is a reliable indication of its function. Neither of these inferences is more than probable, but the assumption of their certainty is a virtual necessity whenever the circumstances are such as to call for immediate action.
There would be a good deal to be said for a measure of linguistic reform which provided a distinction between the copulative and identificatory uses of 'is'; in Spanish, this actually exists. The copula is 'esta', i.e. 'stands'; the spatio-temporal element is clearly implied by the use of this word. The identifying 'is' is replaced by 'es', which unites a name, or a description or ostensive identification replacing a name, with an important function.7 It would be very difficult, if not impossible, to formulate the Theory of Description in Spanish!
7. This includes such persistent elements of appearance as contribute to objectivity or minimum function. Thus, for example, Harold Wilson es an English politician; he also es a shortish, round-faced man; any object without these attributes could not be referred to the same unit-class.
Description and Descriptive Words
The primary use of indicative language is description, which is a substitute for ostensive definition, and which makes it possible to recognise interesting and important objects at times when their ostension is impossible.
In the majority of cases visual recognition is all that is required; in such cases a picture or a photograph is more efficient than any verbal description. This fact is emphatically demonstrated by the police practice of making an 'identikit' picture of wanted men from the verbal information received.
Where other forms of sense-perception are involved, however, there is no good substitute for ostension other than verbal description; this is also necessary to enable men to discuss sign-situations, and to co-operate in the attainment or avoidance of their seminal interpretants.
A verbal description adequate to ensure the recognition of the object described provides what Frege called a "Bedeutung" (deuten = to show). It only includes what he called "Sinne", i.e. instances of function, in so far as they are needed in order to provide an adequate "Bedeutung". In general, it is only spatio-temporal location, one of the elements constituting minimum function, which comes into question here.
Taking Frege's own illustration, the planet Venus, for our example, the "Bedeutung" might be "the brightest celestial source of light apart from the Sun and Moon", but we would probably add "frequently visible for some time after dawn and before dusk", i.e. the "Sinne" or functions, denoted by the earlier names "Morning Star" and "Evening Star", in order to facilitate recognition.
Similarly, the "Bedeutung" of "Scott", would have been an adequate description of a certain persistent (human) object, including his spatio-temporal co-ordinates for the sake of completeness. "Author of Waverley" is one of his "Sinne", but would not have been a necessary part of an adequate "Bedeutung". "Scott" denotes his original "Sinn" - the circumstances of his birth, which was the first instance of his functional importance.
Descriptive words, then, are entirely concerned with appearance - using the word in a general sense to cover all sense-perceptions. This is why it is possible to combine any descriptive word with almost any substantive function-word without producing a logical contradiction - although the result may be unserviceable nonsense. Exceptions arise only where one of the important functions of the object is the production of the sense-qualities involved in its appearance - as in the case of a purely decorative object. In this case the contradiction is between two descriptive words denoting qualities detected by the same sense or senses. For example "a spherical cube" really means "a spherical cubic object". The contradiction is between the adjectives. "A hot iceberg" would be contradictory if coldness was a necessary diagnostic property of an iceberg, but it is doubtful whether an Eskimo would agree that this is the case. Its temperature is not, in any case, a feature essential to its recognition qua iceberg.
Human inventiveness depends in the main on the possibility of making infinite numbers of combinations of verbal and other symbolic tokens of appearance and function. All inventions are initially pure works of fiction, produced by this method. Our old friend the Golden Mountain and our new acquisition the Concorde come out of the same stable; so does 'Hamlet'. The point which distinguishes them from 'facts' is that their symbolic formulation was temporally prior to any possibility of their ostensive definition. In the case of the Concorde and Hamlet, such a definition has indeed become possible, but it has not been worth while to develop the Golden Mountain beyond the drawing-board stage.
Historical 'facts', on the other hand, are events which are believed to have been ostensively definable, with the general assent of the onlookers, before their verbal or symbolic representation became possible, e.g. "There is Cæsar, crossing the Rubicon".
The Formation of Adjectival Concepts
Adjectives of sense-perception, like substantives, are undoubtedly learned by ostensive definition. It follows that pre-verbal concepts must exist, to which they can correspond.
In considering the methods by which such concepts may be formed, I propose to begin with the case of colour-adjectives, for the following reasons. Colour is a purely adjectival quality - a 'secondary' quality or 'accident' in classical philosophy. It cannot be correlated with data from any sense other than vision. It is of negligible importance from an indicative point of view; a black and white photograph is as serviceable as a coloured one for the provision of useful information about the functional aspects of the objects depicted, and colour-blind people in fact only find themselves at a practical disadvantage in the relatively few situations where colours are used conventionally for significant purposes.
It can therefore be confidently asserted that our interest in colour is almost entirely of direct æsthetic origin. There can be no doubt that æsthetic motives alone have led to the proliferation and refinement of colour concepts, because whenever colour differences are used in the construction of signs, it is always the crudest and most obvious contrasts that are chosen for the purpose.
There are, in English, only eight colour words wich are not obviously derived from the names of coloured objects and are not compound modifications of the basic octet. These are - red, yellow, green, blue, brown, black, white and grey. All of these are widely represented in nature by shades lying somewhere along the range which they cover. It is in fact possible to give an acceptable description of the colour of any object with the aid of these eight words, supplemented by the modifying adjectives 'pale' and 'dark'.
Since the primary denotation provided by ostensive definition is always an object or its function - objectivity itself constituting "minimum function" - a multiple ostension of distinct objects will be necessary in order to draw attention to the aspect of colour. All the ostended objects must be of a shade well within the range covered by the appropriate colour-word.
Granted the widespread occurrence of the eight contrasting colours in nature, we can assume with reasonable confidence that the child will already have formed colour-concepts which correspond approximately to the words we are using. The boundaries of the range that they cover will, however, remain vague.
The subsequent multiplication and proliferation of colour-concepts can only be accounted for by the inadequacy of the original eight from the æsthetic point of view. This occurs when a colour, which was expected, thanks to its name, to provide a satisfactory interpretant in a given sign-situation, has proved unsatisfactory in the actual context, although still falling within the range covered by the colour-word usage. For example, scarlet may have turned up where crimson was needed for the colour scheme, so that it becomes æsthetically necessary to sub-divide the concept 'red'.
In this case, which I consider quite crucial, the general concept exists prior to the special ones, each of which represents a differentiation which has resulted from dissatisfaction with the vagueness of the original. There can hardly be any possibility that the general concept, in this instance, can have been formed by the grouping of the special ones; the order of priority is quite obvious.
This method of multiplying concepts corresponds to the conjecture-refutation process which Prof. Sir K. R. Popper8 regards as the procedure typical of scientific research. The sign-situation constitutes the conjecture; the unsatisfactory interpretant constitutes its refutation, necessitating either the rejection or the modification of the sign-forming procedure and the concepts involved.
8. The Logic of Scientific Discovery, and Conjectures and Refutations, passim.
I think that this type of procedure must characterise the formation of all pre-verbal concepts. The earliest concepts are bound to be exceedingly wide and vague; they are gradually sub-divided, providing greater precision, wherever this becomes necessary on account of sign-failure.9
9. Cf. Spinoza, "Omnis determinatio est negatio".
Sign-formation achieved with the aid of any kind of engram or memory-action depends on the inherent expectation of similarity in experiential successions; as Hume quite rightly supposed, it is simply a matter of habit.
Any use of inductive procedure to form general concepts is almost inconceivable in the pre-verbal stages of concept formation, since no permanent symbols are available for representing similarities; and in any case similarities are unremarkable, simply because they are expected!
It is true that we have to assemble a collection of similarly-coloured objects for the purpose of ostensively defining a colour, but the point of this is simply to divert the pupil's attention from the other functional aspects of the objects ostended. Inductive procedure is not really involved here. Indeed, the simultaneous definition of several colours might be achieved by contrasting a number of differently coloured but otherwise indistinguishable objects; in this case a single ostension might be sufficient. All that is needed is to emphasise that the colour itself is the function which is temporarily the important one.
The initial interest in colour obviously stems from the striking contrasts present in nature, and not, at first, from feelings of pleasure or displeasure; the æsthetic element develops later.
In the cases of smell and taste qualities, for which there are only a few descriptive adjectives, the opposite is the case; the primitive dichotomy is simply 'nice-nasty'. In the case of taste, subsequent observation has detected four main contrasting kinds of flavour, which can occur in virtual isolation, namely sweet, salty, sour and bitter.
The first two of these are pleasant, at the level of intensity at which they are normally encountered and constitute the 'nice' group, the others, by themselves, being on the whole 'nasty'. This connotation is well displayed in the metaphorical use made of these adjectives in the field of speech and behaviour. Their ostensive definition is easy and quite reliable.
In the case of smell the net æsthetic effect remains far more important than any subordinate contrast of quality, and it is much later that we learn to use such words as 'acrid' or 'fetid' (nasty) and 'aromatic' or 'savoury' (nice). Their ostensive definition would not be very reliable.
The qualities of sound are sometimes significant, and are frequently of æsthetic importance, so that we need words to describe them.
Just as a picture constitutes the best description of a visual image, so an imitation constitutes the best description of a sound-quality. Consequently, nearly all sound-words are onomatopœic. In cases where the human voice is incapable of producing an adequate imitation, the sound-quality is left in the general category of 'noise' - e.g. that of traffic or aircraft.
As in the case of colour, new words may be invented if the sound to be described is not adequately imitated by any already in existence; "whizz" is of fairly recent origin, while "burp", to the best of my knowledge, has not yet attained dictionary status, although in quite general use. Some imitative oral sounds, like the vulgar "raspberry", are incapable of reproduction in writing but could be considered as words, granted an adequate phonetic alphabet.10
10 I suggest "p~" in this case [Editor's note: the tilde is to be read as if positioned vertically above the p].
Musical sounds, which seldom have any sign-function, needed no descriptive terms until a musical æsthetic was well developed. The vocabulary is sophisticated and derived from extra-musical sources. The differences between the sound-qualities denoted - e.g. musical intervals - seem to be as readily recognisable as those between the eight basic colours, so that ostensive definition can be undertaken with confidence. It is, indeed, far more precise than anything that can be expected in the field of non-musical sound.
It is interesting to note that the basic grammatical form of sound-words, unlike that of colour-words, is the substantive, though in most cases they can also be used, without modification, as verbs. Sounds are object-like inasmuch as they are bounded in time, as objects are in space; also their quality is either the whole or an important part of their function.
In point of fact, if language had been devised with the object of describing sense-experience, which is a process, rather than persistent landmarks of functional importance, it would have consisted entirely of adverbs! "I see a red square" would be replaced by "I-ly-visually-redly-squarely". The process "feel" is taken for granted, while "I-ly" is shorthand for the familiar compresence of visceral sensations, memory and expectation.
Indicative language, firmly based on the substantive in consequence of having ostensive definition as its foundation, is hopelessly inadequate for the description of basic sense-experience.11 Music does the job better - contrary to Ramsey's famous comment on Wittgenstein's Tractatus. There is a good deal that cannot be said but can be whistled! Since, however, this "ineffable" is the source of all that can be said, it makes no sense to refer it to the transcendental realms of the "mystical".
11. Whitehead's 'fallacy of misplaced concreteness' is to some extent an in-built feature of all linguistic expression. Words, and symbols generally, automatically express a pragmatically invariant quality of the entities they represent.
We now have to consider those sense qualities which are mutually significant and thereby contribute to establishing "objectivity", or minimum function. These so-called "primary" qualities are those of shape, inertial quality and position in the visuo-kinæsthetic spatial field.
There are severe limitations to the objectivity of shape. This can only obtain in the case of objects which can be touched, and even then it only characterises elements which, when handled, give rise to fairly precise visual expectations.
These include any curvatures of the same order or sharper than those of the fingers; points, edges and corners are thorougly objective, as are also topological features such as holes. Such objective elements of shape can be ostensively defined with confidence by drawing repeated attention to the appropriate portions of objects which exemplify them.
Touch, however, will not distinguish between gentler curvatures which are obvious to vision, and it is highly improbable that the notion of symmetry could be derived from touch alone.
Now it is quite obvious that it must have been the feeling of visual symmetry which gave rise to geometry and to the identification and naming of geometrical shapes. The actual word 'symmetry' is etymologically unfortunate and question-begging; what I mean here is the impression that an untutored savage might receive on seeing the Sun, the Full Moon, the surface of still water, a spider hanging from its web, trees growing out of a flat plain - all those natural approximations to geometrical form which constitute such a striking contrast with the rest of nature.
The metric properties approximately associated with these forms - and we must remember that all measurement is approximate - were doubtless discovered during attempts to reproduce them symbolically. But they always have been - and still are - quite irrelevant to their ostensive definition. What has occurred, however, is that the visual symmetry of the images constructed with the aid of the metric properties has exceeded that of the originals, so that the geometric concepts have been transferred from the original objects to the manufactured images, or even to the metric formulæ employed in drawing them.
The geometrical terms which can be ostensively defined with confidence are confined to those denoting forms which can be visually demonstrated as some combination of straight lines, right angles and circles - the only geometric forms that are prominently exemplified in nature. These include shapes such as cylinders, cubes and cones. Such shapes are also of great functional importance in developed societies, and are abundant and familiar.
Although the visual aspects of the geometrical faces of such objects usually consist of quasi-ellipses or quasi-parallelograms, they are unhesitatingly identified as oblique views of their 'real' shapes - the circular or rectangular forms which represent their most symmetrical aspect - and which will have been employed for the purpose of their manufacture. If the obliquity is considerable, tactile-kinæsthetic evidence may be accurate enough to confirm this interpretation.
Synthetic curves constructed with the aid of metric formulæ have not attained sufficient general importance to allow of their ostensive definition. We cannot at present contemplate the possibility of a neo-Giotto who could produce a freehand drawing of an ellipse which would satisfy the metric tests of the mathematicians!
Other shape-words are derived from the functional names of objects which are commonly of the approximate shape denoted, e.g. oval (egg-like), tabular, wavelike, etc. etc.
Inertial qualities are those associated with touch - every contact, however light, registers an abrupt change in resistance to movement - and of muscular effort to move the object concerned.
The relevant touch-words are 'hard' and 'soft'. They are objective, in as much as they indicate whether the object yields locally under slight pressure; such movement needs corroboration by the kinæsthetic and visual senses. They are obviously relative, so that their ostensive definition necessitates the use of contrasting pairs of objects. There is no norm of demarcation between them, but the natural contrasts between rigid solids and fluids provides a familiar example of the quality-difference defined.
The relevant effort words are 'massive' - more common, but inaccurate, is 'heavy' - and 'light'. These qualities are also objective, in that corroboration of any movement effected is needed from the spatial senses. 'Light' differs from 'soft' in that the object yields as a whole.
The words are completely relative, and any norm will depend upon the context. Contrasting pairs will again be needed for ostensive definition.
Spatial Position
There is no doubt that upward and downward, forward and backward movements, together with their related prepositions and adjectives, can be ostensively defined. Right and left, and clockwise and counter-clockwise rotation, are rather more difficult, but ostensive definition is usually successful also in these cases, though often a little later.
The genesis of these concepts is not entirely easy to explain. If the physicists and the physiologists are to be believed, the form in which perceptual information reaches our "Central Intelligence Agency" - wherever and whatever this may be - must be that of a multitude of electrical impulses from a great variety of sources. This, in its raw state, can hardly possess the kind of structure which can be regarded as 'spatial' in any ordinary sense of the word. Spatiality must therefore be considered as a device which we use for ordering it.
The television receiver provides us with a very likely model of the procedure, since the signal received by the ærial has likewise nothing spatial about it at all. It is a purely successive pulsation of electrical intensity; just the kind of material that we might expect to obtain from the nervous system.
This material is now translated into variations of illuminative intensity, and the result is flashed with very high frequency across the lines of the screen. It is still a pure succession; the viewer himself has to interpret it as a quasi-simultaneous picture. Just how this is done is something beyond the reach of language, which, thanks to its foundation in ostensive definition, can only begin after spatialisation is assumed to be complete. This process is indeed an excellent example of something which can only be shown!
The engineer knows, of course, the frequency with which the camera has 'scanned' the original picture in order to produce the transmission wave, and can use the same frequency for the purpose of partially re-spatialising the picture on the screen. Human beings have no such knowledge to help them to spatialise their raw material, and have no television screen in their heads. How then does it come about that they all seem to do it in the same way?
When we examine the working of the television set, we find that the position of an image on the screen corresponds to the phase-relation between a repetitive rhythmic pattern in the transmission wave, representing the image, and the frequency with which it is flashed across the screen. Thus it may well be that what we know as spatial position is our direct interpretation of a phase-relation between elements in our raw material and the scanning rhythm of mind.
We are already cognisant of an analogous direct interpretation in the case of sound. We know that this consists of vibrations, because we are familiar with the no-man's-land of very low pitch, where we are in some doubt whether to regard our data as separate vibrations or as a musical note. The transition as the pitch (frequency?) rises is gradual and quite unbroken, but after a bit there remains nothing but the sound-quality; we are no longer conscious of the vibrations.
The physicists' successful conjectures about the properties of light, no matter whether the quantum or wave theory is chosen, all accept rhythmic frequency as one of its fundamental properties, so that our visual sense may also be a direct interpretation of yet another band of frequencies!
Physiological psychologists are increasingly coming to regard the 'mental' part of perception as a rhythmic 'scanning' activity, so that the notion that spatial position may be the direct interpretation of a relation between two rhythms is anything but far-fetched.
Thus if all human beings, in infancy, employ the same scanning rhythm, and also attach interest and importance to the same types of rhythmic pattern on certain fairly well-defined frequency-bands, it is quite natural that they should all adopt the same method of spatialising their raw material.
The initiation of the process may prove to be beyond the reach of scientific research, since the basic space-sense - that of bodily geography and movement - has its internal organ in the inner ear, which probably provides perceptual raw material well before birth; and we can hardly hope to obtain information about the spatial conditions that are interesting and important to a fœtus! It is, however, reasonable to suggest that the three dimensions of Euclidean space, the kind which we 'intuitively' adopt, may be derived from the pre-natal æsthetic necessity of harmonising messages from the three semicircular canals.
In the Meno, Plato shows Socrates demonstrating that a slave, although completely untutored, possesses an intuitive understanding of geometry. So in a sense he does; but it is not, as Plato maintained, a matter of recollection. For if he spatialises in the same way as the rest of mankind, and shares the common interest in the symmetry of the forms used in Euclidean geometry - which quite obviously correspond to a simple rhythmic property in his non-spatial raw material - he can be relied upon to develop his geometry along Euclidean lines.
The Ostensive Definition of Function-Words
Words descriptive of function or mode of function are mainly verbs and adverbs, but seeing that the primary denotation of many object-words is the function of the object, many substantives must be included in this class.
Many active verbs and their modifying adverbs can be defined by multiple ostension in the same way as adjectives, e.g. 'walk', 'run', 'speak', 'hit', 'quickly', 'loudly', 'violently', etc. Their delimitation, like that of adjectives, is ofen vague and arbitrary, and the ostended examples must lie well within the generally accepted range of the denotation employed.
Just as adjectives are defined by displaying objects which exemplify them, so the actions denoted by active verbs are defined by means of objects which are performing them.
This point is of great importance. The ostensive definition of any process - and therefore, by inference, its symbolic representation - is dependent on the prior existence and definition of an object which is, pragmatically speaking, unchanged in other respects and verbally represented by a substantive. This is why every empirical proposition - which represents a non-verbal sign situation - has to be of subject-predicate form.
Pure process can therefore never be symbolically described; even the word "change" itself, it it is to be repeatable in different contexts and thus useful for communication, must denote something unchanging.
This is the point of Zeno's "Arrow" paradox. Zeno, in common with most of his contemporaries, was inebriated by the artistic creations made possible by the exceptionally sensitive Greek language and by the symbolic deductions of the Greek geometers. Word and symbol were, for him, more 'real' than direct experience; they signified something 'eternal'.
Finding that motion was indescribable in terms of object-states which were persistent enough to be symbolically represented and therefore 'eternal', he denied its reality, and his school extended this judgment to all change and time itself.
In our age Russell took a similar view. He did not want to go as far as Zeno and deny the reality of all change, but having, like the Greeks, a respect for symbolic representation which the achievements of modern mathematics and physics had done nothing to diminish, he was on the whole inclined to back their findings as against direct experience, as constituting 'reality'. So, arguing against Bergson,12 he maintained that the arrow's 'motion' simply meant that it was in one place at one time and another at another.
12. "Mathematics and the Metaphysicians" in Mysticism and Logic, p.84.
This is in fact the best that can be done with the aid of mathematical symbolism - a cinematographic picture which enables us to locate the arrow at any 'instant'. Bergson castigated the physicists for taking this view, but did not appear to realise that the same difficulty is inherent in all forms of symbolic representation.
Behaviourist psychology has a similar origin. Feeling is the purest form of process, and it is not even possible to define it ostensively by means of an object which can be observed to be 'feeling', so the behaviourist eliminates it from his subject matter. He is, however, quite unconscious that his very use of language, based as it is on ostensive definition and therefore dependent on the sense of importance attached to the objects so defined, presupposes the existence of feeling!
Complications arise in the definition of functional objects, because the denotation used by the adult usually defines a more specialised function than the general one which is of primary importance to the child. For instance, a child, in this country, who learns the word 'chair' by ostensive definition, will apply it to any manufactured article that is used for sitting on. He will regard stools, benches and armchairs as different kinds of 'chair', since they all fulfil the same basic function. Not until he realises that "chairs" also give dorsal support, whereas "stools" do not, and "benches" support several people, will he seek an independent denotation for the general concept of vertical support for which 'chair' has so far been perfectly adequate.
When I was A HREF="figure9.jpg">a child, my midday meal always consisted of two courses, which I knew as 'meat' and 'pudding'. They might in fact consist of macaroni cheese and stewed fruit, but the specialised denotation - which admittedly was often applicable - retained its general significance for me. Macaroni cheese was 'meat', and stewed fruit was 'pudding'.
I maintain that it is the more general concept which is at first defined by the denotation employed, although the word learned is probably one which, for the adult mind, denotes a specialised application of it.
This circumstance has led to the view, which I believe to be mistaken, that general concepts arise by the recognition of similarity between their exemplifications. It is true that the word which signifies the general concept for adults is often the last to be learned, but this circumstance is irrelevant. In the case of the basic words for colours and tastes, which retain the same significance for adults as they possessed during childhood, nothing of the kind occurs. I take it that the process of concept-multiplication illustrated by the case of colour is that typical of concept-formation at the pre-verbal stage.
We may fairly assume that Occam's Razor - that expression of the fundamental laziness of the human mind - is applicable in infancy as well as in maturity, so that the development of new concepts will only occur when there is dissatisfaction with the old ones. New and more detailed conjectures will then be formulated - hypotheses constructed with the aid of the new concepts - and will be accepted until they in turn prove unsatisfactory.
Pre-verbal concepts, then, are neither 'ideas' laid up in the mind of God, nor are they abstracted from a multiplicity of instances on the grounds of "similarity". They are carved out of an initial experiential chaos - I prefer this term to James' "blooming, buzzing confusion", which seems to imply the confounding of what has already been differentiated - in conformity with human desires and needs, and come into existence whenever important dissimilarities call for further differentiation.
The converse process - the creation and naming of a "new" class by assembling a number of previously named individuals or species - is common enough in the post-verbal stage. It is significant, however, that such a class is only felt to be "natural" - as distinct from arbitrary - in cases where the individuals or species (as in zoology) could be thought to have come into being by differentiation from a common ancestral stock.
Many groups can be regarded in either fashion. For example, a group of people at a bus-stop or in a doctor's surgery can be regarded as a random collection, assembled for the first time; alternatively, they can be thought of as sub-groups of the larger and vaguer classes of "bus-travellers" and "sick people". The actual existence of the bus-stop and the surgery bear witness to the prior existence of the larger classes.
There is a close relationship here with the distinction between 'fact' and 'fiction' already given in this essay.
The Ostensive Definition of Logical Words
Russell maintained13 that words such as "or" and "not" could not be ostensively defined. In support of this contention he advanced the case of a child who, when asked "will you have pudding or pie?" simply replies "yes". In this case, he maintained, there was nothing you could give him which satisfied the description "pudding-or-pie".
13. Inquiry into Meaning and Truth, Ch.4
But this is a mistake. If the child had replied "no", there would have been no doubt that he wanted neither. Conversely, the reply "yes" means that either will do, in other words, that pudding and pie fulfil what is, broadly speaking, the same desirable function. At the moment, the child is regarding them as alternative sub-classes of the larger and vaguer class of "afters" and the difference between them, though recognised, is unimportant.
If the question had been "will you have pudding or a spanking?" the answer "yes" - assuming that both entities had been previously defined ostensively - would have been inconceivable; I disregard the highly improbable case of infantile masochism.
The conjunctive, alternative use of 'or' is confined to objects which have an important function in common, and its repeated use in such contexts will effectively provide its ostensive definition.
In any given sign-situation, the relation between alternative interpretants which are felt to be satisfactory is what is expressed by the alternative 'or' - the 'and/or' of logic. If, however, the interpretant is felt to be unsatisfactory, seriously failing to fulfil the functions expected of it, then 'not' comes into operation.
'Not-p', where p is a predicate, does not refer - or rather its reference is so wide as to be useless. Its use is confined to instances where there is an expectation of p which is disappointed.
If I order red paint, and white is delivered, I shall certainly make use of the concept "not red". This would be quite otiose if I had ordered the paint without specifying the colour.
"Not" is, in fact, the expression of an unwelcome instance of sign-failure. The interpretant has to be one which produces the opposite affective tone to that which was expected.
For reasons already pointed out, the earliest interpretants of sign-situations are nearly always favourable; the same applies to most interpretants which we actually experience in later years. For when we see a sign which we regard as a warning, that is to say, with an unfavourable interpretant, we naturally tend to avoid the process which would lead to it, rather than take the off-chance of a pleasant surprise. Pleasant surprises, therefore, although they do occur, tend to be few and far between, and to arrive out of the blue, not as interpretants of a specific sign.
Thus it comes about that the 'no'-feelings associated with sign-failure are so saturated with unpleasantness that they produce much the same feelings as visceral discomfort. They constitute a kind of shock, which in itself can be highly unwelcome even when the surprise is pleasant; in severe cases of this nature it has been known to result in a faint.
It is quite clear that by the time that speech-learning begins, every child will have experienced unpleasant surprises often enough to grasp the function of the word 'not' which so frequently accompanies them. Any further ostensive definition would be superfluous.
'No'-feelings are frequently produced by verbal propositions. Now a meaningful proposition which purports to refer to non-verbal facts is the symbolic representation of a sign-situation, which enables us to juxtapose our memories of sign, process and interpretant. We condemn the proposition as false when such a juxtaposition results in a 'no'-feeling. But the proposition is no more than an epiphenomenal wraith of the sign-system that it represents;14 so also the 'no'-feelings associated with false propositions are feeble compared with those resulting from the sign-failures which they represent.
14. This is the source of Descartes; epiphenomenalism; his extremely adult ego cogitates exclusively in verbal terms, and the result is the faulty equation:- Mind : Matter :: Verbal expression : Experience.
Compare, for example, the feelings of a passer-by who casually notices that a signpost is wrongly oriented with those of a traveller who has been seriously misled by the sign!
Thus the intrinsic importance of propositional falsehood is very slight. It is much greater when the proposition is liable to be used as a basis for action, 15 or where it upsets the coherence of an interconnected complex of useful propositions which employ some of the same symbolic tokens.
15. Fiction is unobjectionable as long as it is recognised as such; objections only arise when it approaches verisimilitude, say, in the description of one of the characters, when it is liable to be regarded as an attempt at a factual description.
The disjunctive 'or', i.e. 'not p and q together', is not part of the object-language, and cannot be ostensively demonstrated. It exemplifies a syntactical rule of that language, which prohibits the attribution of spatio-temporal coincidence to any two predicates p and q as soon as, say, q has turned up as interpretant in a sign situation where p was expected, has provoked a 'no'-feeling and therefore acquired an independent denotation.
The predicates concerned can be mutually exclusive functions; if they are sense-qualities they must obviously affect the same sense or senses.
This rule arises from the circumstance that every new denotation is motivated by a case either of æsthetic disappointment or of sign-failure, and that what is actually ostended is always a well-defined spatio-temporal object. Breach of the rule is therefore almost certain to result in an undesirable 'no'-feeling.
The derivation of negation from sign-failure and of disjunction from the relation of spatio-temporal coincidence casts considerable doubt on the status of any symbolic logic which manipulates symbols for negative predicates and disjunctions in complete abstraction from their parent situations. Its relation to actual human thinking seems analogous to that of the game of chess to actual warfare, and although it is clearly an interesting pastime for its practitioners, I do not think it should be regarded as anything more. Transcendentalist logic should surely be just as suspect as transcendentalist metaphysics has been ever since the appearance of Kant's Critique.
On the other hand, the reference back to the sign-situation of disputed points of logic can be quite revealing. For instance, the double negative - not (not p) - clearly stands for a sign-situation where the expected interpretant is quite indefinite save for the one proviso that it will be 'other than p'; but p turns up! Thus p and not (not p) are not identical; not (not p) stands for p together with a double ration of the surprise which constitutes negation.
So far I have hardly considered 'yes'-feelings at all. For the most part they are far less intense than 'no'-feelings and usually quite unremarkable, because they are with us all the time; most of our sign-systems have withstood the process of natural selection provided by frequent opportunities for their refutation and seldom provide instances of failure. It is only the unexpected which is really "news".
But the unexpected - and with it "yes"-feelings of great intensity - does sometimes occur when a new conjecture or sign-system proves outstandingly successful, perhaps beyond the wildest hopes of its inventor. In such cases their intensity can be positively inebriating, and the inventor is left with the impression that he has somehow been vouchsafed a glimpse of "absolute" truth.
Such must have been the experience of Kepler, Galileo, Newton, Kant, and, above all, of the Greek geometers. It is from Greek geometry that absolutism entered the mainstream of philosophy, via Plato and perhaps Parmenides, and has bedevilled it ever since.
Whenever we feel tempted to employ any 'absolute' as a foundation for conceptual thinking we should remind ourselves that Kant, profound thinker though he was, never doubted that Euclidean geometry and Newtonian mechanics were absolutely true for the world of phenomena - a view which we now know to have been quite mistaken.
The idea of "absolute" truth makes complete nonsense in the context of any correspondence type of theory, simply because it is obvious that no symbolic representation can ever be a complete and absolutely satisfactory substitute for the non-verbal circumstances with which it purports to correspond.
From the semantic point of view, Tarski may be correct in telling us that the sentence "snow is white" is true if, and only if, snow is white. But what are the criteria for deciding whether snow is white? The only answer is an appeal to ostensive definition; we can say that snow is white when, and only when, the ostensive definition "that is white snow" fails to provoke any 'no'-feelings in its hearers.
This will not always be the case - for instance, in an industrial area, or if one of the hearers is suffering from jaundice. Similar reservations will always be applicable to any general propositions dealing with empirical data. In such cases the "if" of Tarski's formula should be replaced by "when". In its original form it is only valid for tautologies, where the "if-then" relation stands for strict entailment.
Such cases do occur. The statement "crimson is red" is true because "crimson" is red; the objects used for the ostensive definition of "crimson" are, a priori, selected from the larger and vaguer class of red objects. Syllogistic logic, in fact, depends for its validity on the assumption that class and concept formation has actually proceeded by the method of multiplication-by-fission which I have suggested as typical of the pre-verbal stage. It is, in fact, rashly applied where this is not the case, and its validity then becomes extremely doubtful.
Take, for example, the archetypal syllogism connecting 'Socrates', 'men' and 'mortal'. The major premise "all men are mortal" could only be valid if 'men' had been defined as a sub-class of "mortals", which is emphatically not the case.16
16. This point is clearly demonstrated by the widespread acceptance of the counter-examples of Enoch and Elijah.
We can, of course, put the major in the conditional form, but the 'if', in this case, means no more than 'let's pretend'. The whole syllogism can then be re-written as follows:- "Let's pretend that the class 'men' has been created as a sub-class of the class 'mortals'. Then, if 'Socrates' denotes a member of the class 'men', the statement 'Socrates is Mortal' is in accordance with the rules of the game".
Contrast this with "This object is crimson: All crimson objects are red objects, therefore this object is a red object". This is genuinely valid.
The validity of Modus Ponens in any form such as 'From A and AB, infer B' is conditional on the nature of the conjunction AB, and only obtains when A was originally, and still is, defined as a sub-class of B.
Modus Tollens represents what I take to be the basic method of pre-verbal concept formation. The most primitive syllogism runs as follows:- "What I think of as A is nice: This (in a sign-situation where A was expected) is nasty: therefore, I must think of it as other than A (i.e. Not A)".
Or, in a slightly more sophisticated form:- "What I call A fulfils the important function a : This, which looks like A, has failed to fulfil a : therefore I must call it B". But, as it continues to look like A, the result is the subdivision of the original class of appearances.
It is clear that if classes are related in this way, they can be used to construct syllogisms in Modus Ponens. Our positive addiction to the syllogism in this form strongly supports the view that our earliest concept-formation does in fact proceed in the way I have suggested. Scientific nomenclature uses much the same procedure; taxonomic disputes mainly centre around the degree of importance to be attached to function a.
We can now give a precise meaning to the terms 'synthetic' and 'analytic'. They do not apply to knowledge as such, but to the mode of origin of the class-concepts which we use to organise it.
Concept formation is analytic whenever dissimilarities occurring within a recognised and named class necessitate its division into smaller and more precisely defined sub-classes. A wide, vague entity may become a class in this way.
It is synthetic whenever a class is constructed by the association for any reason - generally on account of their similarity - of entities which have previously been identified and/or named.
In the first case the name of the parent-class is always temporally prior to that of its members; in the second, the opposite relation obtains. The first type is factual, the second fictitious, on the criteria put forward earlier in this essay. I think that the term "class" should be confined to the analytic type, in accordance with the etymology of the word. "Classis" signified a division of the Roman People, not an assembly of individual Romans. "Set" or "collection" could be used for the synthetic type.
We are now in a position to consider the ostensive definition of number. In his famous definition, Russell made no distinction between classes and sets, probably because the concept of number had to be applicable to both. He came in the end to regard both concepts as fictitious. This, as we have seen above, is a mistake.
The division of a single entity into members of a class is factual, since each step in the division represents the occurrence of a 'no'-feeling. Such a feeling, and its ostensive expression, must temporally precede the naming of the members to which it gives rise.
Sets, on the other hand, are pure fictions, and can be constructed at random. It follows, therefore, that if there is anything logical about number which is applicable to sets, it cannot have to do with their construction, but must be concerned with their breakdown.
Now when a concept becomes a class by multiplication-by-fission, each stage of subdivision represents a negation, dividing the newly distinguished member from the rest of the class. The number of the resulting class is therefore the multiplicity of negations that has taken place during its formation, plus one - what is left of it. It can be readily ascertained by the progressive elimination of the members one by one. The multiplicity attained at the stage which eliminates the last remnant and thereby annihilates the class is, in fact, its number. This procedure is completely logical. It can also be applied to sets provided that we can assume that their members are related by mutual negation in the same way as members of classes, so that if the set consists, say, of a, b, c, d and e, a must be not (b or c or d or e) and so on for the rest of the set.
It is now easy to see how and why counting can be valid for the ostensive definition of number. We always begin with a set already in existence, and eliminate its members one by one, uttering each time, ind conventional order, the word appropriate to the stage concerned. The number of the set is denoted by the word which accompanies its final annihilation.
Even if we adopt the Frege-Russell definition of number, we can only test the one-one correspondence of sets by starting with the complete sets and comparing their numbers one by one, eliminating them, at least conceptually, as soon as they have been matched up. One-one correspondence is again indicated by the simultaneous termination of the process in the case of all the sets.
This is why the attribution of number to infinite sets is of very doubtful validity; there is no place at which to start the elimination!
Counting is in fact a count-down. When we count a group of, say, six objects, we say "one" when we reduce it from six to five, and "six" when we eliminate the final member. The occasions on which we reverse this process and use what is generally known as a "count-down" are those when we know the number of the set and wish to signal its annihilation.17
17. Zero cannot be a number; it represents the conventional annihilation of a class or set. This is the rôle it actually plays in the Arabic system of numeral notation. This view also eliminates the need to invoke that rather dubious entity, the logically null class. It is curious that philosophers like Russell, for whom Occam's Razor was almost an article of faith, should have been prepared to give serious consideration to classes such as "the class of round squares", for which there is no necessity whatever!
It is true that we can, and often do, build up a set, counting upwards; but we can never guarantee that its members will maintain the relation of mutual negation which is necessary if the set is to possess the logical properties proper to a class. The number obtained by the subsequent breakdown of the set may be very different from that attained at the close of its build-up. In certain cases this is obvious; if the set happens to consist of drops of water or pregnant rabbits the divergence is likely to be considerable!
It follows that arithmetical proofs conducted by the method of mathematical induction depend on faith rather than logic. We believe that we can go on indefinitely discovering numbers (we cannot construct them, since counting is a count-down) to which we can apply the breakdown methods logically applicable to the comparatively small classes with which we are acquainted. Such methods reflect the origins of a class in the successive divisions of a unity.
Our numerical faith is probably based on the phenomenon of rhythm. This aspect of our temporal experience has been largely ignored by philosophers, but it is basic to all forms of structure and seems to be a primary datum, since we cannot conceive of any source from which a sense of rhythm could be derived.
Every rhythm contains within itself an indefinite number of rhythms with frequencies which are factors of its own, so that if we conceive of time as infinite, and, what is more important, as infinitely divisible, a potential infinity of numbers exists in the form of ratios between frequencies.
Summary and Conclusions
In view of the effectiveness of indicative language in facilitating the cooperation of mankind in the attainment - or avoidance - of seminal interpetants, we are justified in supposing that its foundations are sound.
Ostensive definition is the ultimate foundation of all language, so that the use of language must imply the acceptance of any assumptions needed to justify the validity of this process.
The basic assumptions involved are the possession of a common sense of importance and a common sense of spatial structure by demonstrator and pupil alike.
In this essay I hope have succeeded in showing that the concept of importance can be derived from two assumptions which are in fact universally accepted. I am suggesting that these assumptions, rather than "impressions" or "sense-data", should be accepted as the basis of a genuinely empirical philosophy. They are as follows:-
A radically empiricist theory of knowledge must start from something like a solipsist basis. The infant mind, assuming that it is tabula rasa as regards experience, has nothing except the experiential flux that we may describe as 'I-here-now' for its raw material. It does not start with simples like "impressions" and "sense-data", but with chaos - James' "blooming, buzzing confusion". Whitehead has rightly emphasised that the raw material of perception, and certainly that of infantile perception, is far more akin to visceral sensations than to visual ones.
Even for adults, the flux of the 'I-here-now' provides the only certain knowledge. This flux, as we know, contains elements which we conjecturally refer to the past - i.e. memory - and others which we conjecturally refer to the future - i.e. expectation. All these are subject to æsthetic judgment, which motivates the formation of our sign-systems.
"Impressions", "sense-data" and the "qualia" of James and Ayer, represent the end-products of the analytical processes prompted by the human æsthetic; they are no more a part of the original raw material than 'atoms' and 'electrons' are part of the raw material of physics. I hope I have succeeded in showing that these analytical processes can be simply accounted for on a conjecture-refutation basis if my basic assumptions are accepted.
The opposite view, which regards knowledge as built up from "simples" is indeed true of public "knowledge", which is coterminious with language itself - using that term to include all forms of symbolic representation. The growth of public knowledge is in fact identical with the growth of language, and is obviously a synthesis rather than an analysis - although the analytical processes proper to the development of private knowledge can be - and are - applied to the products of this synthesis.
What is truly remarkable is that all human beings appear initially to apply the same analytical methods to their diverse experiences; they seem to share a common sense of importance and a common method of space-construction. Kant's philosophy involved a complete dichotomy between these two. Our spatio-temporal form of 'intuition' and the categorical forms of reasoning applicable to these 'intuitions' belonged to 'pure' reason and were absolutely determined, for all mankind, by the 'transcendental æsthetic'. Euclidean geometry and Newtonian physics were absolutely true throughout the whole of this field.
'Practical' reason and morality, on the other hand, belonged to the province of freewill and the 'Ding-an-sich'.
We now know that alternative geometries and physical systems are available and useful in certain contexts, although it is still true that we use the Euclidean and Newtonian varieties in the great majority of situations.
Conversely, we have far more evidence than was available in Kant's day concerning the extent to which behaviour is affected by environmentalcircumstances - both bodily and external.
I am suggesting here that Kant's dichotomy is unjustified, and that our choice of behaviour and geometry alike is æsthetically motivated, but that the Human Aesthetic is identical for all mankind.
In other words, although we all have different raw material to handle, our initial methods of dealing with it are identical. Without this identity, it is indeed difficult to explain the possibility of language.
This hypothesis is determinist, but avoids the most objectionable feature of mechanical determinism. This is not its denial of the "freedom" of the will, but, rather, that it robs it of causal efficiency, thereby resulting in the annihilation of all meaningfulness in purposeful action; this is generally felt to be intolerable.
If, however, the determining factor is the human æsthetic, which is inevitably regarded as meliorative in character, this objection disappears. We can happily regard ourselves as its agents.
My hypothesis must, I fear, be described as metaphysical, inasmuch as it appears to be proof against any empirical refutation; but it has obvious and radical applications in the field of ethics, and I am examining these in another essay. If these can be shown to be radically unsatisfactory, it would have to be rejected. I trust that the possibility of such a refutation will be sufficient to establish its intellectual respectability.
Although it may seem strange, it is correct to assert that the Apostle's linked pair of statements have nothing directly to do with 'time', in any sense in which we habitually use that word. What is in question is what is referred to by musicians as 'tempo'; he is attempting to express the transcendence of the temporal range of Divine consciousness compared with that of human beings. In his day, however, there was no vocabulary which would enable him to achieve this directly, so he went about it by equating an inconceivably long duration with the shortest 'unit of time' which commanded general recognition in his age.
In our own day, it would never occur to anybody to use "day" to exemplify shortness of duration, but that is because we habitually express moderate durational extensions, many of them much shorter than the 'day', in terms of still shorter ones, sequences of which are intuitively felt to be rhythmically invariant. The "second" is the current equivalent of the 'day' in St Peter's age; it is by no means the shortest that occurs within 'public' phenomenal experience, but all shorter ones can be related to it quite easily by the 'rhythmetic' use of number.
The most important step in this direction was taken by Galileo; he is reported to have used a 'musical' beat of approximately half a second - presumably generated by a precursor of the 'metronome' - for timing his famous experiment with the inclined plane, on which, according to Bergson, "science descended from Heaven to Earth". The fundamental change was indeed the substitution of terrestrial 'tempi' for astronomical repetitions for the purpose of obtaining quantitative estimates of those durational extensions which are important to us in the activities of everyday life; the great majority of these lie somewhere between the 'second' and the 'day'.
The relations between 'invariant tempi' and their corresponding 'durations' can only be directly perceived over a very limited range of the 'temporal spectrum'. Few people will confidently claim to be able to certify the 'rhythmic invariance' of any succession of events separated by intervals of more than three or four seconds, without checking it by 'counting' at a tempo that is more rapid than that of the succession itself. The 'tempo' of a succession of events separated by one second is nowadays officially known as the "Hertz",1 so that the slowest tempo that can be confidently diagnosed as 'invariant' is one of approximately ¼ of a 'Hertz'.
1. This term is curiously appropriate, since it denotes the approximate tempo of a series of 'Herzschläge' or heart-beats.
In the case of rhythmically invariant sequences at tempi greater than the 'Hertz', we find that beyond a certain point, the event-sequences tend to become 'confused' - no pejorative connotation is intended here - into a 'quality'. The critical case is that of low-pitched sound; when listening to the output of a 32-foot organ-stop, it is difficult to decide whether to regard it as a msical note of uniform 'pitch', or as a succession of pulsations occurring at a uniform 'tempo'. In this case of still quicker 'tempi', the perceived invariance, and hence the habitual manner of its verbal description, is one of 'pitch', not of 'frequency'; the latter is only inferred by extrapolating from the correspondences actually observed within the transition zone.
Thus we can fairly assert that the range within which 'tempo' is perceived as such is the very narrow one lying between the approximate limits of ¼ Hertz and 100 Hertz. This range includes the vast bulk of the tempi which characterise the important event-sequences of bodily motion and speech; they are therefore of general interest to all mankind, can be ostensively demonstrated and, within limits, 'defined'.
Christian Huyghens, the famous 17th-century expert in chronometry, was initially responsible for the suggestion that the qualities of visual perception might also be 'rhythmic' in character, although in his day there was no evidence whatsoever in favour of such a hypothesis; one can only suppose that he arrived at it by a further extrapolation from the observed correlation between 'frequency' and musical 'pitch'. It was not until much later that it was discovered that his theory provided a framework for a good many visual phenomena which could not comfortably be accommodated within the fashionable Newtonian 'schema'. Since that time, 'frequency' theories of perceptual quality have been widely accepted, and are nowadays extensively used as the basis of a multitude of human activities, especially in the field of communication. Consequently, a considerable variety of new terms has been invented for the purpose of applying the theory. Those which signify high frequencies are more frequently used than those signifying the corresponding durations; "kilohertz" and "megahertz" are in regular use; whereas "nanosecond" is much less familiar, although it is generally understood, as the durational complement of the "megahertz".
We will now proceed to rewrite St Peter's contrast of "tempi" in a manner strictly parallel to his own, but using a much shorter pair of 'durations'. Neither of these is perceived directly, although both of them are believed to form part of the experience of every adult human being, and they can be 'numerically' related through the intermediary of the hertz/second. We can then proceed to assess which, if either, of the two contrasting 'tempi' is of the greater importance for human experience.
The 'decade' is used in place of Peter's "thousand ages", because although it is believed to occur within every adult human experience, it is clearly 'synthetic', and does not correspond to any natural repetitive sequence, as do the 'day' and the 'year'.
It is clear that two such violently contrasting 'tempi' of awareness cannot possibly be synchronously reconciled within human thought, although there is no harm in suggesting that they may be reconcilable by Deity Itself: "to God, all things are possible". Neither are there any grounds for suggesting that one or other of the contrasted 'tempi' is an ethico-æsthetic 'optimum'; this might well lie in the region intermediate between them.
Now it is immediately obvious that any sentient being for whom the contents of a decade flashed by like a nanosecond could never be aware of any activity occurring at tempi of the order which we normally experience during consciousness; for such a being, these tempi would simply not exist. Thus if (i) were to express any temporal aspect of God's awareness, it must be one which is completely irrelevant to ordinary waking experience. Yet this is the only one generally implied when 'eternal' is used as an attribute of God. "A thousand ages in Thy sight are like an evening gone" lacks the complement provided by St Peter, who had the exceptional insight to realise that 'eternity' can be applied, not only to 'invariance', but to change itself, when its meaning changes from 'unending' to 'unceasing', that is, to 'absolutely continuous'.
In the case of tempo (ii) matters are altogether otherwise. Any conscious being who contrived to accelerate the 'tempo' at which he scanned his raw material so as to slow down that of the changes perceived to such an extent that the experiential content of a 'nanosecond' was extended over a whole 'decade', would be able to detect changes at all kinds of tempi intermediate between the 'megahertz' and the 'hertz', and might well learn to effect changes at those ranges of tempo.2 This principle is the one employed in so-called 'slow-motion' photography; the original material is 'scanned' at an exceptionally high frequency, and the sequence is subsequently represented at the much lower frequency which is 'normal', when the successions of events appear to occur far more slowly than they do when viewed with the unaided vision, so that the viewer is able to notice a great deal of detail which normally escapes him.
2. This possibility was exploited, although only to a very conservative extent, by H.G. Wells in his short story "The New Accelerator".
Within the 'static' field of visual space, a similar function is performed by the microscope. Only a fraction of the total material available within the visual field can be 'synchronously' scanned within the limits of the eye-piece, but the slower rate of presentation, resulting from 'magnification', allows the observer to become aware of a much greater amount of detail.
Thus it is clear that the tempo of awareness expressed in (ii) would be highly relevant to human experience, enabling its possessor to take notice of all changes within his 'raw material' occurring at tempi intermediate between the 'megahertz' and the 'hertz', and perhaps to direct his activities so as to take account of them. But from an æsthetic point of view, it would be a disaster if this were the only tempo of awareness available to him, since all his sense-qualities would be fragmented into rhythmic successions of their constitutent events, or perhaps of their 'atomic durations'. To the extent that æsthetic enjoyment of 'beauty' and 'harmony' depends on our synchronous awareness of a multiplicity of 'qualities', it would be completely annihilated. The dervish-dance of protons, electrons, neutrons, neutrinos, etc. etc., which the physical scientists imaginatively invite us to contemplate as the 'raw material' of our phenomenal expereince, is of no intrinsic value whatsoever; but its instrumental value is considerable inasmuch as it suggests ways for us to manipulate that material at tempi far more rapid than those to which we habitually pay attention.
These points are well exemplifed in television procedure. The 'raw material', for the receiver' is a 'carrier-wave', a purely linear structural pulsation of electromagnetic intensity at a very rapid 'tempo'. Such a structure still characterises the stream of electrons emitted by the cathode in the 'tube', where it is 'cooked', i.e., 'spatialised', by being submitted to two oscillatory angular displacements; a vertical one at a tempo of 25 hertz, and a horizontal one 625 times as rapid. These reverse the 'uncooking' process which has previously occurred in the television camera, where the 'photographic' field has been despatialised by linear 'scanning'. Behind the screen of the receiver, the 'tempo' of the original 'raw material' is still operative; it is that of the successive activation of adjacent luminescent 'phosphors'. These are of no interest whatsoever to the viewers; nor, for that matter, are the 'tempi' employed in the 'cooking' - especially the horizontal one. All that we viewers notice are quasi-invariances and changes at relatively slow tempi, which are, of course, what we are looking for! But if something goes wrong either with the 'uncooking' in the camera or with the 'recooking' in the receiver, the television engineer will seek to remedy the defect by operations conducted at tempi which he has learned to regard as those of 'electronics'.
Now inasmuch as we have learned to presuppose that an appreciable interval occurs between our 'seeing' and 'what' we see, all our vision is 'television'. Our immediate information, or 'raw material', can hardly be anything other than our awareness, from inside, of goings-on within the matter of our nervous systems, and its 'structure' is far more likely to resemble that of the 'carrier-wave' rather than that of the 'picture'. We no longer have any perceptual access to our raw material, because our habits of 'cooking', i.e. of spatialisation, are formed very early in infancy, long before we learn to speak, although since they have been formed by us, or perhaps by the Transcendental Aesthetic through us, they can be regarded as 'synthetic', even though they are 'a priori' for language. It is interesting to note that when we dream, we employ the same techniques of 'spatialisation' for dealing with raw material of non-ocular origin as we do for our normal 'visual' material, retaining our predilection for patterns which are invariant or change relatively slowly. In 'normal' vision, the pragmatic reasons for this are obvious; there is little use in noticing changes which are too rapid for us to do anything about them! For similar reasons our languages, and even our 'private' visuo-tactile sign-systems, are largely based on 'invariances'. C. S. Peirce defined a 'sign' as "something which stands to somebody for something other than itself", but this is not quite adequate; it is the invariance of the sign which stands for the invariance of something else. No passage of experience can possibly function as a 'sign' until it has been recognised!
The value of 'invariance' for the purposes of both internal and external communication is undoubtedly very great, but it is merely 'instrumental', not 'intrinsic'. Thus if by the word "God" we signify a Being, or Aspect of Being, to which we attribute the greatest 'worthship', there are no grounds for including 'static' eternity among Its attributes. This would entail complete self-satisfaction, which we are far from regarding as a virtue in ourselves; how then can we reasonably attribute it to 'God'? Dynamic eternity, in the shape of an unceasing urge for self-improvement, is far more reasonable, and avoids the generation of any 'problem of evil'. A 'Heaven' like Gœthe's would be unbearably smug without Mephistopheles; "der Geist, der stets verneint" plays an invaluable part in the Universe.
We have already seen that a 'statically eternal' God, as adumbrated in the first of St Peter's statements, must be completely irrelevant to human experience. God's 'eternity' should be regarded as dynamic; any expression of Its continuity could only be in terms of a 'transfinitely' rapid tempo. This very likely constitutes the ultimate 'raw material' of our awareness, and only acquires intrinsic value during the 'cooking', which is our job. At present, thanks mainly to the somewhat disproportionate importance that we attach to verbal and visual signs, we incline towards 'overcooking'; by persistently taking a 'long view' we tend to miss much of the enjoyment attainable by concentrating on the 'present'. 'Paranormal' phenomena, among which we may include 'inspiration', are confined to those who manage to retain contact with 'supernormal' tempi of awareness; in a few exceptional instances, these may even include the 'Transfinite' Itself.
Edward Gibbon had evidently conceived an intense dislike for Christianity. This can hardly be described as 'prejudice', since he had experienced the religion from inside as a member of the Roman Catholic Church, and his historical studies had kept him well informed of its works, from its inception up to the time when he wrote his Decline and Fall. It was his considered judgment that the religion had been, on balance, a major misfortune for mankind. Nevertheless, he had felt obliged to suggest some reasons which would account for the phenomenal speed of its growth during its earliest years. But he was careful to refrain from the slightest suggestion that there might have been some historical justification for it. Seeing that the Gospel story seems to be at least as well documented as many of the reports to which he accords some measure of belief, this attitude is somewhat unreasonable.
His rejection of anything that smacks of the 'miraculous' is almost automatic. It is true that any possibility of a 'miracle' is somewhat awkward inasmuch as it makes long-term planning and prediction difficult, and accurate prediction enjoyed a particularly high standing at the time of the 'Enlightenment', mainly thanks to Newton's physical synthesis. We can reasonably define a 'miracle' as 'a very unexpected event, totally foreign to the sequences habitual in the actual circumstances, and brought about by the volition of a single human being'. An attitude of disapproval of beneficient miracles would seem to betoken an exaggerated respect for the 'uniformity of nature' which is unworthy of a reasonable man, such as Gibbon would certainly have claimed to be. One is led to suppose that his disapproval was due to their repeated association, along with a good many faked 'quasi-miracles', with the Christian religion, for which he had conceived a great aversion - not without substantial grounds.
This essay is based on the assumption that the books of the Gospels and the Acts actually contain a central core which was based on eye- and ear-witness evidence, although this has clearly been embellished by a mass of decorative material on which no reliance can be placed. The accounts of Jesus's life and teachings in the Synoptic Gospels are as consistent as we are entitled to expect, yet not so much so as to suggest deliberate collusion by their authors. They would hardly be likely to invent stylistic peculiarities, such as the constant use of parables and of a fortiori argument, which are not part of the teaching, but of the manner of its expression. And if Jesus was as exceptional a type of man as the available evidence seems to suggest, a conscientious disbelief in his possession of unusual powers is as unreasonable as a totally uncritical belief in them. As Samuel Butler pointed out in The Fair Haven, the central miracle of the Resurrection would suffice to account for the sudden outbreak of activity on the part of his disciples, who had previously given him up as a bad job, and deserted him. Butler's book was not written entirely with his tongue in his cheek; its title was taken from Acts 27:8, and is the name of the harbour where Paul, sailing to Rome, warned the ship's master that it would be dangerous to carry on with the voyage. The thesis of the book was that the central miracle alone was a sufficient raison d'être for the existence of Christianity, and that insistence on the uncritical acceptance of all the miraculous elements might prove its undoing.
Now it is hardly likely that Gibbon would have disapproved of Christianity if his acquaintance with its history had been confined to the first two centuries. Apart from the 'miraculous' beliefs, which he describes ironically as 'sublime' and 'specious', the reasons given for its rapid growth all redound to its credit. We can fairly conclude that its evil consequences only began to be felt when it became 'institutionalised' and accepted as an official religion, when the previously rather vague beliefs had to be formulated as definitive 'Creeds' which were the source of all the subsequent troubles.
Most educated men, especially in the Eastern part of the Empire, were adherents of one or other of the Greek schools of philosophy; Paul's contacts with the Stoics and Epicureans are mentioned in Acts 18. Those particular philosophies were mainly ethical in character, whereas Jesus' teaching embodied a strongly metaphysical element, so that when it was considered desirable to incorporate the Gospel story within the framework of a philosophy, for the purpose of formulating a Creed, a mainly metaphysical one had to be selected for the purpose.
The choice fell on a form of neo-Platonism, closely akin to that of Plotinus. His metaphysic was based on a completely impersonal 'Trinity', namely, 'the One', 'Spirit' and 'Soul', the two latter being essentially aspects of 'the One'. Difficulties arose when the attempt was made to incorporate the 'person', Jesus, into this scheme of things. 'The One' is omnipresent, but formless. 'Soul' presumably embodies some 'form', since it includes 'beauty'. It can perhaps be considered as generated by the activity of Spirit immanent in the 'One' - a kind of 'self-analysis'. All these metaphysical entities were considered as uncreated and 'eternal'. On the other hand, the sensible Universe is generated from 'Soul', and it is possible to attribute this to the activity of 'Spirit' within 'Soul', operating at a level which is less 'sublime' than that involved in the generation of 'Soul' itself. Such a metaphysic is easily applicable to the development of human experience. We assume that it begins as an inchoate totality, a 'chaos' rather than a 'confusion', since it is, initially, a 'whole'. This becomes subject to the analytical activity of the 'Spirit', which begins by dividing 'experiencing' into 'consciously' and 'unconsciously'; the latter is dominant, while the former emerges from it. From 'consciously' there emerges, inter alia, 'luminously', from which a subsequent stage of generation produces 'colourly' and 'spatially'. This may well represent the sequence involved in the development of vision in early childhood. We originally learn to apply these habitual stages of analysis to the material which reaches us via the eyes, but as dreams show, we can also use them to analyse 'internal' material, of which we are normally 'unconscious'.
'Phenomena' are the outcome of synchronous analyses of 'Soul', i.e., 'total experiencing', at an enormous variety of sense-frequencies; the process is closely akin to what is known in mathematical physics as 'Fourier-analysis', which is an application of a similar technique to chaotic phenomenal processes, undertaken so as to be able to formulate generally intelligible descriptions of them. At each stage, a 'One' is envisaged as a Heracleitan 'flux'; the appropriate contemporary analogy, or 'myth', is the 'carrier-wave'.
All these modes of analysis, from that of 'the One' downwards, occur 'eternally', i.e. unceasingly, and 'synchronously', although at different 'levels'. Our awareness of 'body' and 'soul' alike should be regarded as 'processes', not 'things'. The 'body' can only be a very partial aspect of the 'soul', since what each of us regards as the 'public' aspect of his body is no more than his visual and tactile awareness of its surface, and this, when contemplated in relation to the remainder of the 'total' experience that is synchronous with it, is relatively insignificant.
Now the metaphysical core of Jesus' teaching was the doctrine of the immanence of 'soul' in bodily phenomena, and of that of 'the One' in 'Soul'. In each case, the generative agent, or 'begetter', was 'Spirit'. This was the aspect of God that he constantly stressed as being of paramount importance, and which he claimed was immanent in every human soul. He himself had evidently retained an exceptional degree of awareness of the totality of 'soul', which for most of us is virtually blotted out on account of our concentration on conscious sense-phenomena. His mission was to do his level best to convince his fellows that they too could achieve 'life more abundantly' if they would only believe in the possibility. His metaphysical teaching was a combination of precept and object-lesson, and its climax was the Crucifixion, which he undertook deliberately, though reluctantly. At one stage he was afraid that he was going to be unable to carry it through, but the final 'consummatum est', uttered in a loud voice, announced its successful completion. The victory was achieved on Good Friday; the Resurrection had to be postponed until Easter Sunday so as to conform with his pre-announced time-table.
The doctrine of an immanent God was extremely difficult to teach; it was anathema to the orthodox Jew, whose God was unmistakably personal, a kind of invisible tribal 'boss', subject to the usual human affects of anger and jealousy. Jesus therefore sought to demonstrate the 'authority' of his teaching by performing miracles, as evidence of his own exceptional endowment with what Bernard Shaw might have called the 'Life Force'. He combined this display with an ostentatious disregard of the letter of the regulations attributed to the tribal 'boss', though this part of the teaching was ethical rather than metaphysical.
The Establishment was naturally horrified at the suggestion that anyone whose faith was sufficiently strong could follow in his footsteps. With their completely external idea of a 'transcendent' God, this was all appalling blasphemy, and it is notable that the most furious opposition to early Christianity always came from the Synagogue Jews. It is not sufficiently realised that although Jesus' ethical teachings did not differ much from those of the Talmud, the metaphysical side of his theology was diametrically opposed to that of the Jews. The paradoxes of Christian dogma spring from the attempt to combine the two; no sense can be made of Jesus if the Old Testament notions of God are retained. Unfortunately, Jesus made this retention only too easy by an injudicious slip in the choice of his vocabulary.
There would have been comparatively little difficulty in incorporating Jesus' life and teaching into a Neo-Platonic trinitarian metaphysic, but for his most unfortunate use of 'The Father' as a name for an entity which, judging by its attributes, is what we and the Neo-Platonists alike would call 'Spirit'. The name did not seem as inappropriate then as it does to-day, because it was generally believed that the 'soul' entered the womb with the sperm, the woman's function being merely to supply the matter. The obvious etymological link between 'matter', 'materia' and 'mater' expresses this belief.
Here it is necessary to point out a sharp distinction between fertilisation and 'begetting', which I interpret as the introduction of new life. This is not the work of the father, who merely cooperates with the mother in producing conditions which are believed to be favourable for the process. The actual incarnation of new life occurs with the fission of the fertilised ovum. This is the work of an 'occult force' (c.f. 'gravity'!), and can only be ascribed to the Spirit, the 'Lord and Giver of Life'. This applies to all 'begetting'; the physical virginity of Mary was not necessary in order to guarantee a spiritual begetting, as was believed at the time. On the other hand, there are no certain grounds for ruling out the possibility of the fission of an unfertilised ovum as a response to some stimulus other than fertilisation; a-sexual reproduction of this kind has actually been stimulated in some species in which the sexual kind is normal. In fact, painters of the Annunciation frequently depict something representative of a 'cosmic ray' - or of a 'geodesic' with a dove travelling along it - as responsible for the 'begetting', and this is entirely in order. But there are no grounds for supposing that the 'ray' has its origin in the elderly bearded gentleman who sometimes appears (he is an 'optional extra') in the top left-hand corner of the picture. Why should the Spirit be anyone's 'agent'? This 'Father' is a pure fiction, the inadvertent result of Jesus' use of the quite inappropriate word as a 'name'. Fathers are never immanent in their children, nor the children in their fathers; this kind of relationship is maternal rather than paternal. When James Joyce considered the natural relation between father and child, at a time when he was still contemplating entry to the priesthood, he described it as 'an instant of blind rut'. This judgment, though roughly expressed, seems sound enough.
It now appears that the whole muddle-headed notion of the Nicene Trinity is the result of an assumption that anything named 'Father' must be a father; it is parallel to the demonstrably false assumption that anything named black must be black. The meaning of the word 'father' is primarily associated with earthly fatherhood, and the 'heavenly' variety does not seem to possess any of the same attributes or relations.
It was almost inevitable that the immanent 'Heavenly Father' would become identified with the transcendent 'Jehovah' of the Old Testament. Jesus also deliberately linked his life, though not his teaching, with the Old Testament; in order to validate the authority of his teaching, he did his best to act out an eclectic selection from the 'scripts' which had been adumbrated for the 'Messiah' by the Prophets. The key text here is Matthew 26:54, 'How then shall the Scriptures be fulfilled, that thus it must be?' It is inconceivable that this could be a later insertion; the Evangelists generally treat the fulfilment of the prophecies as something quasi-miraculous, and use it to reinforce the authority of Jesus' teachings - as, of course, he intended it to do.
The question now arises:- what was the Messianic function that Jesus was supposed to have fulfilled? Clearly, it was not the nationalistic, political one that most of the Jews had been hoping for.
The answer was provided by Paul, who never met Jesus in the flesh, but had certainly heard some of his teachings as expounded by Stephen and the Apostles, and possibly grasped their metaphysical import. He was a fanatically orthodox Jew and doubtless heavily oppressed, like most orthodox Jews, by the guilt-feelings which are liable to accompany the least breach of any of the complicated ramifications of the Law. On the road to Damascus, he suddenly grasped the tremendous liberation that would be effected by accepting Jesus' metaphysic of spiritual immanence. The feeling of relief was so intense as to amount to a major shock, accompanied by what might be described as 'hysterical' blindness; artists generally depict him as falling off his horse.
It is clear that for him 'salvation' meant, in the first place, liberation from the detailed provisions of the Mosaic law. This was why he was convinced that every Christian should testify to his faith by gratuitously disregarding them as ostentatiously as possible, whenever the opportunity offered; hence his quarrel with Peter at Antioch. He proceeded, again reasonably enough, to extend this interpretation so as to remove the 'sinfulness' of uncircumcision - a tradition which was reputed to go back as far as Abraham. It should be noted that up to this point there was no question of remitting punishment for sin; he was actually abolishing the sins themselves. This would seem to be the proper interpretation of 'in remissionem peccatorum'.
Now Jewish 'history' never went back beyond Abraham; the opening chapters of Genesis were always treated as myth and parable, as they still are to-day. The story of 'original sin' was never taken very seriously. Paul could have treated it as he treated the rest of the sins, in which case he would have interpreted Jesus' mission as the complete abolition of the sense of 'sin' itself - and if God is immanent in the soul, this is by no means unreasonable. Instead, he interpreted the Crucifixion as a propitiatory human sacrifice, made with the object of remitting the punishment inherited by all mankind for Adam's legendary 'sin'.
Is it far-fetched to suggest that this is likely to be one of the teachings which Peter described as 'hard to be understood, which they that are unlearned and unstable wrest, as they do the other Scriptures, unto their own destruction' (2 Peter 3:16)? This protest, by the 'plain man', has a very convincing ring about it. Nevertheless, Paul's forceful character and intellectual ability ensured that his interpretation of the story was accepted as the 'official' one.
Jesus' 'Heavenly Father', videlicet, the Spirit, can be identified with the 'Creator of Heaven and Earth', provided that we postulate a 'raw material' which is not 'nothing'. 'Nothing' is unthinkable in any case. We can regard ourselves as experiencing 'No thing', provided that 'thing' is accorded its usual connotation of 'a bounded passage of experience', but 'experiencing nothingly' is a non-starter. Descartes evidently used 'thinking' to express 'experiencing at a minimum level of intensity', and the validity of his 'cogito' derives from the nonsensicality of 'thinking nothingly'. Let us then interpret the 'One' of the Platonists, that is to say, 'Godstuff' or 'Worldstuff' in the raw, as a Heracleitan flux of absolutely continuous change. This will be immanent in every one of the rhythmic sequences begotten within it by the Spirit, by a mode of analysis roughly comparable to the 'Fourier' type. This is analogous to the analyses of the 'carrier-wave' of television that occur within the receiver. The 'One' can clearly be equated with what Jung, in his Septem Sermones ad Mortuos termed the 'Pleroma', and all 'creation', or rather 'begetting' is effected by self-analysis within the Pleroma, which issues in 'structure', or 'form'. Every creation is, in a sense, less than the Pleroma, notwithstanding that the Pleroma itself is immanent in it as its basic 'stuff', but it cannot possibly be qualitatively inferior to it, since the rate of change in the Pleroma is such that it can have no form at all. Thus unless we are prepared to condemn all creation as a mistake - which seems to be a likely interpretation of the 'sin against the Spirit' - we cannot possibly regard reabsorption into the 'One' as a 'summum bonum'.
When synchronous analyses at lower levels give rise to objectionable discords, we do well, from time to time, to abandon the analysis at the lowest levels and attempt to re-sensitise ourselves to the subtler structures to which we doubtless had access during the earlier stages of our development; this is a 'backward' movement in the direction of the Pleroma, but a return to 'square one' can only be contemplated in a case of abject, utter despair. This is expressed in the Requiem Mass by the words: 'Ne absorbeat eas Tartarus, ne cadant in obscurum'; it reappears in Peer Gynt's reaction to the 'Button-Moulder', in Castaneda's Mexican sorcerers' efforts to circumvent the 'Eagle', and in the Baker's dread of the 'boojum' in Carroll's 'Hunting of the Snark'.3 A partial return should always be regarded as 'reculer pour mieux sauter'.
3. The 'boojum' was a variety of 'snark', which, in keeping with Humpty-Dumpty-an usage, should probably be interpreted as 'Snake-ark', i.e., a refuge from original sin.
We are now in a position to show how the historical Jesus can be quite easily fitted into the framework of a Neo-Platonic philosophy. The 'One' - the Pleromatic raw material - constitutes the ''virgin Mater', on whom the Spirit begets, in 'successive' generations, 'Soul', 'Person', and finally the phenomenal Universe, including the 'body'. Jesus was an exceptional, perhaps unique 'person' who retained complete awareness of 'soul', or possibly regained it, since he did not commence his active mission until he was about thirty years of age. His mission had nothing to do with 'Original Sin'; its sole aim was to enable others to share his own experience of 'life more abundantly'; the ethical and metaphysical aspects of his teaching were alike directed towards achieving this goal.
The manifold evils that have undoubtedly resulted from so-called 'Christianity' stem from a gross mistinterpretation of the Gospel story as a kind of 'sequel' to the Old Testament, instead of the refutation that it should have been. For this Paul is primarily responsible, although Jesus himself made a major contribution towards it, in the shape of his unfortunate choice of terminology, and of the Messianic play-acting which he adopted for what may be regarded as 'propaganda' purposes.
- Shalom & Welcome! - 
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