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Copyright © The Neith Network 1999
First published in 1979 by Bibliagora P.O. Box 7 Hounslow TW3 2LA
Copyright © Bibliagora 1979 - All rights reserved ISBN 0 906031 02 8
WorldWideWeb Internet edition introduced and edited by Colin James Hamer 2000
His Benevolence The Extra-Reverend The Preliminary LibrArian emeritus I+N The Neith Network, Doctor Colin James Hamer, who was for several years recognized by Academician Doctor J.D. Solomon as the authority on his Logic and Philosophy, has the honour to be his sole appointed Literary Executor and is also the privileged custodian of the J.D. Solomon Archive, which is currently housed at Creativity House, 9 Oxford Street, St. Thomas, Exeter, Devon EX2 9AG (Tel: 01392-411723).
Academician Doctor J. D. Solomon, M.A., Ph.D., F.R.G.S., (1906-1998) was educated at Felsted School and Trinity College, Cambridge, where he read geology. He was engaged in extraordinarily significant research work - notably in association with Louis & Mary Leakey - for seven years, during which he developed a certain distaste for the academic world (largely, I suspect, because of the all too frequent bickering and back-biting that even today accompany theoretical differences of opinion between specialists), and sought an alternative career in music (it has recently been reliably affirmed that in this subject the depth and range of his knowledge was also second to none - and cf. Victor Gollancz, Journey Towards Music - A Memoir, 1964, Chapter II). His studies were interrupted by the war, during which he conceived the ideas which form the subject of the present work. Invalided out of the R.A.F., he accepted a temporary post in teaching, and found the occupation so congenial that he took it up permanently. After his retirement, most of his efforts were devoted to achieving an adequate expression of his war- time ideas; this book is the outcome.
The Mind's Ear radically questions the assumption, adopted both by science and religion, that values are primarily to be sought in the unchanging, persistent aspects of the Universe. These are admittedly useful for the purpose of description and prediction, but the raw material of our experience, which is the direct source both of enjoyments and disenjoyments, appears to consist of exceedingly rapid change. It is therefore important to show that it is possible to conceive of the Universe in terms of pure ‘activity’. For this purpose it has been necessary to use parables, in which television plays an important part, since language, on account of its structure, is demonstrably unable to furnish an adequate description of such a flux. The ethic appropriate to this world outlook differs fundamentally from those derived from religion and science; it is strongly advocated on the grounds of its superior beauty..
“Hoc enim idea Dei dictat, Deum summum esse nostrum bonum, sive Dei cognitionem et amorem finem esse ultimum, ad quem omnes actiones nostræ sunt dirigendæ. Homo tamen carnalis hæc intelligere nequit, et ipsi vana videntur, quia nimis jejunam Dei habet cognitionem, et etiam quia in hac summo bono nihil reperit, quod palpet, comedat, aut denique quod carnem, qua maxime delectatur, afficiat, utpote, quod in sola speculatione et pura mente consistit. At ii, qui norunt se nihil intellectu et sana mente præstantius habere, hæc sine dubio solidissime judicabunt.”
Benedict de Spinoza, TRACTATUS THEOLOGICO-POLITICUS, cap. iv.
(Quoted on the title-page of J.D. Solomon's copy of Spinoza's
ETHIC DEMONSTRATED IN GEOMETRICAL ORDER AND
DIVIDED INTO FIVE PARTS…, 4th edition, Oxford University Press 1937.)
Preliminary LibrArian's note
According to Benedict de Spinoza
Author's Preface
1. Mind's Eye or Mind's Ear?
2. The Nonsense-Barrier created by our Symbolic Techniques
3. The Values and Disvalues of Falsehood and Truth
4. The Empirical Origins of “Pure Reason”
5. A Herakleitan Cosmology and its Associated Ethic
Appendix: A Criticism of Nietzsche's Ethic
A Method Improving Structural Correspondence between Language & Experience
An Examination of Language Structure from a “Musical” point of view
Truth and Falsehood from the Standpoint of the Utterer
“Existence” and “Reality”
The Basic Principles of Universal Ungrammar (Inversion of a Chomskyan theme)
Appendix: J. D. Solomon & Lonergan's Insight
This book is essentially the outcome of a brief but intense period of metaphysical insight that I experienced over thirty-five years ago. I had never previously concerned myself with philosophy, although I had been in daily contact, in my Cambridge days, with men who were contributing to the intellectual ferment which followed the publication of Wittgenstein's Tractatus. Since this seemed to be entirely a matter of verbiage, I dismissed it as unimportant, and it did not divert me from my main interests, which were geology and music. As a scientists, I passively accepted the common belief that the Laws of Physics, expressed in the language of mathematics, would ultimately furnish acceptable explanations of everything within sense-experience, although certain of my musical experiences engendered mild mental reservations concerning the total scope of such explanations.
A paper-back copy of Whitehead's Science and the Modern World, left in my flat by my brother-in-law, suddenly opened my eyes to the exciting possibility, wildly remote from anything that I had ever imagined, of an ontology based on “changes” rather than “invariants”. Whitehead's own attempts to relate a fluid “cosmos” to the familiar world of concepts did not seem quite convincing, neither did I find Alexander's Space Time and Deity or Bergson's Creative Evolution entirely satisfactory, so I had a shot at solving the problem on my own account.
I started with Einstein's principle that “distant simultaneity is unobservable”, and wondered whether there was any reason why this should not remain valid when “interval” approached “zero”, as for example in the visual field of a single observer. Failing to find any such reason, I concluded that all visual experience, and probably all human experience, must in the ultimate analysis be regarded as a pure flux of succession; “absolute simultaneity” could never be observed! Moreover, it was obvious that the “tempo” of the changes within such a flux must be of an altogether higher order of rapidity than those of any sensible phenomena, or of the “frequencies” assigned by the physicists to electro-magnetic radiations.
Having conceptually eliminated “absolute simultaneity” from my own experience, I wondered whether I could conceive of an intelligible “universe” in which it played no part. The solution proved surprisingly simple; I only had to postulate that in an “ultimate analysis” of the Universe, my own experience might appear to be discontinuous; the “rest of the Universe” could then fit into the gaps. Of course, the tempo of the “ultimate analysis” involved completely beggars the powers of the imagination, but no unfamiliar principle was required by this world-picture, from which “absolute simultaneity” was altogether excluded.
This staggering discovery threw me into a state of wild excitement, which eventually had to be damped down by heavy sedation. I then tried to communicate my findings, but my clumsy efforts met with blank incomprehension. Since my thoughts remained clear to me, and I could rely on remembering them, I decided to wait until I retired before writing them up.
So I tried again thirty years later, but initially met with no more success than before. Eventually I came to the conclusion that the trouble might lie in the structure of language, which perhaps implied the acceptance of an ontology which was incompatible with the one that I was trying to express. On investigation, this turned out indeed to be the case.
The structure of language is based on that of the visual field, which predominantly displays a compresence of quasi-invariant coloured areas, bounded by contrasts of which the shapes, along with the positional relations that they define, also remain quasi-invariant as long as we have no internal awareness of our own movement. “Gap-indifferent” series of visual experiences are also of very frequent occurrence.1 We habitually tend to attach each individual bounded element within the visual field to such a gap-indifferent series; this is what we call “referring it to a concept”. Eventually, we may also attach a gap-indifferent series of word-sounds to the “concept”. The quasi-instantaneous passages between adjacent word-sounds parallel the quasi-instantaneous transitions of awareness within the visual field; thus the structure of spoken language, and of the reading of written symbolism, is a series of “invariances”, or “gap-indifferences”, punctuated by staccato transitions.
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1. When the “gaps” are of negligible duration, we have what Russell called “quasi-permanence”.
The expression of a pure flux in terms of a linguistic or symbolic medium with a structure of this kind is clearly out of the question, so that there can be no possibility of describing its relation to the world of concepts. Fortunately, however, it is possible nowadays to point to familiar, everyday instances where we actually fabricate a conceptualised, visual world out of a raw material which is a pure flux of succession, and altogether beyond the descriptive powers of language or symbolism; this occurs every time that we watch television.
If has now become possible to trace certain of the simpler visual images back to the types of change which have furnished their raw material. This latter consists of changes of intensive quantity, structurally similar to those characteristic of the field of hearing, which comprises nothing but pulsations of this nature. Now seeing that we locate “what” we see entirely “outside” our current experience of it, all vision is, strictly speaking, “television”. Thus we can in principle effect a corresponding translation of the material of “direct” vision; this will only be “efficient” in the case of the simplest shapes, since the complexities which command general recognition within the field of vision are far greater than those within the field of hearing which we can recognise and name.
We can never get right back to the “atomic events” which must form the ultimate raw material of all our experience, but only to series of such events, which persist long enough to allow us to make a judgment of rhythmic “invariance”; this is what constitutes “quality” within the field of hearing. What we have succeeded in achieving is the replacement of “shape” by “rhythm” as the fundamental basis of all “form”. The theoretical feasibility of such a translation removes an important objection to the notion of a universe of pure succession.
But a discontinuous flux of “atomic durations” requires a unifying principle if we are to be able to regard it as a “universe”. I have postulated an all-pervading æsthetic urge as the activity most likely to be responsible for this function. This resembles Alexander's “Nisus to Deity” and Gœthe's “Eternal Feminine”, but both these concepts suggest an attraction towards something that is already in existence. I conceive it rather as immanent in all existence, and as a “divine dissatisfaction” both with the actual present, and with all that is believed to have preceded it. It seems to be more highly developed in mankind than in any of the other sentient beings whose activities we suppose to be manifest within the “world” of our sense-perception.
From this an ethic can be developed, which I have adumbrated in the fifth chapter of this book. It treats “natural selection” as a special case of a more general “æsthetic selection”, and assigns a positive value to “chance”, in view of its function in the creation of “novelty”. Since the “habits” of the Universe are envisaged as resulting, in the main, from the purposeful elimination of types of event-sequences which have given rise to disenjoyments, I have used the term “Pragmatic Negativism” as a title for this process. It will clearly be applicable to the development of human habits, including those concerned with our use of language. The kernel of this work will be found in the first five chapters, which constitute The Mind's Ear proper. The remaining essays are some of the studies of our awareness of symbolism which eventually led me to the discovery of the “nonsense-barrier” which forms the subject-matter of the second chapter. “Reality” is what lies on the near side of the nonsense-barrier, and can be adequately described. But it is only a part, and not the most important part, of “actuality”. Since language is based exclusively on the “real”, it is unable to furnish a description of the “whole”.
I would like to thank Sir Alfred Ayer for his encouraging comments on parts of this work that I submitted to him. I am also most grateful for the efficient and enthusiastic co-operation of Mrs. Gwen Godbold, who typed the whole of my not too legible MS.
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Editor's note:
Although this book reveals its author's awareness of Eastern philosophy, mentions the Michelson-Morley experiment, and refers here and there to the work - or play - of Alexander, Joan of Arc, Aristophanes, Aristotle, St. Augustine of Hippo, A. J. Ayer, J. S. Bach, Cleve Backster, Beethoven, Bergson, Sir Jagadis Chandra Bose, William Blake, Bradley, Peter Breughel, Samuel Butler, Cantor, Carnap, Lewis Carroll, Washington Carver, Casals, Chomsky, Jesus Christ, Churchill, Zerah Colburn, Copernicus, De Moivre, Descartes, Dickens, Einstein, William Webb Ellis (the inventor of rugby), Empson, Epimenides, Euclid, Giotto, Gœthe, Heraclitus, Hume, Huyghens, Ibsen, William James, James Joyce, Kant, Kepler, Kronecker, Edward Lear, Leibniz, Lenin, L. S. B. Leakey, C. I. Lewis, Marx, McTaggart, Michelangelo, Stuart Mill, Newton, Planck, Plato, Popper, Ptolemy, Pythagoras, Quine, Ramanujan, Russell, Schopenhauer, Shakespeare, G. B. Shaw, Socrates, Spinoza, Strawson, Tarski, Tenniel, Tolstoy, Sir Donald Tovey, Von Neurath, James Watson, Whitehead, Wittgenstein and Zeno, it is essentially a highly original and vigorous attack on most forms of religious and scientific dogmatism.
Although no use at all is made of either the term “symbol” or any of its cognates on 55% of the pages of printed text that together constitute this book, such terms are used 188 times in the remaining 45% of the text - “symbolic” 79 times, “symbol” 34 times, “symbols” 27 times, “symbolism” 25 times, “symbolised” 10 times, “symbolically” 6 times, “symbolising” 3 times, and “symbolise”, “non-symbolic”, “symbolisms” and “symbolisation” once each.
As J. D. Solomon uses these terms, “our symbolic technique is derived from speech… symbols function as mnemonics for word-sounds” (1979 edition: pp.50.135; unless otherwise stated, all references are to this edition). “Language, which has developed out of the human urge to cooperate in the tactile and functional fields, is too coarse-textured to do justice to the finer elements of experience… Any process that could conceivably occur within a duration that is too short to permit of a cognition of the invariance of a single visual symbol must be relegated to the category of the ineffable” (pp.144.25). “There is no reason to suppose that pulsations of sound or of electromagnetic intensity - including light - have any shape… The wave-shape… plays no part in the symbolised phenomena, but is merely part of the symbolism” (pp. 19-20). “Sometimes we use a hieroglyph to signal a mode of ‘experiencing visually’ in cases where there is no non-visual connotation… In these cases ‘appearance’ is the sole function; the sign is not a symbol but an icon, which replicates its ‘meaning’. The reference and denotation of the names for these shapes are therefore reliably gap-indifferent” (p.114). “Symbolic formulæ” sometimes, like “visual Gestalte, function merely as signs for the possibility of future intrinsic tactile value/disvalue experiences” (pp.35.40). “Structural contrasts, degrees of difference, relative tempi and intensities of change are the very stuff of all experience. But it is invariances and gap-indifferences which furnish the stock-in-trade - the uncategorised lexical components - of language, because it is these to which the gap-indifference of word-sounds, and ultimately the invariance of written symbols can be attached. For language,therefore, it is the structures of change which appear abstract, whereas for direct experience, it is the relatively invariant elements which are abstracted for the purpose of symbolisation” (p.168). “The circumstance that a mode of experience is not describable in terms of public symbols does not debar us from accepting it as part of the ontology of private experience” (p.59).
According to Solomon: “The concrete nouns which play a large part in our primitive vocabulary are brief, highly synthetic terms used for signalling bundles of phenomena to which we attach importance either for synthetic or practical reasons… Our usual motive for signalling the phenomena symbolised by concrete nouns is not primarily a desire to share our enjoyments, but rather to cooperate with others in avoiding disenjoyments, especially those which we confidently believe to be quasi-universal concomitants of certain types of contact with surfaces” (pp.129-30). For example - “Watch it! Keep your hands off me!” What Solomon calls his theory of eliminative ungrammar clearly presupposes an innate appreciation of structure, and so a capacity for resonance in his fellow humans. “It is,” he says (p.168), “highly questionable whether the structure concerned should be thought of as abstract. It is, broadly speaking, of the type characteristic of music, including temporal succession, rhythm, and changes of intensive quantity.” Consistently with the rest of his philosophy as expounded in this book, Solomon symbolises in order to bring together bundles of phenomena and takes objective meaning to be abstract. “Zero”, he claims, “should not be accepted as a ‘number’, since it does not function as a member of the series used for ordinal signalling. It can only stand for the ‘state of affairs’ which prevailed before the signalling began.”
However, as I (and many others, including José Arguëlles and Terence O'Brien) use words, symbols often mediate a whole bundle of meanings; symbols properly understood are the medium through which personal growth takes place. For me any use of symbols is primarily a function of meaning. I agree with Solomon that arithmetical, logical and modern scientific uses of language are abstract, but I also insist that noumena are not abstractions.
The thesis put forward in this chapter is that our dominant modes of thinking about our experiences provide us with no more than an extremely improverished, partial account of them, tending to rule out an enormously greater richness of content. It is furthermore suggested that we might be able to achieve conscious awareness of the excluded elements, if only we could rid ourselves of the habit of concentrating our attention almost exclusively on what we can see. Our tendency to equate the “real” with the “visible” is constantly reinforced by our use of a language constructed out of what are, ideally speaking, “invariants”, which are intended to correspond with experiential “invariances”; these in turn form a far larger element in the sense-data of vision than in those derived from any other sense, and are notably absent from non-verbal thought, which is extremely fluid.
The quasi-invariant bounded areas which usually fill the bulk of the visual field are mainly important because they function as signs for the possibility of tactile experiences. This circumstance appears to have led both John Stuart Mill and Lenin to define “matter” as “permanent possibilities of sensation”. What is thus defined is, however, certainly not “matter” as we experience it, whether superficially through the sense of touch, or internally, as in the case of our own bodies; such actual “sensation” consists entirely of change. The definition covers no more than the visual aspects of “matter”. These, however, are believed to be “public”, and therefore reliably communicable, whereas our superficial, tactile acquaintance with it is only dubiously so, because it is dangerously “subjective”, while our “internal” experience of it is “private” and not communicable at all.1 It is, in fact, only the visual aspects that we locate entirely “outside” our own experiences.
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1. This form of experience is regarded as suitable material for “knowledge” in the East, but not in the West.
Their “permanence” is provided by contrasting areas with rather sharp boundaries, and with colours and shapes which change slowly compared with the rest of our sense-data. Their mutual relations also tend, in the main, to remain static whenever we are not internally conscious of any movement of our own eyes or bodies. The qualitative diversity of the areas, and of their complex relations, provides us with an enormous variety of “invariances”, to which the distinctive invariance of a great variety of symbolic expressions can be attached.
These visual invariances therefore provide the vocabulary for the expression of so-called “facts”; “eyewitness” testimony is always preferred to any other. The virtual exclusion of the “invisible” from the field of the “reliably describable” is clearly demonstrated by the etymology of the word “evidence”. Thus it comes about that when we learn to use language, we are encouraged to treat “invariances” as the “norm” of experience, and, what is even more important, as the most desirable norm. “Changes” are treated as “accidents”, departures from the “ideal”, perhaps a little bit dirty and disreputable. They manifest a kind of “fall” from “perfection”; evidently, G-d must have “fallen” when He created “time”. St. Augustine, of course, did not express the matter quite as forcibly, contenting himself with describing “time” as “a moving image of eternity”; but the term “image”, as used in this context, certainly carries a pejorative connotation, similar to that suggested by “Maya” in Hindu philosophy. Such views are entirely rejected in the present work. “Change” is regarded as the “stuff” of all experience, both good and bad; the importance of certain quasi-invariant “patterns” of change is not denied, but is rated as inferior to that of experiences of rapid variation. In fact, the aspect of actuality to which the greatest importance will be attached here is that of the causal interactions between individual “experiencings” and “the rest of the Universe”, since these are what are, in fact, of primary importance to every one of us. “I” becomes an activity, apparently manifested, for the most part, within the surface which sight and touch have led me to think of as “my body”. “I” am anything but “invariant”; exceedingly rapid change is the norm of my experience, invariance being a rare exception, confined to states of almost complete anæsthesia. Any “causal” relation between myself and entities within the “external universe” - in which I cannot help believing - is certainly some kind of “change”; if I were “invariant”, I could not affect my “neighbour”, and all my intimations of the influence of the “external universe” certainly consist of changes within my own experience. Language is completely misleading in this context; “I” ought to be linguistically represented by a verb, not by a pronoun, and the vocabulary descriptive of my direct “experiencing” should rightly consist entirely of terms that are adverbial in function.
These views are similar to those expressed by Whitehead when he urged us, if we wanted to understand the raw material of our experiencing, to think in terms of visceral sensations rather than of the field of vision. Such thoughts, however, could hardly be adequately expressed in language, since we have no reliable “public” vocabulary to describe our “visceral” modes of experiencing. On the other hand, the raw material of hearing has a structure which is basically similar to that which Whitehead postulated for the raw material of experiencing in general, and we may therefore be able to give an adequate description of it in terms of the vocabulary of aural experience. This, unlike the visual variety, is partly felt as some kind of “internal” change, even if its source is located “externally”, but there are sufficient quasi-invariances in the pattern of this change which are believed to occur quasi-simultaneously in other “experiencings”, and are thus sufficiently “public” to allow the attachment to them of quasi-invariant or quasi-gap-indifferent words or symbols, for the purposes of communication. Thus although the “norm” of hearing experience is “change”, it is not beyond the range of symbolic expression, and if we wish to communicate a world outlook which is based on change rather than invariance, the vocabulary of aural experiencing will serve our turn. We do not need to “feel within the mind's viscera”; it is sufficient to “listen with the mind's ear”.
Our experience of “sounds” is not, like that of visual “objects” or “areas”, located entirely outside our “private” experiences. This is because we apprehend sound directly as a succession of changes of intensive quantity. The physicists describe them as changes of “atmospheric pressure”, but as far as we are concerned, they are simply changes in the intensity of feeling. The structure of these changes is what we call “rhythm”; under this term I intend to include the form of all variations of the “tempo” of change, which seems to be directly “given” in our experiencing. I do not wish to confine its meaning to the “invariant” tempi of event-successions which are “measurable”, i.e., numerically expressible, this is a crude, “popular” use of the word.
As we shall see presently, the “intensity” of change is, under certain circumstances, an alternative way of expressing its “tempo”, just as in modern physics, “interval” is sometimes expressed in spatial and sometimes in temporal terms. Our choice of descriptive method is determined by the ease with which it allows comparisons to be made with phenomena that are ostensibly definable, and hence suitable as bases for language.
The problem which confronts us is that of using the vocabulary of aural experience for the purpose of providing a description of visual phenomena. A few years ago, this would have been an almost insuperable task, but now, thanks to the general familiarity with television, it is not particularly formidable. The first step is to realise that, since we locate “what” we see entirely “outside” our experiencing, all vision is, in this sense, “television”. We can then regard our own visual field as a kind of television screen, and the “raw material” of visual experience as having a structure similar to that of the “carrier-wave”, i.e., a purely successive pulsation of electromagnetic intensity, similar to the raw material of “sound”. “How” we see - our own internal activity - is closely analogous to the activities conducted within the receiving set. Both the raw material and our own activity contribute to the “finished product”, which is analogous to what appears on the screen of the television set. This, like the sound of our own voices, is subject to immediate “feedback”, so that it in turn contributes to the “raw material”; the problem is to estimate the importance of its contribution in relation to the raw material as a whole. In a sense, since it has resulted, at least in part, from prior activity on the part of the “receiver”, the visual component is already a “finished product”; it is “second-hand” rather than “new” material.
When we begin to look for the structural equivalents within the carrier-wave of the images which appear on the television screen, we must first realise that any “invariances” that the images display are demonstrably altogether our own construction - they certainly deserve to be characterised as “Maya”. They are not “invariant” at all, but are “recreated” many times in every second; when they appear to “move”, all that happens is that the phase of their rhythmic re-creation is varying relatively to the phase of the re- creation of other “images” on the screen.
We, of course, as spectators, are not concerned with the extremely rapid rhythm of their re-creation; we only become aware of its occurrence when something goes wrong with the set, so that we undergo the rather unpleasant experience of “flicker”. All that we want to see are the much slower changes, the tempi of which are of the same order as those of our bodily movements, and we dissect these out of the extremely rapid flux, which is still actually occurring on the screen. They are all that we notice, and we regard them as occurring “simultaneously”; yet none of the activities on the screen are strictly simultaneous, as the television engineers, who have generated them, will testify.
Let us now proceed to think of our own visual field as the surface of a television screen, and try to discover what, in our experiential raw material, can give rise to the structures that we “see”. We begin by extending Einstein's principle, that “distant simultaneity is unobservable”, to our observations of discrete parts of our own visual field, thereby renouncing the possibility of an “infinitely rapid” tempo for transitions of visual awareness. This is analogous to Einstein's renunciation of the possibility of an “infinite tempo” for the velocity of any communication; there may well be some connection between the two. By analogy with the “picture” in television, we will assume that the visual field is produced by the interaction of an invariant rhythm of “visual scanning” with the raw material of the carrier-wave, which is an initially formless flux of change of intensive quantity in television, electromagnetic intensity is what is involved.
We will confine our attention to “black and white” images, in order to avoid the complications which would arise if we tried to consider coloured ones; these would introduce no new principle, but would complicate the exposition. It is clear that the “picture”, when we consider the “black” elements as “positive”, consists of diminutions of the intensive quantity of “illumination”, varying in degree, and repeatedly traversing the field with great rapidity. When the rhythm of any pattern of intensity-variation in the raw material remains constant, and also remains “in phase” with the rhythm of the repetitions of its passage across the screen, the image remains motionless and unchanging.
We need to remember that any persistent dark “quasi-point” does not in fact exist continuously, but is re-created many times every second. A dark “area” will occur when many such re-creations occur in close temporal proximimity with one another. It is in this sense that “frequency” can often be equated with “intensive quantity”. This can easily be verified by looking at a press photograph through a strong magnifying glass; the dark areas are revealed as being due to the high frequency of the black dots. Conversely a “dot-map” indicating density of population appears, when viewed from a distance, as having been produced by differential shading. When we want to examine the “raw material” of such a map, or photograph, we have to increase the rate at which we “scan” it to one above what is normal. Since, however, the tempo at which we scan our “raw material” when creating the visual field appears to be very difficult, if not impossible, to alter, we compromise by scanning a small portion of the photograph in the time that we usually need for scanning the whole of it; this, in terms of our awareness, is the function performed by instruments such as the microscope. Should the tempo of our visual “scanning” ever chance suddenly to accelerate relative to the tempo of our bodily movement, in which we are predominantly interested, we would presumably experience the visual field in the kind of detail revealed by the “slow-motion” camera, which functions in much the same way as the microscope. This might well be confusing, and would probably reduce the practical usefulness of vision by providing too much “irrelevant” detail. For the purpose of “understanding”, it is doubtless desirable to approach as closely as possible to the “raw material” of experience, but this will not necessarily help us to make better use of it than we can with the aid of our usual equipment.
Once we regard the visual field as being “created” by our own repeated “scanning” of our raw material at a constant “tempo”, it is quite a simple matter to formulate a purely temporal equivalent of visual “distance”. The interval between our acts of awareness of two “quasi-points” can be considered as temporal, and when we judge the distance between them to be “invariant”, it is because the oscillation of our attention between them is also rhythmically invariant, like a musical “note”. Should another “quasi-point” intervene midway between them, the tempo of the oscillation between our acts of awareness of the end-points and those of the intermediate one will clearly be twice as fast as that of the oscillation between our acts of awareness of the end points themselves; in musical terms, it will be its first “overtone” or “harmonic”, i.e., the “octave”. In this way it becomes quite easy to derive the importance of numerical ratios in the replication of “harmonious” visual proportions from that of the numerical ratios which relate compresences of musical frequencies that we commonly judge to be harmonious.
This brings us to a fundamental opposition between “spatial” and “temporal” analysis. We analyse large spatial intervals into smaller ones. But when we come to think of the analysis in terms of “tempo”, the relationship is inverted. Suppose I wish to “measure” the distance between the two “quasi-points”, e.g.
The technique that I adopt for this purpose is to insert a series of events between my acts of awareness of them, namely, my acts of awareness of the marks along the edge of a ruler, thus:-
These I proceed to count. My intuition of the regularity of their “spacing” is obviously dependent on my intuition of the invariant rhythm of my successive acts of awareness of them, and the number that I obtain is the ratio between the tempo of this rhythm and that of the oscillation between my acts of awareness of the end-points. In terms of “frequency”, I am expressing the “lesser” in terms of the “greater”. On the assumption that the raw material of our experience consists of extremely rapid change, which we are adopting here, this procedure is clearly in order. We could even employ it in a purely musical context; we normally think of “overtones” as generated by the “fundamental”, but it would be reasonable enough to regard the “fundamental” as resulting from the mutual reinforcement of the “overtones”.
Our ability to make an immediate comparison between distances in the visual field even when there is no obvious geometrical relation between them, can easily be compared with our direct awareness of differences of musical “pitch”.
D
The “pitch” of the oscillation of awareness A - B - A… etc. will clearly be lower than that of the oscillation C - D - C… etc., thus allowing a direct comparison to be made.
It is clearly possible, in an important sense, to “hear” an interval within the usual field, that is to say, to interpret it as the frequency with which our awareness fluctuates between the “points” at either end of it. Distance away from us is a somewhat different matter. It is always conjectural, and its importance is always concerned with our estimate of the temporal interval needed in order to make tactile contact with the surface of whatever we think we see. Such contact is an actualisation of a “permanent possibility of sensation”.
We learn how to form our estimates in early childhood, initially by manual exploration of visible parts of the surface of our own bodies, and we have generally achieved quite a high degree of proficiency by the time that we begin to speak. But misjudgments are quite common, and it is easy, by means of mirrors and other similar devices, to create situations in which “illusions” occur.
When the “object” seen is one like the Sun or the stars, which we have no hope of touching, we express its distance as a temporal interval - the conjectured interval between the departure of a “particle” of light from the surface of the “object” and its arrival within our field of vision; both events are imagined as “tactile” in character. We could perfectly well express our distances from objects that we can touch in similar terms - as “so many billionths of a light-second” - but it is the potential velocities of our own motion that interest us in these cases, and these, unlike that of “light”, are anything but uniform. We therefore prefer to express such intervals in terms of visualisable distances, which we can measure in the manner described above. It is possible that the tempo with which the experiential raw material is scanned when creating the visual field is the same for all human beings; this would account for the communicability of “distances”.
One important respect in which visual perception differs from all other modes of experience is the virtual insignificance of variations of quantitative intensity, or “intensive quantity”. It is differences of quality and structure which are of predominant importance, and even in the case of “black and white”, which actually expresses no more than a difference between intensities of illumination, we tend to think of it, and express it, as a colour-difference. Furthermore, any given shade retains the same name no matter how brightly it is illuminated. This is because the importance of contrasts, apart from purely æsthetic considerations, lies mainly in the indication of the whereabouts of tangible surfaces, and that except in the case of monochrome drawings and photographs, contrasts of colour are the rule.
Nevertheless, methods have been devised for the visual expression of changes of intensive quantity. In the case of hearing, any increase of intensive quantity is usually interpreted as indicating a diminution of the distance between the observer and the tangible source of the “sound”, but in the case of vision, the equivalent indication is furnished by an increase in the proportion of the visual field occupied by bounded areas which are interpreted as signs for tangible surfaces. This equivalence is used extensively in our visual symbolism; we represent changes of intensive quantity by changes of extensive quantity. Since symbolism, in Europe, is habitually read from left to right, we always indicate the tempo of change in the horizontal plane, while the changes of intensive quantity are represented vertically. The simplest instance is furnished by the musical expression marks, << and >>, but the same principle is employed in the graphic representation of any change of intensive quantity, as, for example, the indications of changes of atmospheric pressure recorded on a barograph.
But, on the experiential interpretation of visual distance given above, the greater distance is experientially equivalent to the lower frequency and, therefore, to the lower intensity; thus it is clear that this symbolic practice inverts the structural differences that it is intended to represent; in terms of importance, it presents us with something like a “photographic negative”.
This particular symbolic practice has indeed had the most unfortunate consequences for our modes of thinking. We speak of “waves”, and of “wave-theory”, although there is no reason to suppose that pulsations of sound or of electromagnetic intensity - including “light” - have any “shape” at all. The wave-shape is merely characteristic of our graphic representation of them, but now that it has been widely employed for this purpose, it is extremely difficult to eliminate it from our thought, and to realise that it plays no part in the symbolised phenomena, but is merely part of the symbolism. “Wave-theory” is a serious misnomer, and should be replaced by “pulse-theory”; but “pulsation” has the disadvantage, as compared with the visible “wave-form”, that it can only be communicated by touch, to one person at a time - as for example when a doctor feels his patient's pulse - whereas the wave-form, once we have learned to translate it back into the kind of change that it is intended to represent, can be used for “public” communication. We should, however, be very careful to realise the fundamental difference - amounting to an actual inversion - between the symbol and the actuality, and to accord ontological priority to the latter.
In the above instance the persistent use of terms such as “wave-theory” and “wave-length” shows that this has not been done, and that the symbolic representation continues to be regarded as more “real” than the actuality. This kind of thing is serious, because it leads to the restriction of the attribute “real” to those elements of experience which can be reliably communicated by symbolic methods, and to the complementary depreciation, as “unreal”, of those which cannot be so communicated. This depreciation has the consequence that important elements of experience come to be regarded as “out of bounds” for thought; “shades of the prison house” could certainly tend to “close upon the growing boy” during the course of his education. If we confine the term “real” to what can be reliably communicated, “actuality” includes much more than “reality”, and much of what, from the point of view of enjoyment, is of the greatest value, appears to belong to the category of the “unreal”.
With the rise of physical science, an increasing measure of human co-operation has become necessary in order to achieve and maintain a tolerable mode of living within a technological society, and the material that has to be communicated for this purpose has become extremely complex. Consequently, ever-increasing emphasis has been placed on the accuracy and reliability of symbolic communication, and the degree of success that has been achieved has encouraged the notion that the present tendencies can be continued indefinitely, asymptotically approaching “perfection” in the description and prediction of phenomena.
Were this to occur, not only the “shades of the prison house”, but its very walls, would close upon the whole of human thought. Fortunately, the impossibility of such an occurrence is, I think, demonstrable. It is possible to show that the nature of symbolising technique is such that there are bound to be limits to what it is capable of expressing, and that it may very well be that physical science has encountered those limits. This demonstration furnishes the material for the ensuing chapter.
One basic assumption underlies every attempt to communicate by means of words and symbols and even, more roughly, by means of gestures and behaviour. This is, that the utterance of any distinctive “invariant”, or of a recognisably distinctive member of a “gap-indifferent” series, in the medium of communication employed, is intended by the utterer to stand for a distinctive “invariance” or “gap-indifference” in whatever it is that he is trying to communicate.
When we consider written language, it is clear that the gap-free “invariance” of our visual act of awareness of a <word>1 cannot possibly stand for an “invariance” in our awareness of the corresponding spoken “word”, since this is not invariant at all; it is a rapid sequence of audible change. The “invariance” of the written word can only serve as a mnemonic for the “gap-indifference” of a series of such changes, to which symbolic importance has been attached at some time in the past.
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1. The use of “French quotes”, when the reader is intended to confine his attention to the visual aspects of the symbol, is borrowed from C. I. Lewis.
A “repetition” of written symbols is clearly an imitation of the repetition of the word-sounds which preceded their “reduction” to writing. The “gap-indifference” of the repeated symbols is very different from the “gap-free invariance” of a single symbol. But the gap-indifference of a series of visual symbols differs from that of a series of spoken words only in respect of the length of the gaps; this is a difference of degree, not of “kind”.
To illustrate this point, let the reader read the following formula, first silently, then aloud:-
Our visual awareness of the whole collection of symbols can clearly be accomplished within a “specious present”, whereas, when we read it aloud, there are appreciable gaps, within which other sounds occur, between our utterances of the successive “a”s. Nevertheless, the fact that we read from left to right, and that the order of reading is important, shows that the temporal structure of our awareness of the written expression is intended to correspond to that of our speaking it; it is only the tempi of reading and speech that are, inevitably, different.2
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2. The two tempi are used concurrently when a musical score is read; progress from left to right proceeds at the tempo of the music, which approximates to that of reading aloud, whereas the vertical scanning of a score of, say, twenty staves is clearly effected at an altogether more rapid, though still finite, tempo. Of course, we can also read any written expression “backwards”, thought not “aloud”. Our judgment of its “invariance” probably involves an oscillation of our attention between the beginning and the end of it, which will obviously be accomplished at the quicker of the two “tempi”.
In both cases, our diagnosis of the gap-indifference, whether of the < a >s or the “a”s, is a matter of judgment; we can never be as “certain” of it as we can of the gap-free invariance of the single written symbol <a>.
Sometimes, indeed, we may be very doubtful about it; if I were to read (a + b)(a - b) = A² - B², I would be uncertain whether the utterer had intended the <a>s on the left-hand side of the equation to be regarded as gap-indifferent with the <A>s on the right, and if I read it aloud, I would be inclined to utter “small a” in the first case and “capital a” in the second.
Logic and mathematics clearly depend on the assumption that the utterer, when he repeatedly uses the symbol <a>, intends the gap-indifference of the individual <a>s to be interpreted as representative of an “invariance” at least as “absolute” as that of our “gap-free” awareness of a single individual <a>. This fiction is maintained even when the symbols are handwritten rather than printed, so that the differences between them are actually rather obvious.
Now a mathematic or logical “truth”, to be “certain” enough to serve as a premise from which other “truths” can be certainly “deduced”, should not only be “eternally” true, but should also be true within any portion of “eternity”, no matter how short. This is, however, ruled out by the necessity that even the invariance of a single symbol needs to be observed before any symbolic function can be attributed to it.
Now the “instantaneous” observation of an “invariance” requires the postulation of an “infinitely rapid” tempo of thought and visual perception, and this is “infinitely” beyond the scope both of observation and imagination. It follows, therefore, that no symbolic function can be accorded even to a single letter or number until our awareness of it has attained whatever “quantum” of duration is required for us to arrive at a judgment of its “invariance”. This is, of course, extremely short relative to the temporal “intervals” with which we are ordinarily concerned.
The principle involved can be illustrated in “slow-motion”, and quantitatively. Accepting the undisputed premise that our awareness of “Middle C” is equivalent to our awareness of a succession of pulsations, approximately invariant in rhythm, of about 256 to the second, it is clear that the “invariant”, “Middle C”, cannot come into “existence” until a quantum of duration has elapsed which is at least 1/256 of a second, and is very likely well in excess of that figure.
Similar examples, where much longer “quanta” are required, are quite easy to construct. For example, a good many days will have to elapse before a member of a series of events with circadian rhythm, such as sunset, can be described as “daily”.
What is maintained here is that a corresponding, although much shorter, quantum of duration must elapse before a mark such as <> can be regarded as “symbolic”. It is therefore meaningless to use such a mark to represent any “invariance” that may occur within a duration that does not attain this “quantum”, since our awareness of visual “invariance” is much more rapid than that of any other variety. This quantum appears to impose a limit on the temporal fine-structure that can be symbolically represented. It is clear that it makes no difference whether or not any non-symbolic meaning is actually attached to the symbol; its invariance must be cognised before it can begin to function as a symbol at all!
In actual practice, the limiting “quanta” required for our cognitions of symbolic invariance are usually much longer, since logical and mathematical formulæ tend to be long and complex, and much recognition, as well as cognition, is required. Logicians and mathematicians are trained to carry out the “scanning” process at a much quicker tempo than that which laymen can achieve, but this is still obviously “finite”; and even they often have some difficulty in deciding just what structural elements, in a long symbolic sequence, have been intended by the utterer to be regarded as “invariant”. Whether or not “quanta” actually occur within the raw material of experience, it is clear that the durational quanta required for the cognitions of “invariance” and “gap-indifference” are bound to impose “quantum” limitations on the rhythmic fine-structure that can be symbolically expressed. Any process that could conceivably occur within a duration that is too short to permit of a cognition of the invariance of a single visual symbol must be relegated to the category of the “ineffable”.
It seems likely that the “quantum” that confronts the physicists is a “durational” one; it may well be the minimum required for the “resonance” of the sensitive elements embodied in a photographic plate with the “rhythm” of electromagnetic pulsation to effect a permanently observable change in the plate. We may speak colloquially of “instantaneous” exposures, but we are well aware that this is only a euphemism for very short ones.
Indeed, if this is the case, Planck's quantum equation, e = h v, becomes no more than a methodological tautology. “e”, the smallest observable energy-transfer, or change, is what occurs during the durational “quantum” concerned. Since “wave-theory” postulates that this has been occasioned by rhythmic pulsations of invariant “tempo”, a “frequency”, it is clear that the minimum change imaginable within the context of the theory is that effected by a single pulsation. This, which is unobservable, is symbolised by “h”. Obviously “e” is going to be proportion to the frequency, “v”, which must determine how many “h-changes” can occur within the minimum quantum of duration needed to certify the approximate invariance of “v”. “e” can be observed, and “v” inferred from various “interference”-type observations, but “h” is a priori unobservable, a pure figment created by the theory itself, although its numerical constancy tends to corroborate the theory.
“Wave-theories” express a world-outlook which differs radically from that which seeks to build up a “Universe” out of a compresence of “invariants”. Such a “geometrical” type of world-picture has been the goal of scientists since the days of Parmenides, largely because “invariances” are what we need to diagnose in order to make reliable predictions. Wave-theory, on the other hand, accepts “change” as the natural order of things, and treats invariances, including all invariant qualities, as rhythmically invariant, repetitive patterns of change. But our examination of symbolic expressions has made it clear that once we arrive at the most rapidly observable invariance of “quality”, or repetitive pattern of change, the change which has given rise to it is bound to lie beyond the range of symbolic expression, which is as much as to say, beyond the range of “science”.
We have once more arrived at Zeno's “arrow” paradox, this time approaching it from the world-outlook which Zeno himself sought to exclude. He belonged to the Parmenidean school, which allowed “reality” only to the “eternal”, in the sense of the “absolutely unchanging”. Both “arrowness” and “position” qualified as elements of “reality”. Clearly, if “arrowness” always had to “be” in an unchanging “position” it could never begin to move. The “absolute” view of spatial position was doubtless encouraged by the successful replication of the symbolic constructions effected by the Greek geometers, and eventually unified by Euclid. It persisted up to and beyond the time of Newton, although he relaxed sufficiently to allow “uniform motion in a straight line”, as well as “rest”, as an “invariance”.
The Parmenidean preference for an ontology of “invariance” is of ethical-æsthetic origin; it is common alike to the adherents of all religions, who attribute “invariance” to G-d, and to scientists, who attribute it to the “Laws of Nature”. It represents a reaction from our most intense judgments of disvalue, which invariably accompany extremely intense or extremely abrupt changes. This association has led to the rather thoughtless assumption that the æsthetic antithesis of “too much” must be “none at all”, rather than “enough”. This is why both religion and science have postulated a secure, completely unchanging “heaven” as their ideal, where everything is predictable, and there are therefore no surprises. Religious examples of this “ideal” are too numerous to be worth mention; an excellent scientific one is Einstein's “Principle of Least Action”. Reacting against the excessive effort that is frequently required of mankind, he has postulated a cosmic ideal of “maximum laziness”!
It is clear that Zeno was bound, by his own ethical criteria, to exclude both “change” and “motion” from his fundamental ontology; they had to be relegated to the inferior category of “mere appearance”. Naturally enough, nobody was exactly elated by this conclusion, and it has been tacitly disregarded, both “change” and “motion” being accepted as elements of our basic ontologies. The present study suggests that this disregard may have been carried too far. We can hardly eliminate “change”, since this appears to be characteristic of all “awareness”, but there appear to be limitations as to what we can conceive of as being capable of continuous motion, simply because anything that we can represent symbolically as an “existent” must, for logical purposes, be some kind of “invariance” or “gap-indifference”.
Now as long as “invariant position” was supposed to be a genuine possibility, it could be compresent with “invariant arrowness”. But now that “point-instants” have replaced “points”, this is no longer possible, because neither “arrowness” nor a “state of motion” can exist at an “instant”.
It has not been noticed that an approximation of the temporal infinitesimal, dt, to zero requires an “approximation to infinity” of the tempo of some activity - which is plainly nonsensical. Once we accept change as a basic element in an ontology, the fundamental temporal notion of “tempo” must replace that of “interval”. Its numerical expression, which relates it to the ostensively definable, “invariant” tempo of the “second”, is “frequency”.
All that can occur at an “instant”, or within an “atomic event”, is some kind of change. The obvious candidate for this rôle is change of “intensive quantity” - the kind of experience characteristic of hearing rather than of vision. But this is not “motion”, and we have already seen that the “arrow” cannot be thought of as “existing”, let alone “moving”, within any duration less than the quantum required for a cognition of invariant “arrowness”. Russell was correct when he maintained that what Zeno's paradox showed was that the “motion” of the arrow consisted in its discontinuous appearance in different places at different times; it is impossible to think of it as moving “continuously”. Such, obviously enough, is the status of a “moving image” on the television screen; it is re-created, many times a second, in positions on the screen which are only approximately adjacent to one another.
Now our inescapable intuitions require us to accept “instants” or, at least, “atomic events” as elements of our ontology. We cannot consistently maintain a solipsist position; our own natures compel us to regard our own experiences as being in direct contact with occurrences “outside” them, some of which “causally” affect us, while others are “causally” affected by us. What seems clear, however, is that whatever enters or leaves our experiences at any “instant” can only be envisaged in terms of pure change, probably of intensive quantity, and devoid of any quasi-invariant structure of its own. All such structures must therefore be our own creation, and are doubtless the fruits of our æsthetic preferences. There is no need to relegate such quasi-invariant structures to the realm of “appearance”; their status is that of repetitive patterns of change, which themselves change very slowly relative to the tempi of bodily activity, including speech, in which we are predominantly interested.
Admittedly, the raw material of “external” experience makes it easier to construct certain types of structure rather than others, but the structures cannot be thought of as entering our experiences “as such”. Thus any postulation of “Dinge-an-sich” is altogether superfluous, although inasmuch as each of us regards himself as an “Aktivität-an-sich”, we can postulate such entities as “outside” our experiences. A “Stoff-an-sich”, in the shape of change of intensive quantity is, however, quite in order. The stimulation of our own æsthetic activity may be due in the first place to abrupt, unpleasant increases in the intensity of the experiential flux; these are indeed attributable to the “raw material”. But nearly all our positive value-judgments are associated with “structure”, which is “all our own work”. We may very well choose to regard “ourselves” as the agents of a “Universal Æsthetic”; such a postulate does indeed provide a meaningful principle explaining our feeling of “unity” with the rest of the Universe.
Our “ideas” are in fact æsthetic in origin, and in no way directly dependent on the “impressions”, although the latter are necessary in order to stimulate us to create them. We can liken the “impressions” to the “carrier-wave” that enters a television ærial, the “ideas” to the rhythmic processes occurring within the receiver, and the “phenomena” on the screen to the outcome of the interaction of the two. Obviously, the “ideas” have been chosen in such a way that the phenomena produced are “what we want to see”. Without the stimulus of the “impressions”, the “ideas” would never have come into existence; Hume is quite right here. The impressions are their necessary, but not their sufficient, cause. “Occurrence” has to stimulate the æsthetic activity which creates “existence”. As Nietzsche asserted in The Birth of Tragedy: “Existence can only ultimately be justified as an æsthetic phenomenon.”
We can only talk about certain of the “ideal” elements in the phenomena; the raw material, the flux of “impressions”, is rhythmically so fine-textured that it must always remain beyond the range of symbolic expression. We can only deal with it in the slowed-down forms created by grouping sequences of “impressions”, presumably chosen for æsthetic reasons, into rhythmically quasi-invariant series. Such activities are clearly “synthetic”, but since all human beings appear, from early infancy, to make use of the same “senses” for the purpose, they are “a priori” as far as language and symbolism are concerned. The similarity in the modes of functioning of the senses, as between different human beings, appears to “transcend”, in respect of its importance, any differences that may occur, so that the senses would appear genuinely to merit Kant's title of the “transcendental æsthetic”. But Kant himself, since he believed in the “Absolute Truth”, within the realm of “phenomena”, of Euclid's geometry and Newton's physics, had to postulate the extension of such an “æsthetic” into fields where its “transcendental” character is, to say the least, extremely doubtful.
Euclid and Newton have certainly provided us with excellent general principles for organising our co-ordination of the visual and tactile “sense-data” with which the operation of the genuinely transcendental æsthetic had already provided us; they are most helpful in enabling us to achieve the actualisation of conjectured value-experiences, and to avoid that of conjectured disvalue- experiences. But both disciplines involve the use of symbolic techniques, so that the very fine-textured elements within our experience are bound to remain outside their descriptive range. They therefore cannot approach the ideal of “Absolute correspondence-Truth” even in descriptions of the phenomena which we have assisted in creating; such an “ideal” is a will-o'-the-wisp.
All the so-called “Laws of Nature” are simply symbolic Gestalte, generally regarded as pleasantly “coherent”, i.e., experienced harmoniously, which assist us to further the organisation of our “phenomenal” material, which has already been processed by the “transcendental æsthetic”. The latter has developed by trial and error; we have retained beliefs and habits which have enabled us successfully to avoid certain conjecturally possible types of experience which are quasi-universally accompanied, in infancy, by disvalue-judgments; we have rejected those which have proved unsuccessful for the purpose. Such is the operation of “human-natural selection”.
In the course of the development of our “transcendental æsthetics” we have tended to suppress, or at least to relegate to a position of subordinate importance, any part of our raw material that we have been unable to use for the purpose of avoiding disvalue-experiences.
But as soon as we attempt to discover or create new values, we are at liberty to disregard “Laws of Nature” which have originated in this fashion. It is indeed quite likely that some human beings actually develop additional “senses”, that is to say, original methods of organising their “raw material”. They sometimes claim that with the aid of these methods they can attain a higher degree of æsthetic enjoyment than by the use of those which they share with mankind in general. Where such new “senses” manifest an unusually enhanced tempo of mental activity, it is clear that the structures that this creates will not be symbolically communicable to the majority of mankind, unless they can somehow be translated into “slow-motion” versions that can be symbolically expressed by existing methods. This phenomenon probably accounts for “genius” and also for certain forms of “lunacy”; the “genius” is the man who has effected a successful translation, while the “lunatic” has tried, but failed. This is the field of “mysticism”; it represents attempts by particularly sensitive human beings to express exceptionally fine-textured structures within their phenomenal raw material; but even these are far removed from the primal, unstructured flux which “shows itself”. Such “supermen” might devise an exceptionally fine-textured medium of communication for use among themselves, but even this, if it relied on “invariances”, would be subject to the same kind of “nonsense-barrier” as our existing methods.
It seems unlikely that the notion of “Absolute correspondence-Truth” could ever occur to any people whose language had not been reduced to writing. The gaps between our acts of awareness of the “same” spoken word are too obvious, as is the difference between them. But the shortness of the gaps between our awareness of successive examples of the “same” written symbol is such that we have effectively written them off, thereby inadvertently postulating an “infinite” tempo for transfers of attention within visual awareness and thought. Logicians and mathematicians, in particular, have virtually equated the gap-indifference of a series of acts of awareness of the “same” symbol with the gap-free invariance of a visual act of awareness of a single symbol, and have attributed “absolute” invariance to both.
Scientists, employing mathematical language, have thereupon proceeded to try to describe the whole of experience in terms of the kind of structure that the visual field displays, namely, as a complex “simultaneous” compresence of a vast number of “invariant” constituents. Such types of description are what go by the title of “geometrical”. They can work quite well as long as we are not concerned with trying to describe event-sequences which are too brief to permit of any judgment of “invariance”. In point of fact, physical science, since the 17th century, has proceeded in two complementary directions; Newton, in his great mechanical and astronomic synthesis, described the more slowly changing “invariant” patterns of phenomena, for the most part astronomical, in terms of the tempo of the rhythms of ordinary life. On the other hand, Huyghens and his followers, who presumably took their cue from sound, postulated the hypothesis that many invariant qualities, such as “colour”, were in fact rhythmically invariant patterns of process, the tempi of which were too rapid for actual observation, but could be inferred from phenomena of “interference” type, and related arithmetically with the familiar tempo of the “second”; this could be defined “ostensively”.
Newton and his followers ran no risk of running into the “nonsense-barriers” inherent in symbolic technique, since the tempi of the invariant patterns of change with which they were concerned were either similar to, or much slower than, that of the “second”. But Huyghens' 20th-century successors attempted to approach “quasi-absolute” accuracy in their descriptions of exceedingly rapid change, and having overlooked the existence of a linguistic nonsense-barrier, they attempted, but naturally failed, to express the “ineffable”. The “ineffable” should on no account be equated with the “mystical”; if our intuitions of “direct” causal contact with entities outside our experience are inescapable, the whole of the raw material of our “external” experience is “ineffable”. The source of such “ineffability” does not have to be sought in any æsthetic or even “moral” depravity in the raw material, but in the inability of the “effing” apparatus even approximately to replicate its structure. There is an obvious spatial analogue to this in a limitation to the replication of visual detail that is encountered in photography; this is due to the circumstance that the texture of the emulsion on a photographic plate cannot be “infinitely” fine. It would indeed appear doubtful whether physics, as long as it is entirely dependent on visual and photographic material for its “basic statements”, can possibly probe any further than at present into the fine-structure of “activity”, and still continue to achieve any coherent presentation of its results in language or “linguistic” symbolism.
Physical scientists and scientifically-minded philosophers have tended to justify their claims to pre-eminence, and to inflate the prestige of their activities, by representing themselves as engaged in an occupation to which an almost “religious” degree of respect should be shown - the “Search for Truth”. They have assumed, quite correctly, that the majority of educated people have unreflectively swallowed the “orthodox” view that Truth - with a capital T - must possess unconditional value. The arguments in the present chapter appear to show that this “Search for Truth” can be no more than a “snark-hunting” pastime. Such a view would, however, be reprehensible should anything of genuine value be sacrificed by the destruction of this “ideal”. Accordingly, the next chapter will be devoted to an application of the methods of value- analysis propounded by a logician, C. I. Lewis, to the values and disvalues of symbolic “truth” and “falsehood”. It is hoped that the outcome will reassure readers that nothing of serious value has been destroyed by the criticism of symbolic technique undertaken in the present chapter.
There is a widespread belief, which I think deserves to be stigmatised as a superstition, to the effect that truth is unconditionally valuable, and falsehood unconditionally disvaluable.
In this chapter I propose to challenge this view by applying the analysis of “value” propounded by C. I. Lewis in his Analysis of Knowledge and Valuation to the concepts of “falsehood” and “truth”.
Lewis, correctly in my opinion, confined the attribution of “intrinsic” value/disvalue to the immediate judgments occasioned by acts of awareness; all other uses of the concepts he considered to be derivative from these. Although the origin of “judgments” is generally considered to be “internal”, he regarded both alike as “given”; their association is neither “a priori” nor “a posteriori”; it is “present”, and simply “happens”.1 These views will be adopted for the purposes of the present work.
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1. It may well be the prototype of our notion of “causation”.
“Inherent” value/disvalue can be predicted of all persistent qualities and of “objects”, which are “bundles” of them, provided that acts of awareness of them are sometimes accompanied by intrinsic value/disvalue judgments. It is therefore a conjectured possibility, rather than an actuality with which we are directly acquainted. As far as modes of visual and aural experiencing are concerned, ‘inherent’ value/disvalue can only be attributed to them inasmuch as they themselves are judged to be pleasing or displeasing: “what” they are is of no importance in this context. The values /disvalues predicated of varieties of taste, smell and viscero-tactile sensations are, with a few exceptions, ‘inherent’, since their qualities generally have no importance beyond themselves. Except, on occasion, in the case of smell, they seldom function as signs for the possibility of any other kind of experience.
There is one important point which concerns disvalue-experiences, which Lewis does not appear to have noticed. This is that no matter what the mode of experience, disvalue-judgments invariably accompany acts of awareness that exceed a certain critical level of intensity or, in the case of structural change, of abruptness. In the case of visual and aural awareness, the intensity of a sudden flash or bang actually blots out all awareness of structure; the total description of such an occurrence is simply a disvalue-judgment of its excessive intensity. The phenomenon is what is generally known as “shock”, and its disvalue is inherent in a great many types of refutation. This leads us, mistakenly, to attribute “inherent” disvalue to statements, once actions taken on the strength of them have led to the occurrence of such refutations, since memories of these will be evoked whenever the statements are heard or read.
Such disvalues belong to Lewis' “instrumental” category, which we attribute to qualities and objects, among which we can include symbolic formulæ, when they function merely as signs for something “inherently” valuable or disvaluable, and hence ultimately for possibilities of future acts of awareness of it in ways which are “intrinsically” valuable or disvaluable. In such cases, the æsthetic aspects of our immediate acts of awareness are regarded as being of negligible importance. Most bounded areas within the field of vision are more important to us in respect of “what they are” than of “how they look”, that is to say, their value/disvalue is mainly “instrumental”. They have “inherent” value when they “look beautiful”, but their instrumental value lies in the observer's conjecture of the proximity of some “inherently” valuable object and the prospect, in the future, of some “intrinsically” valuable act of awareness, most likely tactile rather than visual in character.
A compresence of inherent and instrumental values frequently leads to disputes as to their priority of importance; for example, a conservationist may wish to preserve an ancient building because of its inherent visual value, while a would-be “developer”, thinking in terms of instrumental value, gives priority to the non-visual value-experiences which he believes would follow the development of an office block on its site.
The value/disvalue of a written or spoken symbolic expression can, strictly speaking, hardly be other than “instrumental”, apart from any direct æsthetic approval'disapproval of the visual or aural awareness of the actual writing or sound. In general, the importance of “what it means” is so such greater than that of “how it looks or sounds” that the latter is negligible. Only occasionally, in the case of speech, the beauty of an utterance becomes more important than its meaning; we sometimes value poetry for its musical rather than for its semantic content.
In any event, a value/disvalue judgment of the ‘thought-interpretation’ of a written or spoken expression should be clearly distinguished from that of its visual/auditory qualities. For example, an intrinsic value-judgment will accompany “good news” even if it is uttered in a harsh, ugly tone of voice, while a disvalue-judgment will accompany “bad news” no matter how beautifully it is spoken. But, since the thought-interpretation follows the hearing almost immediately, there is a mistaken tendency to regard the value as inherent in the speech itself, especially as there is no time for any action that could affect the value-judgment. The interval between the speech and its interpretation is regarded as negligible, and the two are tacitly identified.
This view is demonstrably mistaken, since our value-judgment of the “coherence” of a written or spoken expression cannot be achieved while the reading or hearing is still in progress; “inherent” value can only be attributed to the thought-interpretation that follows; the value of the actual writing or speech can only be instrumental. On the other hand, a case of “incoherence” can sometimes be experienced, as a “shock”, during the actual course of the hearing or reading.
We can now turn our attention to the “truth” and “falsehood” of symbolic expressions. Following Lewis' basic principle, we must derive all their value/disvalue from our actual experiences of them. In the case of “correspondence-truth”, these are experiences of “verification” and “refutation”. Here, I think, we must accord epistemological priority to refutation, because we have frequently experienced the important refutation of beliefs long before we ever learn to express them in words. On the other hand, it is doubtful whether we ever notice the “verification” of a pre-verbal belief. Our every intentional action is guided by a massive complex of beliefs, most of which we have acquired during the pre-verbal stages of development, and we never bother to formulate them. When we do, their formulations are “tautological” in character, and of no informative value whatsoever. The psychological impact produced by “verifications” of such beliefs is negligible, simply because the actuality conforms, with very little discrepancy, to the expectation.
Refutation is quite another matter. Since the actions or inactions that we base on our beliefs are invariably directed either towards the actualisation of conjectured value-experiences or, and far more importantly, towards the avoidance of conjectured disvalue-experiences, a failure of actuality to conform to expectation is always something of a surprise, which may amount to an intrinsically disvaluable “shock”. It is true that a value-judgment may sometimes surprise us by its unexpected intensity; for example, the strawberries may taste much nicer than we expected. But this hardly constitutes a “refutation” of our expectation, such as we would experience if they actually tasted nasty. We only say that our expectations are “falsified” when the discrepancy between them and the actuality is experienced as something of a “shock”, and whenever this exceeds a certain level of intensity, it is accompanied by an intrinsic disvalue-judgment.
There would seem to be no grounds for explaining the acquisition of our infantile beliefs by any process other than that of “trial and error”; by “error”, we express the experience of a notable discrepancy between expectation and actuality, usually the occurrence of a disvalue judgment as the sequel to our chosen action or inaction, when a value-judgment was expected. There is also another variety, usually somewhat milder, which we call “disappointment”; we experience it when an expected value-judgment either fails to occur at all, or occurs at an unexpectedly low level of intensity. Pavlov's generation of “conditioned reflexes” in his dogs depended entirely on his use of stimuli to generate types of experience which, by analogy with human beings, he could rely on to occasion experiences which would be accompanied by strong value/disvalue judgments. He obviously managed to persuade his dogs to associate expectations of them with some quite irrelevant “signs”. But many “natural” visual signs are, structurally speaking, quite “irrelevant” to the inherently valuable/disvaluable qualities or objects with which an infant learns to associate them, and it is no denigration of the human race to suggest that these associations are formed by the process of “trial and error”, the erroneous ones being discontinued. The process could be termed “human-natural selection”.
The community of infantile beliefs can therefore be largely accounted for by the community of infantile distastes. Russell's sardonic aside: “Prejudice - the synthetic a priori” was clearly intended as a gibe at Kant, but the adverse “prejudices” innate in all infants appear to be pretty much the same, and the most important of them - the objections to very great intensities of sensation and to very abrupt changes of structure - appear to persist, to a considerable extent, throughout human life. Contemplated from outside, these appear “synthetic”, but “enjoyed”, that is to say, experienced directly, they seem altogether unavoidable, and, in this sense, “a priori”.
It is not possible to detect any corresponding measure of similarity between favourable prejudices. Shaw's rejection of the Golden Rule, which ran:- “Do not do unto others as you would have them do unto you: tastes differ”, is justified. But the complement of the Golden Rule:- “Do not do unto others what you would much rather they should not do to you”, is not so readily disposed of, since basic distastes are very much alike. As a basic ethical principle, it appears to be altogether unexceptionable, on the assumption that ethical progress is a manifestation of the growth of human sympathy.
Many philosophers tend to ignore the importance of sympathy in the motivation of human activity. Yet it is quite obvious that in the absence of sympathy for children on the part of the great majority of parents, the human race could not possibly have survived. Human infants are born fœtalised, and are dependent on adults for the necessities of survival for much longer than the offspring of any other animal. Sympathy for very young children can only be regarded as a “prejudice”, or “synthetic a priori”, which develops from tendencies which seem to be innate; it motivates the actions of most parents and, broadly speaking, of adults in general.
Sympathy plays a very important rôle in the process of teaching children to speak. There can be little doubt that our initial acquaintance with language, as infants, is with our parents' attempts to make their wishes known to us, and with our attempts to make our wishes known to them. The primary “moods” of language are therefore the “evitative” and the “optative”.2 Of these, the evitative is much the stronger, since the avoidance of a conjectured disvalue-experience is often a matter of orgent necessity, whereas the attainment of a conjectured value-experience, however desirable it may be, is always in the nature of an optional “extra”. Warnings need to be clearer and more emphatic than recommendations; “No!”, in childhood, often functions as a word of command, whereas “Yes” is never more than an answer to a question. “No!” may even be accompanied by a slap, or be uttered in a harsh, “shocking” tone of voice, which automatically associates it with disvalue-judgments.
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2. The strongest forms of these are the “prohibitive” and the “imperative”.
It would be rash to assert that very young infants feel much sympathy for their parents, so we will assume that the fear of the parent is the beginning of linguistic wisdom. Thus we will consider the evitative mood, which requires immediate reaction, as the primary mood of language. This is shortly followed by the weaker optative mood, when permissive, pleasant-sounding expressions are used in reply to conative gestures on the child's part, which are the visible counterpart of questions.
A child's basic vocabulary must inevitably be learned by associating the distinctiveness of a gap-indifferent series of word-sounds with some distinct gap-indifference in the series of circumstances in which they are uttered. This will only occur provided that the child attaches importance, i.e., some kind of value or disvalue, to the distinctiveness of the circumstances. In a great many cases, this will be the instrumental value/disvalue attributed to most visual “Gestalte” in view of their function as “signs” for the possibility of future intrinsic tactile value/disvalue experiences.
The adults in its vicinity, who naturally wish to be able to communicate with the child as soon and in as much detail as is reasonably possible, take care to utter the word-sounds in contexts which are conventionally appropriate within the community in which they live, so that they provide the child with no motive for doubting the appropriateness of the association, provided that its reactions to the words or word-sequences do not result in any serious discrepancy between expectation and actuality. Its own reactions include “speech” - an attempt to replicate word-sounds, or sequences of them, with which it is familiar. It is said to “know” the meaning of a word or word-sequence when it reacts to it without hesitation, provided that the utterer judges the reaction to be appropriate.
“Doubt” is, after “shock”, one of the most basic forms of intrinsic disvalue-experience. It is a rapid oscillation between evitative and optative moods, and its intensity varies directly with that of the value/disvalue judgments that are conjectured as likely to follow the doubter's choice of action - or inaction. It will be more acute in cases when the choice may be required in order to avoid a disvalue-judgment rather than to achieve a value-judgment; in Hume's terminology, while it may cost us pains to doubt that fire warms and water refreshes, it costs us a great deal more to doubt that fire burns and water chills.
It is only in its more intense forms that it is automatically accompanied by a disvalue-judgment. We generally designate its weaker forms as “curiosity”, a kind of experience which is often accompanied by a value-judgment. Indeed, Hume's “it costs us too much pains to think otherwise” can hardly be applicable in cases where we are not concerned with the avoidance of major disvalue-judgments - including “disappointments”; otherwise an intentional prosecution of “enquiry” would constitute a gratuitous form of self-mortification.
In infancy, however, the use of language is 100% pragmatic; it is “correct” and “meaningful” when it “works”, and is either “wrong” or “misunderstood” when it does not. The appropriate reaction to a verbal expression is some form of action, to which importance is attached, and its rightness or wrongness can be detected immediately. Under these circumstances, Hume's principle is valid; doubt will always be accompanied by a disvalue-judgment, so that the child's desire to avoid it furnishes an important incentive to “learning”.
Now word-sounds, and the muscular efforts appropriate for their utterance, are easily remembered. It costs little effort to replicate them in circumstances which do not in the least resemble those in which they were originally uttered. In such cases they may express and evoke memories of the significant distinctiveness of those circumstances. This enables an utterer to communicate associations, including sign-situations which he uses as a basis for the choice of action, to a hearer who is as yet unfamiliar with them, provided that the hearer is familiar with individual words that the utterer has associated in his expression.
Such expressions constitute “information”. Our experiences in language-learning during childhood have predisposed us in favour of the belief that the utterer's intentions towards the hearer are normally sympathetic, and that he supposes that the expression, sooner or later - often much later - may assist the hearer to choose whatever action is appropriate in order either to avoid a disvalue-experience or to achieve a value-experience.3
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3. It is essential to bear in mind that the achievement of an expected value-experience is always the avoidance of a “disappointment”.
Most of the information that we learn in school consists of recommendations or warnings concerned with verbal and symbolic utterance. A piece of information such as “Battle of Hastings, 1066” can only express the utterer's belief that a replication of the utterance is unlikely to lead to a disvalue-experience, in the form of an expression of disapproval, such as might follow the utterance “Battle of Hastings, 966”. The inclusion of a remote “past” temporal predicate practically eliminates the possibility of the information providing a basis for any action other than symbolic utterance. The second expression might mildly “shock” a historian who specialised in that period, since it would be excessively discordant with the harmonious structure of the complex Gestalt of written statements that he calls “history”. Thus a mild judgment of “instrumental disvalue” is in order, on “sympathetic” grounds.
When an informatory statement embodies no past temporal predicate, a hearer or reader is always likely to use it to assist him in the choice of an action or inaction appropriate for avoidance /achievement, since he is in the habit of assuming the sympathetic intentions of the utterer.4
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4. The affirmative, or “indicative”, mood of informatory statements is here interpreted as a weak form of the “optative” mood. Subjunctives are even weaker.
Strong “instrumental” disvalue must therefore be attributed to general statements such as “red light means go” and “Amanita Muscaria is good to eat”; they are seriously false, which “Battle of Hastings, 966” is not, because the indicated actions, if taken, are likely to be followed by experiences with which a strong intrinsic disvalue-judgment will be associated.
It is clear that the disvalues are not “inherent” in the written or spoken expressions; each of them expresses a recommendation for action, so that the hearer's interpretation of them is likely to be accompanied by a mild intrinsic value-judgment; their instrumental disvalue can only be experienced at a later date, if and when the recommended action is taken.
Falsehoods are often uttered on sympathetic grounds. When a doctor utters a favourable prognosis, even though he is confident that his patient's illness is terminal, he does so because he judges that the intrinsic value-judgment accompanying the “good news” will more than outweigh any eventual disvalue-judgment that may accompany its “refutation”.5 The point here is that no avoiding action is believed to be possible. A Roman Catholic may consider this course ethically mistaken, because he believes in the efficacy of “extreme unction” in mitigating the intensity of the disvalue-experience that is assumed to accompany death - or, in some cases, to follow it!
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5. It is worth noting that the effort required to utter the “lie” will be of sufficient intensity to occasion an intrinsic disvalue-judgment to the speaker.
Our assessment of the disvalue of most falsehood depends mainly on the expected intensity of the intrinsic disvalue-judgment that we expect to accompany the experience of refutation; it is, in fact, instrumental rather than inherent.
There are, of course, important exceptions. If I falsely inform a devoted wife that her husband is dead, her thought-interpretation of my utterance is likely to be accompanied by a violent disvalue-judgment. Furthermore, if she subsequently experiences a refutation of my statement, her intrinsic value-judgment may be so intense as to be excessive, and thereby automatically to become intrinsically disvaluable; a faint is by no means out of the question.
In a lighter vein, it is notable that many Africans tend to accord primacy of importance to the hearers' intrinsic value-judgment of his thought-interpretation of their utterances; they do not automatically assume that the hearer will attribute instrumental value to what they are saying. If such an attribution is intended, a special signal is given. The late Dr. L. S. B. Leakey once explained to the writer that this is the meaning of the word “Atiriri” in the Kikuyu language. Anything that preceded this was a mere preamble, intended to occasion mild intrinsic value-judgments on the hearer's part. It is not surprising that this practice leads to a reputation for mendacity, but this is the hearer's mistake.
We quite frequently utter intentional falsehoods which we expect to occasion immediate intrinsic disvalue-judgments in the hearer because we anticipate that the intrinsic value-judgments accompanying his experience of their refutation will more than outweigh the disvalue-judgments in importance. All hoaxes, and a good deal of verbal humour, are dependent on this type of sequence. Surprises, provided that they are not too intensely experienced, are a major source of enjoyment. Those who attach unconditional value to “Truth” have clearly gone astray; the antithesis of “too much” falsehood is not “none at all”, but “enough”. In this context, “tolerance” and a “sense of humour” are more or less synonymous. But they vary greatly between different individuals, so that a sympathetic utterer, who wishes to avoid occasioning disvalue-judgments to his hearers or readers, will err on the side of caution in respect of uttering statements which he believes to be “instrumentally” false. Nevertheless, it is clear that the line of demarcation between value and disvalue-experiences does not coincide with that between “negligible” and “appreciable” surprise. A virtual absence of surprise, such as accompanies the vast majority of our actions, is “null” as far as intrinsic value /disvalue judgments are concerned. The symbolic expressions of such sequences of expectation-actuality likewise occasion no value-judgment; in fact, the expression of a “tautology” generally occasions a mild feeling of disappointment; it is “too true to be any good”.
So far, there has been little mention of “truth”, simply because it appears that as far as direct experience is concerned, primacy must be assigned to falsehood in respect of its epistemological priority and on account of its stronger psychological impact.
The case of the hoax shows that instrumental falsehood is not unconditionally disvaluable; in such a case, the corresponding “truth” must be inferior in value to the falsehood. A value-judgment would be lost if we replaced the leg-pull by a true statement. Speaking generally, the “instrumental” value of “truth” seems to be no more than coextensive with the instrumental disvalue of falsehood. An increase in the complexity of a symbolic formula, undertaken in order to achieve greater “accuracy”, is not necessarily accompanied by any increase of instrumental value. Let us take an example from mathematics. Can any intrinsic value-experience result from the indefinite extension of the decimal expansion of “II”? At best, it is just possible that some amusement might be occasioned by a refutation of the well-known conjecture that it will not embody three consecutive “sevens”, but the importance of such an “intrinsic value-judgment” is negligible.
It is not clear what gain in “instrumental” value can accrue from an indefinitely continued refinement of scientific formulæ, which is at present sometimes justified as part of the “Search for Truth”. We can admit that the scientists have improved the accuracy of their predictions by attaching importance to progressively minuter differences between actuality and the expectations calculated by means of their formulæ; the permissible “margin of error” is being steadily narrowed. Regarded as a “Spiel-an-sich” - a game played for its own sake, in which, as in athletics, records are broken, it may provide intrinsic value-experiences for the participants. But it tends to militate against tolerance and a sense of humour, even in its practical applications. Take, for example, “Hi-Fi” sound reproduction and the “accurate” colour-replication of artistic masterpieces. This has developed into a type of pedantry, in which the intrinsic value-experience which accompanies listening or looking takes second place to the technical excellence of the apparatus as assessed, not by æsthetic evaluation, but by measurement.
It is highly questionable whether a “completely” predictable Universe would be a tolerable place to live in. Leibniz might perhaps have liked it; his ideal of a “Characteristica Universalis” was wholly in keeping with the notorious aridity of his character. In the cases of William James and John Stuart Mill, contemplation of a similar ideal is known to have led to serious bouts of depression, while Russell, in his famous A Free Man's Worship begins with an eloquent expres-sion of such a world-outlook, and proceeds to devote the rest of the essay to the recommendation of an anodyne against its worst effects.
Fortunately, however, the scientists' “ideal” of attaining “perfect” correspondence-truth can be effectively ridiculed by comparing it to an attempt by an athlete to run an “instantaneous” mile, since the tempo of thinking, like that of running, is and will always be subject to de facto limitations. The game of “accuracy for accuracy's sake” only occasions intrinsic value-experiences for the participants and a few interested spectators; it has no claim to special respect from the great majority of mankind. Its instrumental value is also limited, since its practical by-products never call for anything approaching “absolute” accuracy of measurement.
We can now turn to “Coherence-truth” and “Coherence-falsehood”. These are in a different category from “Correspondence”-relations, since they do not purport to relate the symbolism to non-symbolic experience, but are internal to the symbolism, which is obviously man-made. They include direct value/disvalue judgments of transitions between the thought-interpretations of the words associated in the spoken or written expressions; these are akin to judgments of “melodiousness” in music. But we are, perhaps unconsciously, also combining them with the more relevant elements in our pre-existent background of beliefs, and the intrinsic value/disvalue judgments associated with these compresences are closely akin to those of “harmony” and “discord” in music.
Here again we can most profitably begin with the consideration of “Coherence-falsehood”, and especially with symbolised compresences that seem to be “unthinkable”. “Instant invariance” is a good example. So is the one which worried Russell, who refers to it several times in his Inquiry into Meaning and Truth; it is “red and blue at the same time”. He could find no explanation for the “unthinkability” of this expression, especially in view of the fact that “red and square at the same time” was unobjectionable.
An explanation of these “unthinkabilities” is quite easy if we employ a “logic” which is a “dynamics of thinking” instead of a “statics of thoughts”. We need to reject the notion, implicit in classical logic, that thinking consists of a series of transitions, at an “infinitely” rapid tempo, between “absolute” invariances, and accept that there is, and always must be, a de facto limit to the possible rapidity of all mental process, although different limits may apply to different thinking beings. We treat the structure of our raw material as comparable with that which we attribute to the “carrier-wave” of radio and television, that is to say, as a linear succession of pulsations of “intensive quantity”, occurring at a tempo which is much more rapid than any of the transitions involved in sense-perception, but still finite. Our perceptions are abstractions from this flux, and our estimate of “difference” between them varies directly with the intensity of the psychological impacts accompanying our experience of transitions of attention between them. Correspondingly, when we try to “think” such a transition, the effort required will vary directly with the degree of experienced difference.
We have already noted that in the context of every type of experience, there is always a limit to the intensity that we can endure without the accompaniment of a serious disvalue-judgment. Thus the “unthinkable” will comprise those thought-transitions which we judge to require an intolerably intense effort in order to make them. In practice, we decline to make the attempt, or, at any rate, to persevere with it, just as an athlete would refuse to contemplate any attempt to run a “one-minute mile”. Maybe a “superman” may some day emerge, who can achieve a comparable feat of “mental athletics”, but even he will never manage an “instantaneous mile”.
Meanwhile, the general thinkability of symbolised structures has to be accommodated to the tempo of the sense-perception that we employ for the most rapid cognition of “common” invariances, which is that of vision.
We can now proceed to account for the two examples of “unthinkability” given above. In the first case, we can think of a close approximation to an “instant”, relating it to experienced events of very short duration. We can similarly think of a close approximation to “invariance”, relating it to very slow tempi of variation. What we cannot do is to think of a very rapid alternation between them; the effort required would be so great that we simply decline to attempt it. We cannot in any case ever think of “absolute” simultaneity, because of the finite tempo of our mental process. Short of this, however, incompatibility, within thought, can never be “absolute”, but, as in the present instance, it can be intolerably excessive.
Russell's problem can be elucidated in a similar fashion. A transition of attention within the field of vision can never be “instantaneous”; our experience of the “interval” between different parts of the visual field corresponds to the “time” needed for the transfer of attention, or more likely still, to the “tempo” of the oscillation of our attention between them.
Now “red-invariance” and “blue-invariance” can each be cognised within a very small area of the field; the tempi of our cognitions of them are of the same high order of rapidity. Any cognition of “blue-invariance” is bound to interrupt and destroy any cognition of “red-invariance”, so that they cannot overlap. Of course, if “at the same time” were interpreted so as to mean “absolutely simultaneously”, neither invariance could be cognised at all; “two” is not appreciably worse than “one” in this context.
On the other hand, the oscillation of awareness needed for a cognition of “square-invariance” covers a much wider area of the visual field; it is much slower, and not continuous. Thus there is plenty of time, between the relevant acts of awareness, for the cognition of “red-invariance”. The two different “orders” of tempo involved might perhaps be thought of as distinct “Riemannian curvatures of time”.
The relative importance of a “coherences-falsehood” is always concerned with the effort involved in making a transition between the thought-invariances evoked by the succession of words or symbols in the expression. Whenever this is so great that it is judged excessive, the expression is “incoherent”. The worst incoherences, which actually occasion a mild feeling of “shock”, are what we call “logical falsehoods”. An inexhaustible source of such expressions is furnished by associations of temporal predicates and relation-words, e.g., “The cause followed the effect”, “I will arrive yesterday”, etc., etc. All these will be rejected as “unthinkable” by utterers and hearers alike, and their unacceptability, basically æsthetic in origin, will ensure their elimination, for the purpose of “spontaneous” utterance, from any standard language used for purposes of communication.*
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* Editor's note: Here the author appears either to contradict himself or, alternatively, to categorize his own use of language as non-standard.
“Nonsensicality” is less serious. Take, for example, Russell's example, “quadruplicity drinks procrastination”. Such a thought-transition is exceedingly difficult to accomplish at a tempo comparable with that at which the expression is habitually spoken or ready. But nobody with much experience of solving the more recondite forms of crossword puzzle would condemn it out of hand as “meaningless”; indeed, if “drinks” is interpreted in the wide, figurative sense of “is nourished by”, the expression might be regarded as a tolerable paraphrase of “a stitch in time saves four”. We naturally exclude such expressions from ordinary language, since we often have to use it for urgent purposes, and therefore cannot afford to substitute crossword clues for the words which are their “solutions”.
These transitions are anything but too fast to be thinkable; the maximum tempo at which we are able to effect them is far too slow for the type of thought-transition that normally accompanies speech or reading. We are in effect being asked to transfer our attention from one “dimension” of thought to another, in cases where the “co-ordinates” in the two dimensions are rarely thought of as co-variant. But in the case of “logical falsehood”, we are being asked compresently to attribute two different co-ordinates in the same dimension to a single passage of experience.
When an expression is syntactically incoherent, no question normally arises as to the evaluation of its “truth” or “falsehood”. One exception needs to be briefly considered; it concerns the ambiguous function of the word “is”. Used as a copula, it requires a complement, and is semantically equivalent to “yes!” rather than to “exists”. The “is” of “snow is white” merely signals the current affirmative mood of the utterer to the association “white snow”. The “is” of “snow is” is a different word altogether; in speech, it is always stressed, whereas the copula is normally unstressed, except when a particularly strong affirmative mood has to be signalled. “Snow is” asserts that the word “snow” is a symbol standing for something persistent. We would reject “to is”, because “to” is an “event-word”, and we would likewise reject “gradjbok is”, unless we supposed that the sound was being employed as a word for the first time, as has recently occurred in such cases as “quark” and “neutrino”. Every word must have had a première at some time or other!
“Snow is”, with “is” unaccented, is syntactically incomplete, and no question arises as to any evaluation of its truth or falsehood. The hearing or reading of such an expression is likely to be accompanied by a mild intrinsic disvalue-judgment, inasmuch as we are “disappointed” at the non-occurrence of the expected “complement”. But we call it “incorrect” rather than “false”.
Summing up, we can now conclude that “coherence-falsehood” is an inherent disvalue, attributed to a symbolic expression on account of the intrinsic disvalue-judgments that accompany our experiences of it. These are fundamentally due to the excessively intense, sometimes intolerable disvalue-judgments accompanying the effort experienced in attempting to make either a thought-transition indicated within the symbolic expression, or a transition between our thought-interpretation of the whole expression and the background of our existing beliefs.
At first sight, it seems odd that we ever contrive to construct symbolic expressions of the “unthinkable”. The explanation, however, is quite simple. We frequently wish to express extremely close temporal compresences within our experiences; in particular within the visual field. But our symbolic technique is derived from speech, which is a linear succession, quite leisurely in tempo; it cannot possibly exhibit the closeness of temporal compresence that we try to use it to express. For example, when we say or read “white horse” or, in the case of a Frenchman, “cheval blanc”, the structure of what we are trying to express would be better written - it cannot be spoken - as:
The structure of its meaning is analogous to that of a “chord” in music, whereas our symbolism disposes of nothing but melodic lines.
We have become so accustomed to the conventional expression of compresences by means of successions that we no longer notice how odd it actually is; we perform the necessary “translations” quasi-automatically. The order of a word-sequence which is going in any case to be interpreted as a compresence does not matter; this is why “white horse” can be semantically equivalent to “cheval blanc”. We are, indeed, almost “addicted” to interpreting word-sequences as expressions of compresences; it comes as quite a shock when it is pointed out that the vocal expression “F after C” falsifies itself in the utterance! We automatically interpret it as an expressions of the visual compresence, CF. “Unthinkability” is what occurs in cases where we find the translation too difficult for us; when we attempt to effect it, the effort is immediately accompanied by an intrinsic, intolerable disvalue-judgment.
We are now in a position to examine the values of “Coherence-Truth”. In so far as a “truth-value” is to be attributed to the visible or audible phenomena themselves, it can only be “instrumental”, since it is not “intrinsic” to our acts of awareness of them, and so cannot be “inherent” in them; it is “intrinsic” only to the acts of awareness of our thought-interpretations. These usually succeed them so rapidly that we tend to ignore the distinction between the two modes of experience and to identify them, but this is a mistake, which becomes obvious in the case of long symbolic expressions; the “coherence” of these cannot be evaluated until after their utterance is completed. But even in the case of a single word, the interval is long enough to allow of a choice of thought-interpretations; just think of the alternatives available in the case of a word-sound such as “ball”. It is, however, only a sequence of such thought-interpretations to which the intrinsic value-judgment of “coherence” can be attached. It accompanies, in the first place, the “melodious” qualities of the sequence; it must be enjoyable to “sing”. If this is not the case, then it is to some extent “false”, and if it defeats all our attempts to “sing” it, it is a “logical falsehood”. If we enjoy it sufficiently to be happy to repeat it, we can consider it as “inherently valuable”.
But we can never consider it in isolation; it is inevitably accompanied by a massive background of “echoes”, set up by our replications of former thought sequences that we have “enjoyed”. It may in some cases be so discordant with some of these - which is to say that the effort to maintain a rapid transition or oscillation between them is judged to be excessively intense - that the strength of the disvalue-judgment outweighs that of the value-judgment accompanying the experience of its “melodic” virtues. A symbolic expression of such a thought-sequence will be rejected on account of its failure to “cohere” with language as a whole. When effecting such a transition, we are never on the look-out for a unison between the structure of the current thought-sequence and that of any of the existing “echoes”; such a relation is experienced merely as a replication, or simply as an “amplification”, of the echo itself. Such is the status of “tautologies”, which are closely analogous to unisons in music. Harmony affords far intenser value-judgments, and the most enjoyable language, like the best music, embodies successions which generate a certain measure of discord; the effort required to maintain such a compresence, if not too intense or too prolonged, can be a source of great enjoyment.
The intrinsic value of experiences of “coherence-truth” is, in fact, that of the melodic beauty of their interplay with existing “thought-echoes”. The initial experience of a “truth” of this kind cannot possibly be a “verification”, since it does not succeed any preceding “expectations”; it can only “happen”. One can only suppose that on the occasion of its first utterance, every word-sound must have had some “natural” coherence with the utterer's mood at the time; presumably some such relation connects a baby's wail with the mood that it expresses, and varieties of bird-noise with the circumstances under which they are uttered. A similar natural “coherence” seems to prevail between distinctive types of music and the moods which they express or evoke.
Assuming that a symbolic sequence has evoked a thought-interpretation which is enjoyably “thinkable”, the intensity of every value-judgment of its “coherence-truth” will depend upon the extent to which the hearer or reader finds his interpretation “true to life”. This is how we habitually express our value-estimate of its harmonic or contrapuntal relations with our backgrounds of memory and belief.
“Perfect” coherence-truth is clearly out of the question, since every hearer or reader has his own background, so that even if the underlying basis of all æsthetic judgment were universal - a not unreasonable hypothesis - individual value-judgments must be expected to differ. The nearest approach to “perfection” will be that experienced by an utterer who, when listening to the immediate feedback of his utterance, feels “That's exactly what I meant”. But even this is an exaggeration; who can ever claim to have expressed himself “perfectly”? The rhythmic texture of our utterance and awareness of symbolic expressions is so coarse that it cannot possibly harmonise “perfectly” with the flux of the raw material of experience; an improvement in the structural subtlety of our symbolic expression must always remain possible.
We have seen that there is no value-justification for striving for an unlimited increase in the accuracy of “correspondence-truth”. But our eternal urge for greater richness of experience leads us indefinitely to strive for the attainment of greater beauty in the shape of linguistic and symbolic “coherence”.
Since there is fairly universal agreement concerning what is hopelessly “incoherent”, we can fairly assume that any formula which is in general use is free from serious “incoherence-falsehood”. But this will not guarantee that somebody whose “mind's ear” is particularly sensitive will not reject it as insufficiently coherent, or “harmonious”. The value of coherence-truth, unlike that of correspondence-truth, is much more than co-extensive with the disvalue of its correlative “falsehood”, and the formula may, to a more sensitive ear, occasion an intrinsic disvalue-judgment of “disappointment”. This circumstance provides no ground for its general condemnation, since it may well continue to occasion intrinsic value-experiences for the less sensitive. Most of us will agree that every increase of æsthetic sensitivity constitutes an enrichment of experience, but it needs to be combined with a “sense of humour”. This is the ability to tolerate, or at least “shrug off”, types of experience which previously seemed harmonious, but which now occasion us disvalue-judgments on account of our heightened sensitivity. Otherwise we are liable to lose on the roundabouts what we have gained on the swings. Nietzsche rightly castigated his “higher men” for their inability to laugh; this is an occupational disease of all pedants!
We can now proceed to formualate the stages of æsthetic, i.e. “human-natural” selection which serve to eliminate from language those combinations of words and symbols that are liable to be associated with intrinsic experiences of “disvalue”, and to further the replication of those habitually associated with intrinsic experiences of “value”.
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6. The occurrence of such “melodic disvalue” in symbolic logic itself might be thought to be impossible, but the substitution of the single symbol V (vel) for and/or seems to be a flagrant example. Can we compresently think an “associating dissociation”? I find it difficult to believe that any mathematician would countenance the replacement of ± by a single symbol.
What is asserted here is the converse of Bradley's famous dictum, “What may be, and must be, is”, namely: “What can't be, or mayn't be, ain't!”
The most inherently valuable expressions are those of which the thought-interpretations are immediately, or almost immediately, accompanied by strong positive judgments of intrinsic value. The value is, strictly speaking, inherent in the “meanings” rather than the expressions themselves, to which we should, rather, attribute “instrumental” value. The temporal compresence of the two awarenesses is, however, so close that this inaccuracy is unimportant; it would only be manifest if we failed to find a “meaning” for part of our visual or aural experience.
The above criterion is clearly the one that we apply when judging the value of poetry or fiction. “Perfection” - an “infinitely” strong positive value-judgment - is out of the question.
The best “scientific truth” will satisfy this criterion of “inherent value”, but, in addition, must occasion no objectionable experiences of refutation when its “instrumental” value, for predictive purposes, is tested. James Watson's “argument” in favour of his model of the D.N.A. structure is an excellent example of this view; reiterated several times in his book The Double Helix, it runs:- “A structure as pretty as this just had to exist”. Of course, extensive tests were also needed to assure the permissibility of its “existence”, that is to say, its “warranted assertibility”. Even if this eventually proves to have its limits, the “inherent” value of the model still remains.
Similarly, Newton's symbolic synthesis still retains its enormous inherent value, even if the Michelson-Morley experiment, conducted some 200 years after his death, showed that his language became incoherent when employed in circumstances such as he himself had never contemplated. This led to Einstein's construction of a new mathematical language, which allowed him to construct a theory with which, incidentally, certain observations, discordant in Newton's scheme, such as the perihelion of Mercury, could be harmonised. But even the few people who can understand Einstein's language still use Newton's for the purpose of most of their astronomical predictions. They “shrug off” any inaccuracy involved as unimportant - as, of course, it is. An even more radical case of this kind of “inattention” is furnished by the continuing use of the terms “sunrise” and “sunset” by people who genuinely believe the Copernican hypothesis!
I think that pragmatists have concentrated too exclusively on the instrumental value of language, and that a more radically pragmatic view requires us also to take account of its inherent values and disvalues. This chapter can indeed be considered as an extension and an elucidation of Hume's conclusion that “belief is more properly an act of the sensitive than of the cogitative part of our nature”. I am well aware that almost all subsequent philosophers have tried to refute this view, but I suspect that their motive, of which they may not have been fully aware, has been to maintain the privileged, “ivory-tower” status which has been traditionally accorded to the practitioners of “pure reason”, especially logicians and mathematicians. The widespread belief that their activities take place in some kind of “higher world” seems to me to be a superstition which should be destroyed.
They can still retain a pre-eminent status as creative artists, whose chosen task is the construction of beautiful, and often useful, symbolic languages. “Pure reason” can then take its rightful place as a specialised department of the “practical” variety, dealing exclusively with the æsthetics of symbolic construction.
- Shalom & Welcome! - 
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