"We lack words to say what it is to be without them."
P.F. Strawson, Bounds of Sense
Professor Strawson's dictum is a typical expression of the reluctance of philosophers of the linguistic school to make any attempt to get behind language to the pre-verbal thought-processes which must underlie its foundations.
This essay is an attempt to show that the task is not really a difficult one, the main obstacle to bridging the gap between pre-verbal and post-verbal thought being an almost complete reversal of emphasis, which occurs during the establishment of verbal habits.
Such a reversal is, indeed, no more than we should expect. The main taks of post-verbal thought is the formulation of communicable descriptions of portions of the experiential flux in terms of words and symbols which stand for concepts.
The bulk of these concepts - certainly all the basic ones - must clearly have been formed before speech can begin, so that it is clear that pre-verbal thought must be mainly concerned with dissecting them out of the experiential flux.
The two-types of thought-process are therefore virtually opposite in direction, like those of integration and differentiation in mathematics.
Philosophical problems arise from the mistaken assumption that the later, post-verbal thought-process is fundamental. Once this view is rejected, many of them can be quite easily solved; the origins of the subject-predicate structure of language and of syllogistic logic are dealt with in this essay, and I believe that many others can be resolved in similar fashion.
I shall assume that all experience includes direct acquaintance with the following elements: change, changes in the intensity (tempo) of change,1 and judgments of importance, derived purely and simply from likes and dislikes - especially the latter. I trust that nobody will seriously dispute that these elements form part of the empirical material of infantile consciousness.
1. We use the word "intensity" when a change is regarded as one, but "tempo" when we think of it as sequence of "atomic" events. The "tempo" (frequency) with which the latter occurs is clearly equivalent to the "intensity" of the change, regarded as a whole. Cf. Planck's quantum equation, e = hn.
From a linguistic point of view, we find it convenient to describe experience in terms of "states" of comparative invariance, punctuated by "events", i.e. brief periods of intense change.
Now in direct experience it is events which are of primary importance; conversely, it is states, i.e. situations of relative invariance or gap indifference, which are symbolised by the repeated use of the "same" word or symbol. Indeed the assumption that this is the case is precisely what renders a word or symbol useful for communication purposes.
It is clear that every "event" is a transition, or experienced difference, between the states which it conjoins; it is also clear that on account of the need for invariance in its reference, no single word or symbol can stand for a single event, which is a close approximation to "absolute" change.
Single events are represented in language, but only by the transitions between the words and symbols, each of which stands for some kind of invariance. The reader or hearer is expected to repeat the thought-transitions in an order which does not differ importantly from that which the word-sequence is intended to express. The expected order is that which conforms to the grammar and syntax of the language, of which logic is the schematism.
Conventional logic has laid stress on the invariant property of words and symbols, making "substance" and "identity" the basic categories. If, however, we regard the event as of primary importance, we will maintain that every concept originates in an event, namely, the initial awareness of an important difference,2 and that this difference constitutes the basic meaning of the concept.
2. Hume treated his "impressions" as simple and unanalysable; the analysis suggested here turns them into suitable raw material for "knowledge".
Mental inertia will ensure that any subsequent event which does not differ importantly from the memory-echo of the first act of awareness will be subsumed under the same concept; it always "costs us too much pains to think otherwise", and "Entities are not to be multiplied without necessity". The judgment expressed by these celebrated dicta appears to be the common judgment of all human beings.3
3. The normative "entia non multiplicanda sunt" becomes an empirical generalisation, viz., "entia non multiplicantur", generally applicable to human judgment in the same way as our dislike of violent impacts, burns, etc. Russell made extensive use of it, but, as far as I know, never inquired into its status. I am treating it as part of our inborn "prejudices", which he correctly diagnosed as the source of the "synthetic a priori".
Necessities, however, do occur, even in the post-verbal stage of thought, and prompt us to take pains to multiply entities. They occur every time that an increase in our sensitivity obliges us to attach importance to a difference which we have previously ignored. Every time this occurs, the newly recognised difference generates a fresh concept. A repetition of the process within the field of this concept may in turn give rise to a new generation of sub-concepts, and so on.
By the time that speech begins, this proliferation of concepts by multiplication-by-fission has already attained quite an advanced stage.
The vital transition from direct experience to its linguistic expression is always initiated by the learning of individual words by ostensive definition. It is therefore instructive to determine just what factors are invariant in the references of words so defined. We find, in fact, that the invariance is always concerned with some type or property of an event. "Identity" of reference is initially secured by the assumption of quasi-simultaneous acts of awareness in the experiences of teacher and pupil, signalled - though not described - by the use of the word "that!" or the equivalent gesture.
As Russell pointed out, the ultimate egocentric particular, which excludes everything else in private experience, is "this". The use of "that" is to denote an event which is other than "this"; in private experience, it can only refer to a remembered event, hence "this is/that was". But when "that" is used ostensively, the separation is spatial rather than temporal in character, the word referring to a simultaneous "this" in another experience, which will exclude everything else in that experience. Simultaneity is an important respect in which the "thises" are presumed to be invariant. This applies also within private experience; events which cannot be temporally separated are part of one "this".
Both "thises" must also be assumed to be important, otherwise we cannot be confident that they are acts of awareness. The combination of simultaneity and importance establishes a gap-indifference as between the communicants and bestows invariance on the reference - Frege's "Bedeutung" - for the word which is being defined.
In actual practice the ostensum generally consists of a visual image, bounded by sharp colour-contrasts. Its importance is derivative; we can fairly well assume that by the time a child learns to speak it will have experienced plenty of "thises" which are simultaneous abrupt changes of sight, touch, muscular feeling and sometimes hearing, on making contact with solid objects, and it will ordinarily interpret most sharply-bounded images as signs for the possibility of tactile and muscular events, which are of primary importance.
The primary importance of such contacts, which is exclusively tactile and muscular, is initially communicated directly by way of pain-behaviour.
But the meaning of a word extends far beyond the assurance of a common Bedeutung.
Take, for example, the simple word "chair". This expresses the widespread recognition of the difference distinguishing those events conceptualised as "sitting down" from all other contacts with material objects. This difference is the "Sinn" of the word.4
4. Anybody who doubts this statement should test his own reaction to the imaginary ostensive definition of a sharp vertical spike as a "chair"!
The definition will only be valid for those who share the judgment of the importance of the difference concerned. Repeated use of the word also demonstrates invariance within each private experience; separate instances of "sitting down" are not judged to differ importantly.
This particular type of contact with an object - in company with a good many other types - must have been differentiated out of the more general concept, which gives rise to the Bedeutung, well before speech begins. The general concept retains its validity, since all contact with surfaces is important, but has become a class-concept by internal subdivision.
The function of the concept "chair" is, in fact, the exclusion of all types of contact which differ importantly from the experience of sitting down.
Spinoza's famous dictum needs re-stating in its stronger, modus tollens form: "Sine negatione non est determinatio". Every concept originates in an event, the awareness of a new type of difference, which is echoed in memory on account of its importance. Subsequent events which are not judged to differ importantly from the empirical archetype are automatically - as a rule even unconsciously - included under the concept.
The invariance of a type of event is, for the most part, equated with the invariance of the state which immediately follows it. Events are not instantaneous, and always include the inception of the subsequent state. As soon as this is established in consciousness, the event fades in intensity to the memory-level, although continued awareness of the state can well be interpreted as the repetition of the original act of awareness at constant tempo.
The close association of the type of event with the succeeding state is clearly demonstrated in language by the use of verbal participles as adjectives standing for the states which follow the type of event represented by the verb, and, conversely, by the construction of verbs of becoming from the adjective which stands for the final state.
Thus, a man who has sat down is "seated"; a sky which has "reddened" is red. In cases where the verb is derived from an adjective which represents the state preceding the event, the departure from the usual procedure is always indicated by a negative prefix, e.g. "dislocate", "dehydrate", "unfrock", etc. Even in this case, the past participle is still used to stand for the state which follows the event; the joint remains dislocated, the (ex)-priest unfrocked.5
5. Compare the meanings of a sentence such as "the door is closed" when used (a) as a description and (b) as a stage-direction.
The present participle stands for the state of change which follows the event which initiates it. This is the form in which verbs have to be ostensively defined; a "timeless" present is indescribable. The present tense is always interpreted either as continuing or as habitual, even in languages which do not distinguish these uses grammatically like English.6
6. "Performatives" are only an apparent exception. The umpire's "Out!" and the priest's "I pronounce you man and wife" do in fact convey information as to the state which succeeds their utterance.
Once we accept the principle that the basic function of a concept is to differentiate and exclude rather than to assimilate and include, the problems of Universals and of the subject-predicate structure of language are easily solved.
The "problem" of Universals only arose because the Greeks, understandably elated by the success of "deductive" reasoning in geometry, chose to regard the sophisticated, highly differentiated geometrical "forms" as their archetypes, instead of such crude, vague differentials as "hard", "dirt", "red", etc. Plato did indeed have second thoughts in the matter, which he expressed in the Parmenides, but his earlier views prevailed. It was concepts such as the "straight line" which were thought to be "simple" and incapable of analysis; consequently, the character of all complex entities must be analysable into the shape of their 'triangles'. This is the cosmology set forth in his highly influential Timæus.7
7. This may sound fantastic, yet Einstein's attempt to formulate a description of the physical universe in terms of the 'curvature of space-time' is no more than its modern, sophisticated equivalent.
We now know that his views were quite mistaken. The "self-evidence" of straightness has completely vanished, and we cannot define it better than by referring it back to an empirical archetype, which was probably something like the thread from which a spider was hanging on a windless day. The concept was formed by the men who first noticed the difference between this and other shapes. The practical uses of material replicas of this and other geometrical shapes - the Sun's disc is the obvious archetype of the circle - have made them so familiar that their origins have been forgotten. Among primitive peoples, however, many of them have not yet been conceptualised!
Once we abandon the idea that any universal represents a simple, unanalysable "idea", we can easily define it in terms of difference.
We have seen that every initial awareness of the inception of a state, which differs importantly from any that have previously been experienced, creates a concept. Subsequent events which do not differ importantly from the archetype are included under the concept.
The repeated use of the "same" universal, i.e. separated instances of words which do not differ importantly, symbolises this absence of important difference from the empirical archetype, which itself represents the initial experience of an important difference.
The principle of the subject-predicate relationship, in cases where it is felt to be necessarily asymmetrical, is quite simple. The rule is that the concept or concepts which make up the predicate must never exclude more than those which made up the subject.
"That!" is obviously the ultimate logical subject, since it stands for a "this" which excludes everything else in the experience of each person who hears it. The subject-status of the demonstrative pronoun is carried over to its use as a demonstrative adjective, and confers subject-status on anything that it qualifies - or, rather, quantifies, since it obviously asserts its existence.
Proper names are given to persistent objects, with temporally gap-indifferent boundaries, which are so complex that they are believed to differ importantly from everything else. Any attempt at their adequate description would be intolerably prolix. They have predicate status only to 'That!', which could well stand for a single act of awareness of their reference, including all the others.
Their subject-status is not felt to differ importantly from that of any description which stands for any class-concept which defines a unit-class. "Scott is the author of Waverley" and "the author of Waverley is Scott" are both accepted, although the former is not, strictly speaking, correct; it would not be an adequate answer to the question "Who is Scott?" This is because "author of Waverley" excludes the whole of the reference of "Scott" except his actual writing of the book.8
8. Scott's "identity" - i.e., the distinctive and roughly invariant distinction between him and others - could have been established, during his life-time, by means of his finger-prints. Since his death, however, the only way of delimiting the use of the word "Scott" is to regard it as a predicate, applicable only to events within his biography.
Editor's note: Russell's major difficulty was not that of establishing the 'identity' of 'Scott', but that of 'the individual' correctly named as 'the author of Waverley'. Although the historical 'facts' most closely associated with this particular problem appear never to have been noticed by Solomon, their nature is already clearly apparent from even a single reading of the book itself, which, we may confidently presume, was readily available to him as a boy.
Here, by way of example, I refer to Macmillan and Company, Limited, of London's 1910 copyright reprint of Waverley with "Introductory Essays and Notes"by Andrew Lang as a volume within the Border Edition of "The Waverley Novels" originally collectively dedicated by their previous and until-June-1900 publisher to the Hon. Mrs. Maxwell Scott of Abbotsford and her children, Walter, Mary, Michæl, Alice, Malcolm, Margaret, and Herbert - the Author's great-granddaughter and great-great-grandchildren, but on 1st January 1829 collectively dedicated by Walter Scott of Abbotsford himself to the then King's Most Gracious Majesty agreeably to his gracious permission, on which occasion this 'Walter Scott', whom the afore-mentioned details of public record quite properly incline us to identify as both the natural and legal great-great-grandfather of another 'Walter Scott' who is certainly not the author either of Waverley or of any other novel in the Waverley series, informed His Majesty of certain suppositions previously entertained by a person referred to in that dedicatory letter as 'The Author of this Collection of Works of Fiction'.
Andrew Lang's London, September 1892, "Editor's Note" in this same 1910 reprint, which categorises Sir Walter Scott's own "Introductions" as 'delightful', also quite specifically states that they were written 'hastily' and 'with a failing memory', and that they had occasionally been corrected, not by Scott, but "by Lockhart himself", adding that, although some "fragments of information may be gleaned from Sir Walter's unpublished correspondence", it is Lockhart's Life of Scott that "must always be our first and best source", assuring us for good measure - and if Russell found this particular circumstance especially enigmatic, I don't believe he would then have found himself alone - that "the twenty-four large volumes of letters to Sir Walter, and some other manuscripts, which are preserved at Abbotsford… yield but little of contemporary criticism or remark, as is natural, for Scott shared his secret with few."
What was this 'secret'? Was 'he' not 'the author of Waverley'? Was 'he' not the natural progenitor of each and every one of the children, grandchildren, great-grandchildren and great-great-grandchildren legally 'his'? Was 'he' actually other than the natural as well as the legal heir of his presumed 'father'? One is scarcely surprised that Russell asked his question!
Attempts to answer it are hardly helped by an unsigned Abbotsford, January 1829 "Advertisement" prefaced to this edition of Waverley, not however precisely because it is Waverley, but because it is part of "the voluminous series of Novels which pass under that name". Now, quite evidently, we find ourselves placed in additional and very considerable uncertainty. Which particular novel, if any, among that 'voluminous series' passing under 'that name' is the original and authentic novel to which 'that name' most properly and originally belongs?!
The unnamed author of this "Advertisement" - for all we are from its contents entitled to suppose regarding his identity is that he was resident in, or at least visiting Abbotsford when he wrote it - also assures his readers that "the course of the events which occasioned the disclosure of the Author's name" have "in a great measure restored to him a sort of parental control over these Works".
As readers we, quite naturally I think, feel we mustn't fail to take into account the aura of persisting uncertainty that is so unmistakably conveyed to us by the expressions "in a great measure" and "a sort of", and so we are pleased to find that the same "Advertisement" additionally contains a statement that, pari passsu with the publication of the rest of this series, "The Author also proposes to publish… the various legends, family traditions, or obscure historical facts which have formed the groundwork of these Novels, and to give some account of the places where the scenes are laid, when these are altogether, or in part, real, as well as a statement of particular incidents founded on fact."
But then we aren't very much the wiser, are we? I certainly wouldn't know where to start looking for finger-prints!…
Read the much more detailed "General Preface" to Waverley for yourself, if you wish; it is certainly interesting, but I don't think you'll find it makes answering Russell's question any easier! Solomon on this occasion has, I believe, not even begun to address any of the many fascinating questions that originally gave rise to Lord Russell's now notorious interest in the matter.
Words standing for material objects have subject-status relative to words which stand for single qualities, since a surface is the locus of changes of quality in several senses at once; they therefore automatically exclude more than any word which stands for only one. Similarly, words describing primary qualities, which are at least approximately corroborated by more than one sense, have precedence over secondary ones; we can speak of a 'white circle', but not of a 'circular white'.
The most interesting and instructive case occurs when there is a one-way subject-predicate relationship between alternative words either of which can be used to stand for the same concept-forming difference.
We have already seen an example of this in the differentiation of contacts with chairs from those with objects in general; "chairs are objects" is correct, but "objects are chairs" is not, since "chair" excludes more than "object". This particular differentiation, however, must have occurred during the pre-verbal stage and we are unlikely to remember any period when it was not recognised as important. We will therefore examine an instance which usually occurs after speech-learning has begun; in this instance, most of us will retain some memory of a period previous to its occurrence.
"Crimson is red" is correct, whereas "red is crimson" is not.9
9. N.B.: 'That red is crimson' is correct, for reasons given above. 'Some red is crimson' implies that the proposition 'That red is crimson' has occurred at least once.
The concept "red" is formed during the pre-verbal stage, simply because marked colour-transitions, often ending in an act of awareness of this type of colour, are important in delimiting the surfaces of objects, which are themselves the source of the primarily important tactile-muscular sensations.10 On the other hand, no imporance is attached at that stage to the minor variations which accompany transitions within a "red" area.
10. Primary colour words are chosen according to circumstances; the Navajo do not distinguish between green and blue, but have two words for black!
These first become important when a visual æsthetic begins to develop. The increase of colour-sensitivity necessitates the conceptualisation of the difference between "crimson" and other types of red.
Some people may fail to attach importance to the difference, but for those who do, the meaning of "crimson" will be the memory of the first occasion on which they were aware of the importance of a transition from some other kind of red to that particular shade. They are unlikely to remember many details of the actual occasion, but they will remember a time when they were not aware of the difference, so they can be confident that such an event did actually occur.
Since the original differentiation was between "crimson" and some other kind of "red", it is clear that their archetype of "crimson" will differ less from that of "red" than from that of any other colour-word.
Thus the proposition "Unless a colour can be called 'red' it cannot be called 'crimson' ", stemming as it does from a directly experienced event, will be accepted as analytic.
The same process gives rise to analytic contradictions, e.g. "If any colour can be called 'crimson', it cannot be called 'scarlet'."
The original concept "red" has now become a class-concept by multiplication-by-fission. It is clear that there is no theoretical limit to the repetition of this process, but the adverse tendency expressed by Occam's Razor limits its occurrence to the occasions when it is necessitated by an increase in our process of discrimination.
These analytic propositions quickly become rules of language, which can be used as major premises in syllogistic reasoning; our addiction to this type of reasoning is strong evidence in favour of the theory that pre-verbal concepts are actually formed by the progressive differentiation of an originally integrated but inchoate experience.11
11. James' "Blooming, buzzing, confusion" is almost certainly a misnomer. There can be no "confusion" until differentiation is well advanced. This is a typical example of the misapplication of a sophisticated, post-verbal type of thought to a pre-verbal type of experience.
But we tend to overlook that the form of a syllogism is no guarantee of its validity unless the major premise is a rule of language; otherwise, its conclusion is always liable to be false.
For example "All men are mortal" is not such a rule, and many people believe that the statement is falsified by the cases of Enoch and Elijah. The truth of any conclusion reached with the aid of such a major is therefore suspect from the start.
The use of the conditional form "If all men are mortal"12 in logical argument is open to similar objections. "If all men were mortal" could be acceptable as a suggestion that the categorical form would be valid if the major were made a rule of language! This is unlikely, since there is no genetic relationship between the conjoined concepts, as there is between "red" and "crimson", which gives rise to a language-rule almost as a matter of course.
12. The status of the conditional form is clarified by substituting "when" for "if", e.g., "When all 'men' are 'mortal', and 'Socrates' denotes a 'man', we can safely infer that 'Socrates' denotes a 'moral'."
By the time that speech begins, concept-differentiation has gone so far that it is not easy to find simple examples of its post-verbal occurrence except in directly æsthetic fields like those of colour and taste. Any new awareness of an important difference - generally the work of a handful of exceptionally gifted men - usually applies to a good many species which have already been conceptualised on account of differences from altogether different fields of discourse.
The class to which the newly-discovered difference gives rise is therefore constructed by assembling such species as differ from the rest of experience in the respect which defines the class-concept.
"Mammals" is an obvious example of such a class, defined by means of a class-concept which represents an important and diagnostic difference. But the class of mammals will comprise a list of species which were already differentiated before the class-concept came into existence! The discoverers - or inventors - of the class-concept had to convince the man in the street - or his educators - that the diagnostic difference was more important than the intra-specific differences defining the members of the class. Only then could such a proposition as "All whales are mammals" become a rule of language; this actually asserts the prima facie unlikely proposition that the difference between whales and sharks is more important than that between whales and mice!
We can now distinguish clearly between analytic and synthetic methods of class-formation.
A class is formed analytically when the single concept under which it was included is sub-divided owning to necessities arising out of a finer sense of discrimination. The original concept - which becomes a class-concept - is temporally antecedent to the member-concepts.
A class is formed synthetically when its differentiating class-concept has been defined later than the concepts which differentiate its members.
Only in the first instance is there an a priori logical connection between the class-concept and the member-concepts; in the second case their defining differences may be drawn from altogether different fields of discourse.
It is only in the case of post-verbal concept formation that the name for a concept can be acquired at the same time as the concept itself.
The name attached to pre-verbal concepts, learned as they are from adults, tend to be those for sub-concepts, far more specialised than the general one to which the child attaches them.
For instance, a child who learns the word "chair" in this country will regard it as a suitable name for any object commonly used for sitting on, although the word, for an adult, differentiates objects which give dorsal support from other kinds of "seat".
It is because the name for the general concept is so often learned later than those for the specialised sub-concepts that it was ever possible to suppose that the general concept arose by abstraction from the specialised ones. It is clear that this order of word-learning is characteristic of synthetic class formation, which is overwhelmingly predominant in the post-verbal stage.
This is why the counter-example of colour-concepts is so crucial. But a little reflection will suffice for the reader to convince himself that the concept "mammal", like the concept "crimson", must have originated in the initial act of awareness of the importance of the difference denoted by the word.
The origins of logic in analytic class-formation have been so widely overlooked that a philosopher like Russell can concern himself entirely with synthetic "classes", erected by the random collection of individuals. Yet, in his famous definition of number, 'The Class of all classes similar (numerically) to a given class', the first instance of the word is a genuine class-concept, differentiating the method of numerical comparison of groups from any other method. The second and third instances simply stand for groups which are compared.
Russell shows little awareness of the difference between the differentiating class-concept and the class assembled with its aid, and his use of the word in his Introduction to Mathematical Philosophy is frequently an unintelligible hybrid of the two meanings.
A definition of number on Russell's lines, but starting with differences as empirical material, would run:
One-one correspondence between groups can be verified by a method involving the simultaneity of events. If one member at a time is simultaneously eliminated from the groups which are being compared, one-one correspondence is established by their simultaneous annihilation.
Arithmetic in fact assumes that if (0) + 1 + 1 = 2, then 2 - 1 - 1 = (0), in other words, that there will be one-one correspondence between the stages of the one-by-one construction of a group and its one-by-one breakdown.
This requires that the entities comprising the group shall possess the following empirical properties:
The archetype which best satisfies these conditions is clearly the standard solid, contained within a persistent, closed surface. Arithmetic and algebra are in fact the schematism of important types of transition between types of compresence of such entities as do not differ importantly from standard solids in these respects.
The logic which results from the accordance of epistemological primacy to difference can be summarised as follows:-
We first learn to use words for indicative purposes, and our rules of language are established so that it is efficient for that purpose. But we very soon discover that they make excellent play-things, since every verbal sequence which is not self-contradictory, and therefore meaningless, evokes a corresponding thought-transition.
This need not correspond to any event that has ever been experienced at the full peceptual level of intensity; it may neverthless be judged to be important, and, if so, will set up a memory-echo of its own, which may be distinctive enough to be conceptualised and provided with a word to stand for it.
Human inventiveness largely depends on this power of word-combination to suggest new kinds of compresence. Many of these are translated in terms of material states, and give rise to events at the full perceptual level of intensity. Sometimes this materialisation proves to be empirically (but not logically) impossible.
The main philosophical problem here concerns the concept of existence.
Should events corresponding to these verbal transitions be said to exist, unless and until they have been experienced at the full perceptual level of intensity?14
14 Did the 'Concorde' exist while it was only in its designer's mind?
Commonsense says "No!", and we are probably well advised to respect it. In this case, Meinong was right to invent the word 'subsistence' to denote the status of such event-sequences before they have been experienced at the perceptual level of intensity. It is the drastic difference of experienced intensity which distinguishes "existence" and "subsistence" as sub-species of "experience".15
15. I suggest that the referent of a description should only be said to "exist" when it has been experienced at the highest level of intensity that the description could imply. Abstract entities can be said to "exist", because we only expect to experience them at the "mental" level; "golden mountains", on the other hand, do not, since the necessary tactile "mountainousness" has never been experienced concomitantly with visual goldenness. Editor's note: Without entering into the particulars of Meinong's life and work, it is, perhaps, well to remember that the terms subsistere and subsistentia already feature in late-scholastic philosophical and theological writings.
If we adopt this view, we must be careful to avoid the mistake of identifying an image with its object. When a friend shows us a photograph, announcing 'That is my wife', he is indeed showing us an object, and we can verify this by the simultaneity of visual and tactile-muscular events when we make contact with it. But the colour-contrasts shown on the image provide no tactile correlate when our fingers cross them, as the surface of the lady herself would do; our friend's description of the object is, in fact, false.16.
16. This type of falsehood is accepted as a matter of course. Ostensive definition would be too laborious if every visual ostension had to be accompanied by its tactile correlate. The Balniborlians could perfectly well have substituted pictures of the objects under "discussion" for the objects themselves.
This visual image certainly exists, but its tactile correlate, a necessary component of an object, only subsists at the memory-level. Substitute a verbal description for the photograph, and it is the sound of the words, or their written appearance, which actually exists.
In this case the description, a photograph, is being used indicatively, but it is clear that a description of "photograph" - quite easy to fake - of "The Golden Mountain", which only exists qua words or image, will evoke a tactile response at the subsistence level. There is no imporant difference between the two cases.
The rejection of "absolute" identity involves the rejection of the concept of "absolute" Truth. Just as "identity" becomes "absence of important difference", so "truth" becomes "absence of important falsehood".
"Correspondence-truth" requires that the psychological impact made by the passage from an experienced event, or its memory, to the memories evoked by the statement describing or predicting it17 shall be negligible.
17. An inventive design is a prediction; the Concorde has turned out to be "true" to the intentions of its designer.
The event is "subject" to the statement's "predicate", almost always including detail additional to that mentioned in the statement.
In the case of "coherence-truth" the statement-memories are the "subject", and the memories evoked by the complex of statements already accepted as "true", and using the "same" words, form the "predicate". Whenever the transition from the statement-memory to the background-memory makes no psychological impact, the coherence of the language is corroborated.
To be generally regarded as "true", a statement must be free from important falsehood in both respects, but correspondence alone suffices for the verification of statements employing only "terms of first intention (Occam)".
Correspondence-falsehood makes a far greater psychological impact than coherence-falsehood, since it is experienced at the full perceptual level of intensity. Coherence-falsehood is experienced at the much lower memory-level, and can often be easily eliminated by a minor modification of the rules of language.
Verbal and symbolic representation is in fact a mere "epiphenomenon" of direct experience, generated, for the purpose of communication, by the human judgment.18 The attachment of supreme value to the "Truth" attributed to certain sectors of this epiphenomenon by philosophers ever since the time of Plato is absurd, and is largely responsible for the mass of absurdity which characterises much philosophical writing.
18. Even visual "percepts", until a specifically visual æsthetic has developed, are no more than epiphenomenal signs for tactile experiences; these are of primary importance on account of their far greater intensity.
The estimate of the truth of a statement is obviously relative to the sense of discrimination of those who use it.
As we have seen, the use of repeated examples of the "same" symbol (note the inverted commas, which we would feel no inclination to use when referring to different ones) is intended to symbolise the lack of important difference between their references.
Thus, although an artist will not repudiate the use of the word "red" to describe the colours of both pillar-box and peony, he will recognise that this usage is to a certain extent false, since it fails to express the difference between them. He nevertheless accepts it, since he remembers that he himself found it adequate during the earlier stages of his development, and also because to deny it would be to assert an even greater falsehood, namely, that the colours differ more from his memory-archetype of "red" than from that of some other primary colour-concept.
It is clear that the incidence of our judgments of this type of falsehood is bound to increase with every improvement of our sense of discrimination.
Hence the perpetual demand for greater accuracy, for the employment of an ever-increasing number of predicates - each effecting an additional measure of exclusion - in our descriptions, or for the sub-division of existing predicates into bundles, each sub-concept excluding more than the parent-concept.
We may well wonder how far the intrinsic value of truth justifies us in extending this procedure!
The most fanatical devotees of "accuracy" are the physical scientists, men who have attained a very high sense of discrimination within their own field. The conjectured invariances and uniformities which they seek to express symbolically are high-order differentials, well outside the range of ordinary language.
Language symbolises no differentials of higher order than the second; substantives and adjectives symbolise invariant states, verbs, invariant states of change, and adverbs, invariant states of states of change.
Mathematics, starting with symbols representing familiar types of transition between certain familiar modes of compresence exemplified by standard solids, has produced a language capable of symbolising differentials of a very high order. It is particularly well adapted to the needs of the physicist, since his "basic statements" are pointer-readings, which are precisely - modes of compresence of standard solids!
But ordinary language, used in accordance with the laws of grammar and syntax needed for descriptive accuracy, is a quite unsuitable medium for expressing the finer nuances of direct experience. Bergson's criticism of the "intellect" is in fact, a criticism of language; the presupposition of invariance in the reference of the "same" word or symbol, essential for the communication of "solid fact", restricts it to a cinematographic technique when it comes to symbolising the fluid transitions of feeling.
We can partly overcome this deficiency by the free use of literary invention, poetic imagery, metaphor and allusion; indeed, Plato himself partially grasped the situation - his "Socrates", in the Republic, asserts that the higher subtleties have to be adumbrated as myths. Unfortunately, he described these subtleties as "Higher Truths".
But there are no "Higher Truths"! Truth is supposed to be accessible to all, and the need for its general intelligibility restricts the vocabulary of "true" statements to words expressing the crudest and most obvious differences, which can be relied upon to have importance for all, incuding the least discriminating, who are able to use the language in which they are expressed. This practically confines it to the realm of solid fact, in the most restricted sense of the word.19
19 Cf. Russell: "Naïve realism gives rise to physics, and physics shows that naïve realism is false, therefore it is false." This argument is only sound if naïve realism is bound to give rise to physics. This is only the case where our dominant interest is in increasing the accuracy of our communication of solid fact. But most direct experience is anything but "clear and distinct", and ordinary language communicates it better than that of physcis!
The extremely high valuation of truth in Greek times stemmed from its practical triumphs in the realm of solid fact - to wit, geometry. Since the 17th century the practical success of physical science in the same field, aided by the development of a powerful new technique of symbolic representation, has reinforced this tendency.
Unfortunately, it has also led to the attribution of supreme value to what is unchanging or, in theological terms, "eternal". This valuation is surely a mistake. It is true that extremely rapid tempi of change are always unpleasant; the imporance of the surfaces of solid objects is first learned by the pain of bumping into them, our first experienced "event" being the slap administered at birth to set us off crying and, therefore, breathing. But it is not true that our highest enjoyments are experienced during dreamless sleep or anæsthesia, which are the closest approaches to changelessness within our experience.
Intense enjoyment and pain are very close to one another, and we probably experience our highest enjoyments when the tempo of change approaches the margin of the intolerable. As Blake said, we never know what it is to have enough until we know what it is to have too much.
The reaction against "too much" change has resulted in the over-valuation of "none at all" - a tendency which has been powerfully reinforced by the mistaken view that our linguistic habits of thought are fundamental. Philosophers who have reacted against the "static" view of experience, such as Heraclitus, Nietzsche and Bergson, have tended to go to the opposite extreme, and to over-rate change for its own sake. This also is a mistake; we can, and often do, have too much of it.
I hope it will be clear that this dissertation on values is not irrelevant to epistemological considerations, my whole thesis is that most epistemological problems, and probably many ethical and theological ones as well, stem from the exaggerated importance that has been attached to invariance on account of its value - which I do not for a moment dispute - in the verbal and symbolic communication of solid fact. But in pre-verbal experience, where the source of our thinking habits must be thought, invariance is of minimal importance; it is only the new that is news!
Conclusion
My answer to those philosophers who seek to confine the subject to the investigation of linguistic usage is a criticism of language itself!
Only a little commonsense is needed to distunguish those elements of experience which it communicates well from those that it communicates clumsily and with difficulty; it soon becomes obvious that the built-in element of invariance is the serious limiting factor.
It is clear that if the raw material of experience is the flux which it seems to us to be, it must always contain elements incommunicable by word or symbol. Music can sometimes do better; Ramsey's famous comment on the conclusion of Wittgenstein's Tractatus "What you can't say you can't say, and you can't whistle it either" is a myopic mistake, since music is precisely an attempt to communicate elements of experience which, on account of their fluidity - not on account of any mystical obscurity - are beyond the scope of language.
I have, I hope, succeeded in indicating a method whereby quasi-invariant concepts suitable for verbal representation, can be dissected out of an experiential flux by the simple agency of the human judgment, with its inbuilt tendency to mental inertia.
I have in fact accepted Hume's "impressions" and "habits" as the foundations of our thinking, but have gone beyond him in diagnosing an "impression" as an "act of awareness of an important difference", thus making judgment an essential element in our empirical raw material.
Such acts of awareness cannot possibly be described, but I hope I have sufficiently characterised them for my readers by using language to point to instances of their occurrence.
Conventional logic starts from the notion of "truth", its basic assumption being that there can be propositions, statements or beliefs which are "absolutely" true. No such assumption can possibly be embodied in our basic habits of thinking, which develop during the pre-verbal stages of infancy, since the concept of "truth" has no application except in connection with verbal and symbolic description - in which we can include pictorial representation.
It follows that if we wish to understand the nature of the concept, we must look for its origin in some element which is present in experience during our earliest years.
Now "error" is repeatedly experienced, from early infancy and throughout our lives, under circumstances in which no question of verbal expression arises. Furthermore, differences in the intensity of our experiences of it are also directly "given".
It is not very difficult to show how "falsehood", which is its semantic equivalent, is derived from the more primitive, non-linguistic form of experience, which must clearly be accorded epistemological priority. We can then interpret a "true" statement as differing from a "false" one, not in kind, but with respect to the relatively infinitesimal degree of its falsehood. The final step is to ignore the infinitesimal, conceptually1 annihilating it for the purposes of symbolic expression, which we do our best to keep simple for purposes of communication.
1. The mistake made by logicians is to suppose that it can ever be actually annihilated.
The most important instance of this approximation is firmly embedded in language; it is the ambiguity in the sense of the word "see". We know, i.e., are directly acquainted with, vision and visual structure, but "what" we see consists mainly of conjectures of tactile possibilities. In the one sense, seeing is "knowing"; in the other, it is only "believing". It would, however, "cost us too much pains" to doubt the veridicity of these beliefs and to reject them as guides to our choice of effort; by doing so, we would become virtually as helpless as blind people, for whom they do not exist. So we identify the two senses of the word both for practical and linguistic purposes, in spite of occasional experiences of error in the form of "hallucinations" and "illusions"; these are not important enough to upset our confidence in the tactile conjectures which form the bulk of "eye-witness testimony" - including the basic statements which form the raw material of science.
We experience 'error' whenever actuality differs importantly from expectation. The degree of error experienced varies with our estimates of the relative importance of the experienced difference; this, in every instance, is clearly a matter of individual judgment.
All expectation requires the previous existence of a sign-situation, which comes into operation whenever a present sensation evokes conjectures, varying in precision and intensity, of the possibility of other sensations differing from itself in respect of their structure and of their greater importance. Such possibilities are the "meanings" of the sign-situations.
"Meaning", in its most general sense, can be applied in every case of the evocation of a feeling of importance; it is in this sense that we say "His approval means a great deal to me", and "Listening to great music is a meaningful experience."
In a semantic context2 it is assumed that both the sign-sensation and the conjectures are to some extent distinctive, and the "meaning" of the distinctiveness of the sign is the distinctiveness of the conjecture's importance.
2. Think of this primarily in terms of our interpretation of visual sensations in terms of the possibilities of tactile contacts. Of course, it applies to the interpretation of words as well.
It could reasonably be asserted that everything that we notice is "meaningful" by virute of the circumstance that we notice it. But words with an application as wide as this are virtually useless, and it is preferable for present purposes to confine its use to semantic contexts, in which it is not applied to the sign-sensations themselves, but only to the more important (meaningful!) conjectures that they evoke.
The empiricist hypothesis identifies such conjectures with structural echoes of the later parts of "remembered" event-sequences in which the sign-sensation was succeeded, after a not too lengthy process, by an experience of its "meaning". The intervention of a process in every case requires that any actualisation of the conjectured possibilities will always occur later than the act of awareness of the conjecture itself.
By far the most important type of sign-situation is the visuo-tactile one. Visual sensations, except when we are simply enjoying or disenjoying them as æsthetic spectacles, are of negligible importance otherwise than as signs for tactile possibilities - "what" we see - which become actualised when we move toward the image or the image moves towards us for a sufficient time. This process in both cases involves a progressive change in the visual field, whereby the image occupies a steadily increasing proportion of it. In the case of our own motion it is also accompanied by changes of kinæsthetic3 and usually of tactile-muscular sensation.4
3. 'Kinæsthetic' sensations are the generally unnoticed data concerning spatial acceleration and change of orientation, provided by the inner ear. They are badly disturbed when this region is affected (e.g. giddiness, and the sense of rotation when drunk!)
4. Except in the hypothetical case of "uniform motion in a straight line". This circumstance probably explains Newton's choice of this type of motion as the archetype of "invariance". It is the only kind of which a blind man could not, theoretically, be conscious.
Actualisation or "verification" of a visuo-tactile conjecture is achieved by the quasi-simultaneous occurrence of abrupt changes of vision and touch when any portion of the body - usually the hand - which is situated within the field of vision, makes contact with the conjectured "surface" at more or less the expected time.
Error is experienced whenever the tactile change differs importantly from expectation in respect either of structure, intensity or timing. A high degree of error is experienced when it completely fails to occur within anything like the expected time.
Suppose, for example, that I experience the visual sensation of an "apple-image", and select such efforts as I regard as appropriate signs for the initiation of processes appropriate for actualising the pleasant conjectural possibilities that it evokes.
If the "apple" turns out to feel like jelly and to taste like roast beef, I experience fairly severe error in respect of structure.
If, instead of the "normal" tactile sensation of moderate intensity, it scalds me or gives me an electric shock, I experience error in respect of intensity.
If (cf. Macbeth's 'dagger') I completely fail to experience any appreciable change of tactile sensation, I may regard my experience of error as being either negative in respect of intensity, or as being in respect of timing. Such errors lead me to describe the visual sign-sensation as "illusion" or "hallucination", and although they arise from "non-events", they make, qua errors, the strongest psychological impact of all.
On the other hand, if, as usually happens, the actuality turns out to be an "apple" both as regards feeling and taste, the "verification" of the conjecture will occasion no extra psychological impact comparable to that which accompanies its refutation. Most experiential "verification", in fact, is psychologically null. The actualisations of conjectures concerning which we assume the "right to be sure" are as stale, flat and unprofitable as the tautologies which are their verbal expressions.
Verification is only notable when there is some degree of doubt as to the correctness of the conjecture, as there always is in the case of scientific investigations. The more alternative conjectures that are refuted by the actuality, the more notable it becomes. This is the meaning of Prof. Popper's assertion that a "scientific" principle must be one which has a low statistical probability - at least at the beginning of the investigation.
The processes which lead to verification/refutation are frequently movements of our own bodies, which occur as almost invariable sequels to our exercise of appropriate types of effort. Obviously we select the types of effort which we interpret as signs for the initiation of movements which lead to the actualisation of pleasant conjectures, and to the avoidance of the actualisation of unpleasant ones. It follows that the great majority of our experiences of error are unpleasant; in fact, we seldom speak of "error" in cases when the actuality turns out to be more pleasant than our expectation of it, except when the difference is so great that the intensity of psychological impact amounts to a "shock".
This is why experiences of error have come to be regarded as inherently undesirable. But this view is a mistake; all our enjoyment of verbal humour is occasioned by our discovery of unimportant error, and the victim of a mild "leg pull" generally laughs with the perpetrator.
Our somewhat unreflective condemnation of "error" has in turn led us to accord an altogether exaggerated respect to "truth".
Such ethical merits as it possesses are entirely derivative. They follow from our assumption that anybody who communicates "information" intends to assist his hearers or readers to avoid experiences of error which are intense enough to be unleasant or even painful. He enables the hearer to share his sign-systems, since, provided that the utterer's intention embodies the assumed sympathy towards his hearers, his utterances will only express sign-systems which have functioned satisfactorily, and remained unrefuted, within his own experience. Any ethical merit ascribed to "truthfulness" simply reflects our approval of the utterer's sympathy with his hearers and the consequent pains that he has taken with the verbal expression of his sign-systems, or "beliefs".
In the case of "fiction", the utterer's intention, still perfectly compatible with a laudable degree of sympathy, is that his hearers or readers shall simply enjoy their interpretations of his utterances, but not make use of them to supplement their own sign-systems for the purpose of coping with doubtful situations.
Much of the enjoyment that we derive from fiction is due to the unexpectedness of many of the related events. There are bound to be limits; stories can be "shocking" even if they are not believed to be "true". But this generally occurs when the word-signs evoke conjectures which are so unpleasant as to be intolerable even at the low intensity-level of thought itself, although there is no likelihood of their actualisation. The condemnation attaches to the utterer's lack of sympathy - the insensitivity which has allowed him to express such conjectures. It has nothing to do with their "falsity". It is, in a sense, an experience of "error", since the utterer's attitude differs grossly from our expectations.
No account of any "past event" can be verified or refuted by the presence or absence of difference between expectation and actuality, since experience of the latter is ruled out a priori. We are bound to regard such accounts as "false" when our interpretations of them differ importantly from expectations derived from the totality of our firmly held "beliefs", especially those of which we make habitual and satisfactory use, and which are repeatedly subject to the possibility of "correspondence-refutation".
The main difficulty in assessing the "truth" of statements about the past is that of deciding whether they were originally uttered as expressions of "fact" or "fiction". The exercise of judgment in this field forms a large part of the task of the historian; his eventual product embodies whatever combination of statements occasions him the minimum experience of important error. He discards whatever is most seriously discordant with the bulk of the available statements. His criteria of "importance" are more stringent than the layman's, but even he expects some discrepancies between the statements that he examines. such statements as he believes to have been uttered as "fiction" he condemns as historically false.
It is clear that similar treatment should be accorded to fictitious statements in the present tense, such as the notorious "The present King of France is bald". This is 'false', because anyone who attempts to verify or to refute it will almost certainly suffer disappointment, which is assuredly an unpleasant experience of error. We do not condemn it as a "lie", because we do not believe that the utterer has supposed that any of his hearers would make any such attempt. But comparable attempts are actually made; interpretation of the "Flood" story as information rather than fiction has led [among other thingss!] to expeditions to look for the remains of the Ark on the slopes of Mount Ararat. Conversely, the statement "The remains of the city described by the author of the Iliad still exist quite near the Dardanelles" formed the basis for Schliemann's excavations, and the results (he was ridiculed when he went out to excavate 'Troy', which was thought to be entirely mythical) actually led to the refutation of the belief that the poem was intended altogether as fiction.
No prediction can be said to be "true" until it is verified, i.e. "made true". But its verification will not be noticed unless it also involves the refutation of alternative conjectural possibilities. There must in effect be some element of doubt about it, so that it cannot express any belief about which all who use the language habitually assume "the right to be sure". (If it does, it says nothing, so there is nothing to 'verify'.)
The importance of general propositions lies in their usefulness for purposes of prediction. The "if" implicit in "all"-propositions ('All men are mortal' can be reworded as 'If anything is a man, it is mortal') expresses a doubt as to whether their hearers will actually attempt to verify them; if we wish to assert the "right to be sure" that this will be the case, we can replace "if" by "when". The element of doubt depends on the necessity of the intervention of a process between our awareness of the conjectures and our verification or refutation of them.
Take, for example, "Fire burns":
This provides valuable information as the expression of a confident belief that if anybody moves very close to a fire-image, he will experience a very unpleasant sensation. The utterance of the statement is actually intended to discourage the hearer from attempting to verify it, since any efforts that are based on it will obviously be directed towards avoiding such verification.
On the other hand, Hume's "Fire warms" expresses a pleasant conjecture, yet the process appropriate to its verification does not differ appreciably from that appropriate to the verification of "Fire burns", except as regards the length to which we carry it. "Fire burns", in effect, warns us against carrying it too far.
The example provides a good illustration of what appears to be an important psychological "axiom", namely, that all pain and discomfort consist of psychological experiences of excessive intensity, but that some degree of intensity is a necessity for all enjoyment, and that, in general, the intensity of our enjoyment tends to increase with the intensity of experience, up to the limits of tolerability.
When this principle is applied to our experience of "refutation", it is clear that the pursuit of "absolute truth", as an ideal, is an ethical mistake. For any kind of experience in which every actuality corresponded "precisely" with expectation would be a psychological nullity, as stale, flat and unprofitable as the tautologies which express approximations to this state of things in everyday life. Violent refutation is what we call "shock", and is extremely unpleasant, but it certainly does not follow that a state of "bliss-consciousness" is one in which there is no experience of error whatsoever.
The value of true is coextensive with the disvalue of falsehhod. "False" statements include all those which occasion experiences of error by their hearers and readers, but some of these may well be enjoyable. Disvalue attaches only to falsehoods which occasion excessively intense experiences of this character, which can often be unpleasant enough to be called "painful".
The limit of tolerability depends on the sensitivity of the individual hearer. An error-experience which may be "shocking" for one may be of negligible importance, or even a source of mirth, for another. The most fortunate man is one who, while his sensitivities are acute enough to enable him to detect quite minute errors, can tolerate, and even enjoy, fairly considerable ones. Tolerance and a sense of humour go together.
As far as we can judge, however, every human being experiences some intensity-level at which shock bcomes excessive; the sudden incidence of pain is an obvious instance. This is why major falsehoods are not tolerable in statements which evoke conjectures of the possibility of tactile experiences, since these are major souces of pain and pleasure. The verification of such statements is "hard fact".5 For blind people, such statements have even to take the place of the visual sensations which evoke conjectures for most of us and which we do not bother to express in words, since we automatically assume the "right to be sure" of their veridicity.
5. Even this may be subject to exception, since many Indians accept as "factual", the belief that certain Yogis can materialise and dematerialise their bodies at will. Such beliefs, however, call for a more "agonising re-appraisal" of our ordinary stock-in-trade than most of us are willing to undertake.
Language has its roots in primitive sympathy - the desire of human beings to help one another in the avoidance of tactile unpleasantness. Logic, which is the schematism of successful linguistic communication, originated from geometry, which was a coherent description of methods favoured by the Greeks for assuring that the verification of tactile conjectures evoked by visual sensations occurred, as nearly as possible, at the expected time; a "point", from the experiential point of view, is the locus of a tactile sensation of minimum duration, which has intensity but "ideally" no extension.
Within this field of visuo-tactile conjecture the elimination of error, which can be greatly assisted by improvements in the precision with which the sign-systems are verbally or symbolically expressed, is universally accepted as desirable. Leibniz' "Characteristica Universalis", which would allow complete accuracy of prediction, expressed in terms of generally accepted tautologies, expresses the ideal aim of physicists and mathematicians.
Unfortunately, the ideal of "absolute truth" has been transferred to attempts to describe and predict types of experience which lie well outside this field. Value has been, and still is, repeatedly attached to "Holy Writ" on the strength of the claim that it represents an actual achievement of this ideal.
Excessive emphasis on the intrinsic value of truth in any field breeds intolerance and fanaticism. There is no humour in physical science, mathematics or logic, and devotees of these "disciplines" - Leibniz himself is an excellent example - tend to be markedly deficient in this sense. This, I think, is why many of us feel that these pursuits are ethically defective, useful though they undoubtedly are.6
6. The present writer was trained as a scientist, and speaks from experience!
Metaphysical and religious fanaticism is, of course, much worse. Predictions based on the scientists' verbally or symbolically expressed dogmas can at least be repeatedly submitted to the possibility of refutation, whereas this is impossible in the case of metaphysical or religious "truths". Religious fanatics are notoriously devoid of any sense of humour where anything that touches their beliefs is concerned.
The attribution of intrinsic value to all "truth" can, I think, be confidently attributed to the cross-fertilisation of Plato's two ruling enthusiasms - mathematics and mystical religion. Furthermore, "truth", thanks to his exaggerated respect for the durable and apparently magical efficiency of "universals" in effecting communication, had to be "absolute" and "eternal".
The mistake of attaching supreme value to the "unchanging" characterises every version of the "Perennial Philosophy". It is self-reinforcing, since the longer the belief persists, the greater the value the believer tends to attach to it. The very description "perennial" is intended to serve as a recommendation.
Truth is in fact of limited and provisional value. It is not an end in itself, but only a means to an end, namely, the avoidance of unpleasant experiences of error, which sometimes arise when actualities refute the expectations evoked by verbal or symbolic statements.
This view can be regarded, without serious error, as an application of Prof. Popper's "refutationism" to pragmatism, using the empirical observation that intense experiences of error are often "shocking", i.e., intrinsically unpleasant, quite independently of the nature of the actuality involved in the refutation.
I suspect that the treatment accorded to "truth" in this paper could well be repeated in the case of other ideal "absolutes" such as "equality", "freedom" and "justice". In every case, existing practice is to attach positive significance to an experiential nullity, which, because it can be regarded as an "invariant", can conveniently be represented, for communication purposes, by an "invariant" word or symbol.
From the point of view of experiential importance, all verbal descriptions of experience tend to resemble photographic negatives; the relatively unchanging "substances" are highlighted, the all-important "accidents" relegated to the background, roughly and inadequately expressed by the transitions between the words rather than by the words themselves.
Familiarity with subject-predicate structure seems to have blinded even the most acute thinkers to the circumstance that every subject-predicate phrase, even a simple one, such as 'white snow', is a radical falsification of its subject-matter.
The falsification has nothing to do with the semantics; we may be entirely justified in believing that the sound 'white' is a member of a gap-indifferent series of sounds which we habitually use as a 'signal' for any member of a certain gap-indifferent series of visual colour-experiences, and that all English-speaking people will agree on the appropriateness of the association at very nearly the same times.
It does not matter whether their several experiences, either of the sound or the colour, do or do not differ from one another; it is quite likely that they do. As long as we all continue to agree as to when sound and colour are appropriately associated, the vocal signal, and its written 'mnemonic' will continue to perform their communicative function.
The same considerations apply to the word 'snow', although in this case, in addition to visual appearance, there will doubtless be conjectures of tactual texture, temperature, etc. The gap-indifference of a rather more complex 'bundle' of quasi-permanent qualities will be expected to correspond with the gap-indifference of the sound-series. But appearance alone suffices to justify an utterance of the sound-signs; it would be a perfectly appropriate reaction to a picture of a snowstorm at the cinema or on the television screen.
What is - inevitably and radically - falsified is the 'syntax', i.e., the mode of temporal association, of the meanings of the word-sounds. We experience the meaning of 'white snow' as an extremely intimate temporal compresence, or overlap, of the separate qualities. But we cannot express this in language, or in any of the linear symbolisms that we use as substitutes or mnemonics for it, simply because they are linear, extended in the single dimension of 'time'. They therefore cannot exhibit the structure of a temporal overlap, so that when we wish to communicate one, we have to 'make do' with a temporal succession.
It is easy to demonstrate that this constitutes a radical falsification; we have merely to point to the technique of a two-dimensional form of symbolism in which overlap and succession are clearly distinugished, namely, the written notation of music. It is obvious that when a composer has an overlap, or 'chord', in mind he will write, not
Were he to write (a), the symbolism would be a gross falsification of his meaning, and the structure of its normal executive interpretation would be altogether unsatisfactory as a replication of that of his original sound-thought, as he would assuredly be able to testify.
Musical symbolism, like written language, is read from left to right. When this is done, the symbols in (a) are actually experienced successively, those in (b), as temporally overlapping. Thus the difference between their meanings is actually exhibited during the reading of the symbolism.
Now there can be no doubt that the temporal structure of what I am obliged to express by means of the verbal succession 'white snow' is that of an overlap, or 'chord', rather than that of a succession, or 'melody'. It could be more appropriately expressed in writing, as
But writing does not qualify as 'language', unless it can be read aloud, so that this type of notation is not acceptable. If I had two mouths, I might be able to utter the sounds 'white' and 'snow' compresently, but this also would be empirically unsatisfactory; it is essential, for signalling purposes, that the individual signals should be as clear and distinct as possible. In this particular instance, it might be possible to distinguish them, but in the case of a more complex 'predicative compresence', such as
{ tall
{ dark
{ handsome
{ man,
it would be quite out of the question.
Since we constantly require to use language to communicate overlapping qualities, we have had to put up with this syntactical falsification. Mankind has universally, and more or less instinctively, dealt with it by adopting the convention which keeps the falsification to a minimum. The closest possible approximation to an overlap of words is their immediate juxtaposition, so that the 'natural' convention to adopt is to express a temporal overlap of qualities by means of an uninterrupted sequence of the words which express them, and, conversely, to interpret such sequences as expressions of temporal overlap unless some counter-indication is provided.
This convention is so generally accepted that I can be quite confident that although 'white snow' is a succesion, it will be interpreted in terms of an overlap of the meanings of the separate words. So will 'soft white snow' and 'white snow falling softly'. Each of these words denotes a quasi-permanent quality, or 'bundle' of qualities; in the case of 'falling', the quasi-permanent quality is one of 'process'.
Predicative compresence, or overlap, is counter-indicated by every interpolation of a tensed verb, conjunction, and preposition. 'White snow fell softly' expresses the sequence of the utterer's observations; so does 'white snow falling softly to earth'. So does 'white and softly falling snow', but in a rather different way; it expresses the utterer's consciousness of a qualitative transition between his modes of awareness, but does not negate the overlap of the phenomenal qualities.
There are, however, limits to the field within which the compredicative convention can be applied. Whenever an ostensive contrast between two qualities has played a part in defining the words which stand for them, any 'predicative compresence' of the qualities is 'unthinkable', or in other words 'logically false'. 'Red blue' and 'square circular' are obvious examples of this state of affairs. It obtains on account of the circumstance that every ostensive contrast involves a temporal transition between the acts of awareness of the contrasted qualities; their temporal overlap wold therefore nullify the meanings of the words which stand for them.This state of affairs can only obain when the qualities concerned belong to the same 'dimension' of sense or thought.
It is quite clear that the differences between the 'dimensions' of sense become established, and taken for granted, during the pre-verbal stages of our development. We all became familiar with the radical differences between seeing, hearing, smelling, tasting and touching long before we learned to speak, and, within the 'dimension' of seeing, learned to distinguish between our awareness of colour-differences and of differences of shape. We were therefore able to proceed directly to learn the names of contrasting colours and shapes such as 'red' and 'blue', 'square' and 'round'. Having already achieved a more advanced stage in the differentiation of experience, we had at this stage no use for 'dimension-words' such as 'colour' and 'shape'; our familiarity with the major dimensional differences could be taken for granted, so that their verbal expression would be altogether redundant.
It now becomes evident that it is precisely because the meaning of 'red' differs more from that of 'square' than it does from that of 'blue' that an area within the visual field can be described as 'red square', but not as 'red blue'. It is clear, on reflection, that 'red' and 'square' are not descriptive of qualities within the same 'dimension' of perception; 'red' describes the interior of the area, 'square', merely the boundary. The invariance needed in order to justify the use of the universal term 'red' can be cognised within a microscopically small area, that is to say, extremely rapidly. Any cognition of 'square-invariance' will take much longer, since it requires the scanning of a much larger area, and the scanning will include traverses of the interior; during these traverses, there is plenty of time for cognitions of 'red-invariance'. There is therefore no difficulty in conceiving an overlap of the two 'tempi' of cognition. In the case of 'red' and 'blue', however, the tempi for cognitions of 'invariance' are of the same order, so that any cognition of one quality will destroy the 'invariance' of a cognition of the other, and their overlap is therefore 'unthinkable'.
The minimum area for the cognition of the separate 'invariances' could be quite easily ascertained experimentally. We have only to paint a surface 'purple' by means of a mixture of red and blue pigment, and examine it under progressively increasing degrees of magnification. At a certain stage, the separate grains of red and blue pigment will become visible, because the duration of our awareness of them will have become long enough for us to cognise their separate 'invariances'. This, however, will not suffice to justify a description of the area as 'red blue', but only as 'red and blue'.
'And', from the point of view of the utterer, is a linguistic 'performative', publishing the 'banns' between the words that it separates, and signalling a close temporal proximity of their meanings within his present, or, more accurately, very recent experience. But from the point of view of the interpreter, it may be disjunctive, indicating that the temporal proximity of the meanings falls short of what would be required for the expression of an overlap, or 'predicative compresence'. This, however, cannot be taken for granted; the disjunction may be purely qualitative, within the mind of the utterer, and not temporal at all. The surface-structure of the language gives no indication as to which type is expressed; semantic considerations determine our judgment as to which type is intended. In a case such as 'red and blue' the disjunction is clearly temporal, but in a phrase such as 'tall dark and handsome man' it is not; it simply expresses the utterer's awareness of the qualitative difference between the 'dimensions' of the visible qualities and that of his æsthetic assessment of them. The hearer will continue to interpret the descriptive phrase in terms of a 'predicative compresence' in spite of the interpolated 'and'.
The distinctiveness of the two meanings of 'and' can be clearly shown by referring back to the two examples of musical notation given earlier in this essay; the 'meaning' of either of them could be correctly described as 'F and C'.1 In (a) there is temporal overlap and only qualitative disjunction; in (b), the disjunction is temporal. Thus the mutually contradictory relations, 'overlapping' and 'not overlapping' are both included within the descriptive meaning of 'and'. It is therefore difficult to see how the word can possibly form part of the vocabulary of any logic which claims to be 'accurate'.
1. Since the 'compredicative convention' is not needed in musical notation, the sequence 'FC', in practice, is given its natural interpretation as a succession, which corresponds structurally to the symbolism. 'F and C' wold therefore generally be interpreted as an expression of the overlap, or 'chord'.
From 'p and q', we can only infer 'p some of the time', unless we treat the expression as synonymous with 'pq', and proceed to interpret this in accordance with the 'compredicative convention'. This is still required if we are to infer 'p all the time' from 'pq'; when we read the expression, it is clear that while we are experiencing q we are experiencing 'not-p', since the difference between the symbols p and q, and between the corresponding sounds, 'pee' and 'cue', is an intentional feature of the symbolism.
The 'compredicative convention' admittedly works very well over a wide range of experience. We can nearly always assess the type of conjunction signalled by 'and' by referring to the semantics of the words that it conjoins - although this clearly cannot be done when their place is taken by algebraic symbols. It is only when the discrepancy between the temporal structure of the symbolism and that of its 'meaning' becomes particularly acute that the symbolism becomes uninterpretable, and we run into logical falsehoods and paradoxes. 'Red blue', 'hot cold', 'odd even' (in a numerical context) are obvious examples, and any assertion of their overlap by means of the copula, such as 'red is blue', which could be paraphrased as 'blue red, yes' can likewise be dismissed as 'logical absurdities', or 'axiomatic falsehoods'.
Such discrepancies are not the most serious that can occur. Zeno's 'Achilles' paradox manifests what seems to be the 'ne plus ultra' in this respect. Achilles is supposed to run a race with a tortoise, giving it a start of one mile. He runs twice as fast as the tortoise. Clearly, when he has run one mile; the tortoise will still be half a mile ahead; when he has run the next half-mile, the tortoise will still be a quarter of a mile ahead - and so on, ad infinitum. If this description of the proceedings is valid, it is clear that Achilles can never overtake the tortoise.
Arithmetically, this is expressed by the 'fact' that the sum of the series
can approach indefinitely close to 2, but can never reach it.
Such series are called 'convergent', and 2, or its equivalent, is known as their 'limit'.
But are such series 'convergent'? In order to make my point more quickly, I will rewrite the series in question, expressing the denominators of the fractions in the 'binary' scale used in computers. The series then appears as follows: 1 + 1/10 + 1/100 + 1/1000 + 1/10000 … etc. etc. At this point, all I have to say is 'Just look at the symbolism! It is indefinitely divergent, and has no imaginable 'limit'. It inverts the temporal structure of its 'meaning'; the smaller the extension expressed by each successive term, the greater the extension of the symbol. An indefinitely extended symbol will be needed to express an infinitesimal extension, and an 'infinitely' extended one would be required to expess attainment of the limit. Can the symbolism be acceptable as a description of what it purports to 'represent'?
Of course it can't! The series is not, in fact, a 'description' at all, but an 'imaginative prescription'. Zeno's mistake lay in his assumption that a 'predicative compresence' of anything like the 'whole' series could be 'thinkable'. The case of the Achilles is worse than that of 'predicative compresence', because the temporal structure of the symbolism manifestly inverts that of its supposed 'meaning'. Indeed, the formulation of every 'infinite series', whether convergent or divergent, requires the construction of an infinitely divergent series of symbols, so that any attribution of 'existence' to either type appears to be highly questionable.
In conclusion, I would like to stress that this essay is not intended to be a frontal onslaught on language and symbolism, but to demonstrate that their expressive powers are restricted owing to the limited extent to which they are able to exhibit the syntax, or temporal structure, of their subject-matter. This restriction clearly imposes limits to the applicability of all verbal and symbolic 'reasoning' outside the field of language and symbolism itself. This has frequently been overlooked, and the 'absolute' validity attributed to such reasoning has repeatedly led men to become slaves to verbal and symbolic formulæ, instead of simply recognising and using them as the extremely useful communicative instruments that they are. I can see much advantage, and no serious drawback, in a frank admission that they can never be applicable over anything like the whole range of human experience.
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