Western philosophy, ever since its emergence in Greece during the sixth century B.C., has been plagued with an apparently unbridgeable gap between “appearance” and “reality”. Behind the “phenomenal” world of appearance there is supposed to be a “rational” world, which alone is “real”. Ethical superiority was accorded, by the Parmenidean school and its followers, to the “rational”, which consisted of those elements of experience which possessed such a degree of invariance that complex “Gestalte” could be constructed from them, and re-analysed completely into their original components. When the processes were such that they could effectively be represented by verbal symbols without any apparent risk of ambiguity, the representations were considered to be “absolutely true”. The pastime went by the name of “pure” or “deductive” reasoning, and the participants found it so enjoyable that they developed the hypothesis that a similar treatment of all aspects of experience would ultimately be possible; in that case, granted an adequate development of “knowledge” and “wisdom”, it would be possible to achieve a “perfect” understanding of the whole of our experience, and, ultimately, of the whole Universe. Such is the hope expressed by Plato in his parable of the cave in the Republic; it is also implicit in St. Paul's “Now we see through a glass darkly, but then face to face: now I KNOW in part, but then I shall KNOW even as I myself am known.”1 At a much later date it was echoed by Leibniz's ideal of a “Characteristica Universalis” - a kind of all-embracing symbolism which would allow the calculation of a solution to every problem - even one concerned with ethics or æsthetics.*
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1. 1 Co 13:12 with capitals added.
* Editor's note: Leibniz's chief hope was that by its means religious differences might be resolved and Christian unity restored within Europe as he knew it.
The attribution of ethical priority to the “rational” over the “phenomenal” can be traced back to Pythagoras, who noticed a frequent association of simple numerical proportions between measurements of length with the æsthetic qualities of proportion and, more especially, of harmony. From this he drew the conclusion that “all things are numbers” - in “effect”, that “number” could provide the key to the construction of everything in the Universe. Arithmetic must therefore be the most important branch of study. From the construction of numerically large groups and the demonstration of the equivalence, as far as the result was concerned, of different ways of constructing them and breaking them down, he developed a “deductive” type of reasoning. The “rational” numbers were, in fact, those which lent themselves to this procedure.
But “deductive” methods proved also to be applicable to visual shapes, and, unfortunately for the Pythagoreans, the very theorem which the Master himself is supposed to have formulated, namely, that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the areas of the squares on the other two sides, showed, when applied to the diagonal of a square, that the ratio between the length of the diagonal and that of one of the sides could not be expressed “rationally” in terms of the integers.† Thus it came about that by the time that Plato wrote the Timæus, plane geometric shapes had replaced numbers as the fundamental components of the “rational” world. Geometry of the Euclidean type became the model for all “deductive” reasoning, retaining this status up to the beginning of the present century.
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† Editor's note: Cf. Peter Tompkins, Secrets of the Great Pyramid (HarperColophon 1978, p.285): “Eratosthenes was obviously not the first to measure the circumference of the Earth. Hipparchus was not the inventor of trigonometry. Pythagoras did not originate his famous theorem. Mercator did not invent his projection - though he did visit the Great Pyramid and leave his graffito to prove it. Whoever built the Great Pyramid knew the dimensions of this planet as they were not to be known till the seventeenth century of our era. They could measure the day, the year and the Great Year of the Precession. They knew how to compute latitude and longitude very accurately by means of obelisks and the transit of stars. they knew the varying lengths of a degree of latitude and longitude at different locations on the planet and could make excellent maps, projecting them with a minimum of distortion. They worked out a sophisticated system of measures based on the Earth's rotation on its axis which produced the admirably Earth-commensurate foot and cubit which they incorporated in the Pyramid. In mathematics they were advanced enough to have discovered the Fibonacci series, and the function of II and Ø. What more they knew remains to be seen.” Zecharia Sitchin's more recent books contain several valuable indications.
Unfortunately, the Pythagorean ethical apotheosis of the “rational” was unthinkingly accompanied, most probably on religious grounds, by the attribution to it of ontological priority. Now “In the beginning was the word”, even allowing for an element of mistranslation, is not easy to accept; “in the beginning were the numbers” is even worse, and “in the beginning were the right-angled triangles”, which is Plato's version in the Timæus, is equally deplorable.2 Pythagoras and Plato had transferred primacy of importance from the æsthetic value of harmony and proportion, which must initially have been the object of interest and attention, to the means employed for replicating and communicating them.
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2. Einstein's up-to-date version runs as follows:- “As it was in the beginning, is now, and ever shall be, Curvatures of Space-Time, Amen”.
Now it is quite clear that actual “feelings” of harmony and discord are beyond the descriptive range of language and symbolism, although we almost universally interpret certain forms of visible and audible behaviour as signals for them. This is why the “behaviourists” seek to exclude such feelings from the ontology of psychological “science”; for them, the data for a genuine “science” should be restricted to those structural elements in visual and aural experience which we confidently believe to be “public”, and this is obviously not the case where æsthetic judgments are concerned.
But the circumstance that a mode of experience is not describable in terms of “public” symbols does not debar us from accepting is as part of the ontology of private experience. The behaviourist preference for the elimination of æsthetic judgments from “data” is intself an æsthetic judgment, and one which I believe runs counter to the direct experience of every one of us - even to that of the behaviourists in their non-professional moments. I therefore propose to include experiences of “value” and “disvalue” as part of our “empirical” material, although they are admittedly elements of experience which we regard as of “internal” rather than “external” origin. I think this was what Hume meant when he wrote:- “Nature, by an absolute and uncontrollable necessity, has compelled us to judge as well as to breathe and feel”. “Feeling” in this context appears to denote the “impressions” which form the raw material from which phenomena are synthesised, and I think that it is a mistake to regard them as the whole of our “empirical” material.
Having now accepted an æsthetic element within experience as the “empirical” foundation of all judgment, we will proceed to invert the ontological order of priority adopted by Pythagoras and by most of the important philosophers since his day. Instead of asserting that “all things are numbers”, we will say instead that “numbers and numerical ratios have been found to be very useful for the purpose of replicating and communicating many phenomena which are of general æsthetic and practical importance”. Neither words, numbers, nor geometrical shapes are “a priori”; what are genuinely “a priori” are the value-judgments accompanying certain types of experience, and the importance of the “rational” concepts is a posteriori, and simply due to their frequent association with those types of experience.
There is plenty of evidence which can be adduced to support this order of priority, especially from the field of music. If the Pythagorean order were correct, we would expect to find an improvement in the quality of our enjoyment every time that the measured ratios associated with the music achieved a more precise approximation to numerical simplicity. In practice, this turns out to be far from being the case.
The field of music is clearly the most suitable one for testing the Pythagorean theory, since its æsthetic appeal is world-wide, and certain musical “intervals” are encountered in tunes all over the world. Practically the sole purpose of musical utterance is to express æsthetic feelings, and sometimes to attempt to communicate them to others. It only occasionally communicates information, or commands, by means of a code, such as that of bugle calls, and these are only recognised by hearers who can be relied upon to attach æsthetic importance to the intervals employed.
On the Pythagorean hypothesis, the maximum enjoyment should be achieved by the use of a strict “tempo”, and by ensuring that the ratio of the frequencies of the notes employed approximates as closely as possible to one of the lower integers, or to some product of them. This is completely at variance with the facts. Every musician knows that a “metronomic” performance is hardly worth listening to; it is true that listenders do appreciate the sense of a roughly invariant rhythm underlying the music, but its purpose is to provide a contrast with the subtle variations which make the major contribution to the excellence of a performance.
The same considerations apply to relations of “pitch”. As in the case of rhythm, an approximate standard of underlying “invariance” is needed, but only so as to emphasise the subtleties of the performer's divergences from it. Casals, certainly one of the most outstanding soloists of the last generation, used to insist on this point to the handful of aspiring ’cellists to whom he consented to give lessons. He would reprove them for playing too well in tune! “This” note should be played a little sharp, “that” one a little flat, in order to enhance the æsthetic effect of the music; it was essential to employ “intonation expressif”.
The notion that “arithmetically perfect” intonation is desirable has been completely refuted by the general adoption of J. S. Bach's practice of tuning keyboard instruments in such a way as to render all the intervals “gap-indifferent” no matter in what key the music was written. Since his day, the frequency-ratio between each keyboard note and its neighbour a “semitone” away has approximated to the utterly “irrational” 12Ö2 [12 square-root 2]. In practice the quasi-uniformity of this “semitone” has tended to make keyboard music sound a trifle colourless compared with that produced by instruments whose players can vary the pitch of the notes within certain limits. But the freedom of key-modulation and the contrapuntal possibilities that it has provided have, generally speaking, been considered to be more than sufficient compensation for this disadvantage. Even when a soloist, playing or singing with a keybord accompaniment, uses “intonation expressif“, his divergence from the “norm” of the keyboard is productive of pleasure rather than displeasure; quite a wide range of variation is permissible before the notes become unacceptably “out of tune”.
It is clear that the field of music provides no support for the Pythagorean ontological order. Corresponding evidence within the field of visual æsthetic is not easy to find, because most visual forms owe their importance mainly to the tactile and functional possibilities for which they serve as signs, so that a pure æsthetic of the “forms” is difficult to disengage from that of their interpretations. But it is clear that some kind of importance is widely attached to the modes of visual experience that we call “straight lines”, “circles” and “right angles”, and perhaps generally to the feeling of “symmetry” about a vertical axis in the field of vision.
But it is also quite clear that none of these forms represents a “ne plus ultra” of æsthetic experience. The Pope's emissaries were scandalised when Giotto proposed to send him, as a testimonial of his ability, a simple circle which they had watched him draw freehand, precisely because it seemed to be devoid of æsthetic appeal. But Giotto knew very well what he was about. He was content to rely on the testimony of others as to the customary beauty of his output, and probably on the orthodoxy of its religious feeling. What he wanted to prove was that his hand and eye were skilful enough to replicate any shape that he wised to communicate. He chose the circle, because that form is easy to replicate mechanically, and the accuracy of its replication is easy to test by standard methods of measurement, so that it would provide the Pope with irrefutable evidence of his skill in replicating shape in general.*
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* Editor's note: Similarly J. D. Solomon's skilful treatment of certain publicly communicable logical and philosophical questions in this book witnesses to his probably kindred skill in confronting other more sensitive vital issues that challenge us now.
I do not think that there are any grounds for supposing that the attribution of “perfection” to shapes such as that of the sphere and the “regular solids” was significantly due to their æsthetic pre-eminence. It is due to the highly practical consideration, that almost anybody could easily learn to replicate their visual appearance with a degree of accuracy that was self-evidently greater than anything that could be achieved in the case of any other visible shape.3 The exceptional degree of “gap-indifference” between the replications was almost certainly what gave rise to the Socratic notion of an “idea” in the mind of G-d, of which individual instances were merely imperfect copies. Here were multitudinous replications of geometric shapes, which appeared to differ hardly at all; it followed that they must all be very close indeed to the ideal archetype which was the source of their “essence”. There could be no doubt, or even appreciable ambiguity, about the ostensively definable meanings of expressions such as “straight line”, “square”, “circle”, etc., etc. The word-sounds themselves could be replicated with a recognisable degree of gap-indifference, and could accordingly be used to express the “essence” of the geometrical shapes. Consequently, when the geometers began to construct more complex “Gestalte” out of the simpler forms, and to demonstrate how they could be re-analysed into them, it became possible to describe these processes in verbal terms, with a high degree of accuracy. Such descriptions furnished the archetype of “deductive” reasoning in general. Their beauty has fascinated intelligent men right up to the present day; it is the works of Euclid rather than those of Aristotle which have most commonly provided the introduction to deductive reasoning during the course of the last two centuries. The whole validity of the “deductive” type of reasoning depends on the assumption that the gap-indifference of repeated instances of a word or symbol can be relied upon to stand for the “perfect” gap-indifference of its reference. In the case of “quasi-permanent” elements within the visual field, the “gaps” between successive “acts of awareness” are so short as to be negligible, and allow for practically no variation, so that we speak of “invariance”, or even of “identity”. We are prepared to condone the extension of the duration of the gap to transfers of visual awareness from one “circle” to another on the same page, and also to the transfer of awareness from one <x> to and “identical” <x>, thereby attributing an identical “essence” to the two shapes.
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3. In the case of the “sphere”, the “divinity” attributed to the Sun and Moon must have reinforced this tendency. Editor's note: Originally it was not to the physical solar and lunar bodies that divinity was in any degree attributed. Solomon's theory of how ‘Socratic notions’ originated is also untenable, see my note on p. 11 - 54 above.
But the extension of the notion of “essence” to the imperfectly replicable meanings of words in general was an exremely dubious procedure. It is difficult to judge how far Socrates, or Plato, or the “Platonic Socrates”, meant this process to be taken; in the discussion on “Representation” in Part Ten of The Republic it is accepted without reservation, but in the later Parmenides it is subjected by “Parmenides” himself to a good deal of ridicule to which “Socrates” can find no satisfactory reply.
Its uncritical adoption certainly appear to be necessary in order to validate “syllogistic” logic as developed by Aristotle. His typical major premise, which takes the form “all A is B”, asserts that the “essence” symbolised by B forms a necessary part of that symbolised by A, so that it is not legitimate to use A for the description of anything which cannot be described by B. There are two cases in which this provides a useful regulative principle for language. Firstly, when the term A has been invented as an abbreviation for the purpose of signalling a complex description which includes B, as, for example, “stallion” as an abbreviation for (sexually active, male) horse; secondly, when it has been invented for the purpose of signalling a new differentiation within the “extension” of B, as, for example, “Crimson” within the field of “red”.
The use of “every” rather than “all” in the construction of major premises would certainly be an improvement, since they would then sound more like the linguistic prescriptions that they assuredly are, and less like dubious, “eternally true” inductive generalisations, which is how they have often been interpreted. As prescriptions, they are often useful for preventing the attachment of gap-indifferent word-sounds to series of experiential elements which differ importantly; such procedures are liable to lead to disastrous misunderstandings. But they can never be “absolutely” binding, and can sometimes be disregarded without any untoward consequences whatsoever. Take, for example, the negative “major”, - “No circles are square”. This could be ostensively demonstrated “on the blackboard”, but should a member of a group of “pop-fans” take to frequenting the company of academics, they are likely to describe him as “moving in square circles” without the least suspicion of linguistic impropriety. There is no way of ensuring that a word does not become commonly associated with circumstances widely removed from its original field of application. We cannot even guarantee that the “essence” expressed by B is included in that expressed by AB; “white horses” are not always “horses”, and “black widows” are not always “widows”†
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Editor's note: Mediæval discussions in Latin of logical arguments suppose readers to be familiar with the distinction between “first” and “second intention”, thanks to which, to mention only one important example, “verbum” commonly primarily means what we might call a “proposition”, and only indirectly the sentence or set of spoken or written words in and through which that proposition may be conveyed.
The “self-evidence” of the “ostended” visual relationships which provided the foundations for “deductive” geometry is not supplemented by the “self-exaudience” of any corresponding relationship between the words which describe the demonstrations. The point is, that the repetition of our awareness of visual shapes is so rapid as to amount to “quasi-permanence”, whereas that of spoken or even of written words is only “gap-indifferent”; the gaps never approach the near-zero which characterises successions of visual awareness. The time taken to “scan” a written description of part of the field of vision is much longer than that required to “take in” the compresent features described, and the gap-indifference of repeated acts of awareness of a complicated formula can be neither “self-evident” nor “self-exaudient”. Even if it is structurally “gap-indifferent”, there are bound to be differences of “tempo”, and of the relative intensity with which the meanings of the symbols are “thought”.
For these reasons, I do not believe that any truth can be expressed, let alone “proved”, by means of verbal or symbolic expressions.‡ No lengthy symbolic expression can be “self-evidently invariant”, and there can be no “self-exaudient truths”, at least, not in language. In music, the note-by-note construction of a chord, and its destruction by silencing them progressively, might provide a kind of “self-exaudience” roughly equivalent to the “self-evidence” of geometry, because of the “quasi-permanence” of the notes.
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‡ Editor's note: This is clearly not a statement about propositions but about sentences. Not all criticisms of language are applicable to speech.
We can, however, conditionally prove some “falsehoods”, because we are empirically acquainted with some verbal sequences which, when normally interpreted, as “predicative compresences”, turn out to be “unthinkable”. These are liable to infiltrate our language should we use an abbreviation of which the meaning includes one “incompossible”, and proceed to combine it predicatively with the other.
The trouble with language is that it can never exhibit any really intimate temporal compresences, such as can be easily maintained both in vision and in thought.* Since we frequently wish to signal or to describe such compresences, we have adopted the habit of quasi-automatically interpreting word-successions as “predicative compresences” unless any specific indication is given to the contrary. But even in vision and thought, there are limits to the closeness of temporal compresence which can be maintained.
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* Editor's note: Appropriate symbolic gestures both in dreams and during our waking life are, on the other hand, frequently an excellent means of intrapersonal and interpersonal communication. The evocative power of great art also owes much to its reliance on symbols so understood. See my previous notes above.
We cannot see a “red blue area” or a “circular square shape”, nor feel or think a “hard soft surface”.º Each predicate calls for the cognition of some degree of “invariance”, which requires a certain minimum duration, and in each case, the “tempi” of the repetitive changes which give rise to the cognition are of the same order, so that if they overlapped, they would inevitably destroy one another's “invariance”. On the other hand, we can see a “red square”, because the awareness of “red” is effected inside the area, while that of “square” is a discontinuous series of awarenesses of the boundary. They belong, temporally speaking, to different “dimensions” of visual activity.
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º Editor's note: Yet some masochists evidently experience intense pleasure when alternately, repeatedly and rhythmically both lovingly caressed and severely spanked by a velvet-gloved, gentle yet firm, strongly sensitive hand! Indeed, Solomon's own use of “on the other hand” to mark a contrast suggests that he, too, somehow appreciates this as compresence… Compare his later remarks about “oscillation” and “STRICT truth” (emphasis added).
“Spatial” contiguity within the visual field is probably the most intimate form of temporal contiguity encountered anywhere within “external” experience, so that “one and the same” spatial coordinate implies “one and the same” temporal one, and cannot be assigned to two “different” qualitative coordinates within the same temporal dimension of sense. Every ostensive definition of a difference between qualities belonging to the same “dimension” is bound to have involved a spatial or temporal transition between them, so that there is no possibility of “thinking” them in very close spatio-temporal compresence.
The most obvious instances of purely “unthinkable” compresences are those of the interpretations of word-sequences with explicitly temporal meanings. “To-morrow is yesterday”, “I will arrive last week”, “The beginning followed its sequel” are examples, which could easily be multiplied indefinitely. Their falsehood is so obvious that it is completely harmless for communicative purposes; nobody would ever think of using them for the purpose of “spontaneous” expression. Some comparable falsehoods are, however, so well hidden that they have even infiltrated “logic”, without being noticed by the logicians. Take, for example, Leibniz's term “indiscernibles”. One might suppose that it would be impossible for a single term to embody a logical contradiction, but the suffix “s” is an abbreviation for “plural”, and conjoins “plural” with “indiscernible”. Now an act of conjunction is meaningless unless it succeeds a state of disjunction, i.e. of “discernment”, but a “plural undiscerned” is unthinkable, and whatever is “indiscernible” is, a fortiori, “undiscerned”. “Indiscernibles” is therefore self-contradictory, and nonsensical; so, therefore, must be its “identity”.•
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• Editor's note: This argument does not quite convince, since the validity of what is asserted in the last sentence appears to require the logical equivalence (and in that sense indiscernibility) of “indiscernible“ in the sentence just before it and of “indiscernible” in the sentence just before that, i.e. of two indiscernibles! But does “=” = “=”? And is that a question?
The use of the abbreviation “vel” or simply <v > for the symbol and/or is open to a similar objection. The function of “and” is to conjoin what was disjoined, whereas that of “or” is to disjoin what were conjoined, so that they cannot be “thought” in the intimacy needed for a “predicative compresence”. The “stroke” was inserted so as to indicate that this was the case. Its abolition by the use of an abbreviation has made it possible to use <v> as though it expressed a single, enduring relation; this is nonsense. At best, it can only be regarded as expressive of a kind of “oscillation”, or radical state of uncertainty, and as completely unsuitable for use in any expression for which “strict truth” is claimed. Like ±, it expresses a degree of ignorance, or permissible error. In practice, the “symbolic identity of indiscernibles” misdescribes the application of symbolic gap-indifferences to passages of experience which are not worth the trouble of discerning, i.e. are themselves judged to be “gap-indifferent” in certain important respects. The business of verbal “logic” is to try to ensure that symbolic gap-indifference is not employed except when this state of affairs actually obtains - for good and obvious practical reasons. The existence of such a state can never be guaranteed; neither, therefore, can the “Truth” of any verbal assertion. Visual geometric shapes still appear to provide the closest approximation to it, so that Euclid's work remains generally acceptable, at any rate within the field of unaided visual perception. As we have seen, the falsehood of the normal interpretation of certain verbal juxtapositions can be guaranteed provided that the words are used in their primitive sense, which is to say, within the same “dimension” of experience. That is as far as verbal “proof” can go.
Arithmetic and algebra are generally considered to be within the sphere of “pure reason”, within which “certain truth” can be formulated. The symbolic techniques of algebra have been extended to fields which have no connection with “number”, but it is clear that they originated in the first place as generalisations of arithmetic, so that we must look to the sources of arithmetic for their “grass-roots”.
Let us start with the “integers”. These are simply a series of sounds, muttered in a conventional order, often quasi-simultaneously with a series of brief, outstanding events. Their “meanings” are absolutely dependent on the maintenance of the conventional order, as is demonstrated by the following story, which I believe to be “factual”. A young cousin of mine was in a room where there was a dish of sweets, and his parents, who had to go out for a short time, told him that he might take four of them while they were away. When they came back, it appeared that rather more had disappeared, and they taxed him with it. His reply was:- “I only took four; I counted ‘one, two, three, five, four’.” Apart from deploring his breach of the usual conventions, how can this be faulted?
The interpretation of “number” as primarily a property of “groups” is a mistake. Its primary use is to individuate the discrete stages of their construction and/or their breakdown. Russell defined the “numerical similarity” of groups in terms of a “one-one correspondence” between their members, but this can only denote a quasi-simultaneous pairing of the acts of dismemberment of each group, which terminates simultaneously for both groups. In practice, the series of the “integers” provides an ordered, indefinitely extensible variety of “groups” with which such comparisons can be made, so that the “numerical similarity” - or difference - of groups can be determined without comparing them directly. But the numerical constancy of any group clearly involves the additional requirement that there shall be no important variation in the method of breaking it down - assuming, of course, that nothing has been added to or taken away from it in the meantime - otherwise the consecutive steps of the breakdown cannot remain “numerically” gap-indifferent.
Russell's definition of “number” as “The class of classes (numerically) similar to a given class” is open to serious objection on logical grounds. His first “class” expresses an intension, or class-concept, while the others express extensions of the general concept of “similarity”, or “inclusion”. But the function of the class-concept is to exclude all forms of similarity but the “numerical” one. He has thus committed the logical sin of attaching a series of gap-indifferent words to a series of “meanings” which differ importantly.
Throughout his work, Russell seems to repeat the Pythagorean mistake of regarding “number” as given a priori as a concept, and then of seeking a “logical” passage to its “extension”. He fails to realise that it was an æsthetic interest in different degrees of plurality which gave rise to the concept, and to the use of a series of word sounds uttered in a gap-indifferent, conventionally accepted order for the purpose of communicating it. Numerical difference is what is of primary importance; numerical “similarity” is only useful as a means of the indirect comparison needed for the communication of differences. There can never be a logical passage from a “concept” to its “extension”; every instance of the concept follows the “noticing” of a current “existent” - which might even be the name of the “concept” - i.e., something which “stands out” within experience, and is judged to be structurally harmonious with the concept. In the words of William of Occam (I quote from Russell's History of Western Philosophy): “The Universal is the first object by primacy of adequation, not by the primacy of generation”. “Generation” is a necessary preliminary to “adequation” although it is probably a mistake to suppose, for example, that a visual sensation is needed in order to stimulate “adequation” to a visual concept - as is shown, for example, by what happens when we dream. Our innate tendency is to attempt to harmonise every new experience with the massive background of memory, perpetually active at sub-threshold levels of intensity, which has developed in response to our feelings of æsthetic and practical importance.
I think there is little doubt that a highly developed sense of “number” is equivalent to a highly developed sense of “rhythm”. Music and dancing are world-wide; binary rhythm is met with everywhere, while ternary rhythm, though less ubiquitous, is widely appreciated. Significant happenings within the series of names for the integers tend to occur when certain important multiples of two and three are passed. Musical phrases of eight beats are common, and it has frequently been remarked that the word for “new” in European languages is normally very similar to that for “nine”. In Russian, the usual word for “again” is closely related to that for “five” - the successor to “four”. In the Nordic languages, new integer-names give way to “teen-words” after “twelve”; in French and Italian, the corresponding change occurs after “seize” and “sedici”. Of course, the “standard groups” provided by the fingers have also been influential, and once the use of “number” for differentiating the multiplicity of more or less permanent groups became firmly established, their importance has tended to outweigh that of the original rhythmic impulse. It is noteworthy that many engineers hold that calculation would have been much easier if we had employed a scale of six or twelve rather than one of ten,* while computers manage with one of two, their extremely rapid tempo of operation compensating for the extreme syntactical complexity of their “language”; this is an inevitable consequence of the drastic use of “Occam's Razor”, which has reduced their vocabulary to two terms, corresponding roughly to “yes” and “no”.
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* Editor's note: In 1942, at the end of lifelong research, August Oxé, the archeologist, published a monograph explaining that in the ancient world practically all units of volume and weight existed in two varieties related as:
Solomon's engineers have not had a new insight! Cf Professor Livio Catullo Stecchini's “Notes on the relation of ancient measures to the Great Pyramid“, an appendix to Peter Tompkins, Secrets of the Great Pyramid (HarperColophon, 1978, pp. 287-382), p. 309.
All this evidence suggests that the primary use of number was connected with the grouping of successive “events”, and that its connection with quasi-permanent “groups” is secondary. An “intuitive” understanding of large numbers, perhaps without bothering to “name” them, would correspond to a high-frequency rhythmic “scanning” of one's own experience; this is probably the explanation of the ability of “numerical geniuses”, such as Ramanujan and Zerah Colburn.4
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4. It even explains why they die young; their hypersensitivity must render them extremely vulnerable to “shock”.
I doubt whether even the most rabid of contemporary Pythagoreans would maintain the ontological or epistemological priority of “numbers” over “rhythm”, especially in view of the current “wave” explanations of light and sound, and even of “matter” itself. Even animals, judging by their movements, attach importance to the same kind of rhythmic invariance as we do, although there are few grounds for supposing that they enjoy “numerical” consciousness. Rhythms can be “signalled” directly, but the delayed form of signalling that we call “information” requires their description by means of some symbolic device, and “number” is excellent for the purpose. It is likely that only the first few integer-names were used until numbers had come to be used extensively for comparing the multiplicity of “permanent” groups; most of us have difficulty in “intuiting” any repetitive rhythm of more than five beats or so, so that the later integers would have been useless in a purely rhythmic context; rhythmic geniuses like Ramanujan are rare. Even to-day, there are some living languages in which the only verbally expressed pluralities are “one”, “two”, and “many”.
The generalised use made of what are often “numerical expressions” rather than “numbers” is due to the circumstance that a reliable and indefinitely extensible set of labels for ordering transitive sequences of events provides an excellent linguistic device for symbolising the order of transitive asymmetrical relations in general, those of magnitude being the most important. Relations of this kind are very common among those elements of experience which we all confidently believe to be “public”, to wit, the fields of sight and hearing. They appear to be given empirically, and the differences may be qualitative or quantitative; in the latter case, the “quantity” concerned may be either intensive or extensive.
“Form” or “structure” comprises differences of quality and of extensive quantity, but not of “intensive quantity”. It is notable that “intensive quantity” is precisely what is lacking in memory, as distinct from direct experience; such changes of intensity as we remember are altogether vague, remote “echoes” of what we suppose to have been the original experience, whereas its “structure” often appears to be replicable in considerable detail. Now language, especially the written variety, is the vehicle and repository of “reason”, and relies to an overwhelming extent on the veridicity of memory. Written language, unlike the spoken variety, exhibits no appreciable change of intensive quantity during the reading; all changes are exclusively “structural”. Speech is another matter, but I do not think that inflections and changes of tempo can be included in the “rational” content of an utterance. This would be confined to an agreed interpretation of the written transcription;† it might include its retranslation into sound, but “mezzoforte” - and at a fairly uniform “tempo”. It is only the structural content which is “rational”.
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† Editor's note: Solomon's confinement option seems unwarranted, especially if the agreement he mentions is supposed to precede the individual interpretations it excludes!
I maintain that the outstanding utility of number and of generalised numerical techniques for the expression and ordering of structure flows from their close association with rhythm, and that rhythm is in fact the raw material of all “structure”, even including that of visual shape. I believe that the visual shapes which we regard as “public” are constructed by us, or possibly even imposed by us on raw material which is purely rhythmic in character. I am hard put to it to express this “point of view”; all the idioms which deal with perception draw their material from vision, which I believe to be the “end-produce” of the process. Kant used the word “Anschauung”; what I need is something corresponding to “Zuhörung”. “Anschauung” is literally an abbreviation for “way of looking at”, but Kant clearly meant it to be interpreted in a wider sense, and translators have usually rendered it as “intuition” - a word which has all sorts of doubtful connotations. What I need is an equivalent for “way of listening to”, which does not appear to exist.*
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* Editor's note: The meaning is: ‘What I need is an equivalent, which does not appear to exist, for “way of listening to”.’ In conversation J. D. Solomon has agreed with me that Eric Mascall's “contemplative contuition” may meet the need.
Still, although the visual bias endemic to our vocabulary of perceptual terms prevents me from adequately expressing my meaning; it is easy enough nowadays to point to an example which illustrates it very satisfactorily. Every visual shape on the television screen must be assumed to have a structural counterpart in the purely rhythmic activity of the “carrier-wave” which is its “raw material”. There is no “picture” which comes through the air and enters the ærial, and unless we credit the television camera with the ability of “seeing”, no picture occurs at any part of the “causal”5 chain, which concludes with the fabrication of one by the viewer out of the flux which is still occurring behind the screen. Nowhere in the proceedings is there any “Ding-an-sich”; there is only a “Stoff-an-sich”, and this is pure change. The activity which goes on inside the receiver is an excellent exemplification of the workings of something like Kant's “transcendental æsthetic”. Nor is there any reason to suppose that the activity of “direct” vision is very different; we cannot imagine that any “picture” can possibly travel up the optic nerve. In this instance, we are actually “inside” the set, or rather, an activity analogous to that performed by the set is part of our activity. How has this state of affairs arisen?
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5. I find it impossible to form any notion of “causation” which does not include that of “change”. There is no need to think in terms of “impact”; bare “communication” will do. Editor's note: In this connection I have pointed out to Solomon that when this book is read with understanding by a new reader, and not before that moment, Solomon, without himself changing, becomes the effective cause of that reader's consequent increment in understanding of its contents, which is a change, of course, but only in the reader.
Here again a simple explanation is available if we forget about the “behaviourists” and take the obvious view that judgments of value and disvalue, which we are accepting as “internal” empirical material, are what determine our habitual modes of activity. So far, I have only been concerned to maintain that the raw material of vision and hearing is a flux, out of which our æsthetically motivated activity constructs the “phenomena”. But if all our raw material is a flux, then even our awareness of matter from the inside, as distinct from the superficial awareness of the “surfaces” that vision and touch provide, must also be a product of our own æsthetically motivated activity, although we do not seem to have made much progress in “structuring” it.6 When vision or hearing becomes intolerably unpleasant, we shut our eyes or stop our ears. When our internal awareness of matter becomes intolerable, we likewise “switch off”; this is what we call “dying”. Now the visible signs that we manufacture from our “external” raw material are merely valuable for enabling us to avoid tactile contacts that we believe likely to be painful, and to achieve those that are likely to be pleasant. Our survival - the continuance of our internal awareness of “matter” - depends on our success in avoiding the intolerably painful, including very severe experiences of “shock”, which can sometimes be lethal even in the absence of “physical” pain.
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6. At least, not in the West. Oriental “yoga”-practices appear to be attempts at doing something of this kind.
Consequently, the survival of the “human race”, which is to say, the continued replication of human habits of behaviour, has depended on the development of habits of visualising activity which have helped us to succeed in attaining this end. The one that we appear to have in common has withstood a considerable period of “natural selection”, and we regard the phenomena that it produces as the “facts” which provide the fundamental basis for the “rational”.
At this point I think we need to make a distinction between the “unreasonable” and the “irrational”. We can use the word “unreasonable” to characterise action or inaction which appears to most people to be unsuitable for the avoidance of serious disvalue-experiences which are generally considered to be likely, and to any action which appears deliberately to seek them - unless there are some grounds for supposing that the agent has conjectured the possibility of some future value-experience which will more than compensate for them, as in the case of martyrs. Verbal or symbolic communications which are likely to lead to such experiences can also be categorised as “unreasonable”, and a major function of logic is to make sure that our misemployment of language and symbolism, by attaching gap-indifferent series of words or symbols to experiential series which actually differ importantly, does not inadvertently lead to communications of this nature.
The “irrational”, on the other hand, allows an extension of the use of verbal and symbolised concepts far beyond the contexts to which they should be confined from a “strictly logical” point of view. This can be appropriately illustrated by showing what has happened to the concept of “number”. Numbers, as we have seen, originate as members of a distinctive series of sounds used for signalling a succession of events. Their application to the discrete stages of the construction and breakdown of groups is logically unobjectionable. The “ratio” between them is derived from their use in relating series of event-sequences which are partly simultaneous, or for describing single event-successions some members of which are outstanding in intensive quantity. This is its “musical” use, for the expression of a relation between the tempi of several “invariant” rhythms, and since an intuition of rhythmic “invariance” underlies “structure” and appears to be common to the whole of mankind, the concept of “ratio” is valuable for purposes of communication. But once number-sequences are divorced from discrete “events”, and are used for trying to order continuous magnitudes, they are radically separated from their original function, and should be called “numerical expressions”. From the point of view of a radical empiricism, it is doubtful if “convergent infinite series”, for example, are ontologically admissible, since they cannot, a priori, be visually formulated or ostensively defined. The name “II” is perfectly in order as a signal for the “invariant” visual aspect of the difference between the length of the circumference of a circle and that of its diameter, but it has no equivalent “number”.
When we use a “minus” sign in front of a number, we are clearly in the realm of “applied” rather than “pure” number. There are no “negative“ numbers; the “minus” sign is not an attribute of the number but of the events that it is being used to “number”. It is most commonly used to certify that they are stages in the breakdown of a group rather than of its construction. It is only necessary to hink of the use of number in music, which is probably its most primitive context, to realise the absurdity of the concept of “negative number”. There can assuredly be no such thing as a “negative frequency”. As for the compound symbol "the square-root of -1", this, as far as “number” goes, is purely imaginative poetry; surely “imaginary” numbers do not belong to the sphere of “reason”? Analogical meanings have been found for this symbol, notably a reversal of direction, effected in two gap-indifferent stages by rotation rather than by linear movement.
“Zero” 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. There are indeed occasions when we use a “count-down”, as for example the sequence “three, two, one, go!” for starting a race, but the “go” is not the “zeroth” number of the series.
Much of higher mathematics appears to consist of the æsthetic creation of symbolic Gestalte intended to express and relate complex patterns of process which have caught the fancy of their creators. When two symbolic expressions are equated, this asserts the view that the changes of state effected by carrying out the differing processes do not differ importantly. The principle can be illustrated by the very simple equation: (+) a + a = (+) 2a.
This states that two gap-indifferent acts of association, which need not be numerical, when performed successively, produce the same net change as when they are performed simultaneously. The writing of the first a and of the 2a are actually acts of association of the symbols with the paper, and the initial term is always treated as a “+” in computation, although the symbol is usually omitted.
Clearly, arithmetic will not be valid in cases where +1 +1 ‡ +2, and such cases are common enough; two “gap-indifferent” musical notes played successively do not effect the same change as two played “simultaneously”. “Arithmetic” is, in fact, what its name implies, namely, “measurement with the rhythm left out”. Since the language of physical scientists - algebra and the calculus - has always to be eventually reducible to arithmetic, it is clear that their measurements must conform to the conditions necessary for its validity. Seeing that there are plenty of circumstances, such as the one cited above, in which these conditions do not obtain, it is clear that there must be a very large field of phenomena which are bound to remain beyond the reach of physical science, as long as it is ultimately dependent on the validity of arithmetic. In particular, it would appear that the “equations” of arithmetic are invalid precisely within the sphere of the phenomena which originally gave rise to the invention of our numerical vocabulary.
It appears that a good deal of higher mathematicis, if considered to be a development of arithmetic, must, from a “logical” point of view, be regarded as “irrational”. An ascetic school of mathematical philosophers, led by Brouwer, have extended to the “irrational” the ethical stigma which is justifiably attached to the “unreasonable”, and condemned it. Kronecker, the forerunner of this school, went even further. “G-d made the integers”, he said, “the rest is the work of Man”. Even this dictum echoes the Pythagorean superstition, and a radical empiricist must go even further; if G-d made the “integers”, it was assuredly through the agency of Man, who did so for the purpose of expressing that æsthetic urge towards the grouping of events which he calls “rhythm”.
But this ethical condemnation of the “irrational” is out of place. There are no grounds for condemning the flights of fancy indulged in by the higher mathematicians, though it may be necessary to divorce them from “number”, just as the “geometers” have divorced theirs from “space”. As in the case of /-1, their poetic inventions may prove to be descriptively useful in fields where “pure” arithmetic fails. It would appear that Cantor's “transfinites” are interesting in their own right, but it is stretching the use of the word “number” beyond all reasonable bounds to apply it to them. It is not, I think, far-fetched to suggest that it was Cantor's efforts to “think the unthinkable”, by maintaining the connection, which ultimately led to his mental breakdown.
The obvious course to adopt is to include much of higher mathematics, together with music and a good deal of poetry, in the “irrational”. While we are bound to recognise an ethical divide between the “unreasonable” and the “reasonable”, there is no need to postulate one between the “rational” and the “irrational”. The latter represents the imaginative attempts made by human beings to break out of the straitjacket imposed by insisting that all symbolisms should obey certain rules which have, in practice, proved useful for avoiding the expression of the “unreasonable”. As soon as any form of symbolism is exclusively concerned with the expression of the “enjoyable”, there is no particular reason why it should obey any rules at all - except, possibly, for the fun of doing so!
Our “irrational”, purely æsthetic activities are in no way opposed to rationality; reason itself is a manifestation of the human æsthetic urge within that field of cooperative communication where the purpose is that of avoiding disenjoyments rather than that of achieving enjoyments. It is for this reason that the “intellect” concerns itself very largely with the visuo-tactile aspects of “matter”, but it is not thereby working in opposition to “intuition”; it is simply concerned with avoiding the “unreasonable” within the field of symbolic communication. Bergson mistakenly interpreted a radical difference in terms of a contradiction. The æsthetic motivation is the same for “intuition” as for “intellect”; their differences are due to an extreme divergence between the tempi of the phenomena with which they are concerned. “Intuition”, which includes what we call the “irrational”, is concerned with immediate enjoyment, which is often rapid and very brief; “intellect” looks for, and discovers, persistent structures, based on invariant rhythms or the interaction of invariant rhythms, which sometimes helps us to replicate our “irrational” enjoyments and even, if we are lucky, to improve on them. But above all, we use the discoveries of the intellect for the avoidance of grave disenjoyments - also “irrational” - which may become so intolerable that we find ourselves compelled to discontinue our activity of judgment, at any rate in any form which can be cognised as “manifest”. In other words, we die.
The search for low-frequency structures is an interesting pursuit in itself, which increases our range of structural experience and heightens our appreciation of structure in general. There is no justification for denigrating the operations of the intellect, after the manner of Bergson. But it is a mistake to accord ontological priority to the “unchanging”; changes can never be generated from invariances, as Zeno showed more than two thousand years ago. His excessive respect for the “Truth” of verbally expressed “reason” even led him to exclude change altogether from his ontology. But there are excellent grounds for supposing that invariances, or at least appearances of invariances, can be generated out of “change”; this assumption underlies all “wave-theories”, whether of “sound”, “light” or even “matter” itself. Among our modes of sense-perception, it is vision which presents us with the closest approximations to “invariance”; this is what made deductive geometry possible. The technique of written and printed communication is also entirely dependent on the assumption of the “invariance” of shape on the part of our symbols. For this reason, the generation of “invariant” shapes on the television screen, out of a flux of which the structure can only be conceived of as a rhythmic pulsation of “intensive quantity”, is a triumphant vindication of the possibility of the ontological priority of change. But there is no possibility of reconstructing even a first approximation to a description of the structure of the flux from that of the invariances which we, the viewers, have extracted out of it.
There appears to be a strong case for according ontological priority to the most rapid change that is occurring “anywhen” or “anywhere” in the Universe, with the proviso that it is bound to remain “inconceivable” in terms of any “invariances” resulting from rhythmic repetition, and will therefore remain beyond the range of symbolic description.
But there are no grounds for identifying ontological priority with ethical or æsthetic supremacy. This is only necessary if we postulate a state of initial ethical “perfection”; in this case, all manifest beings result from a “fall” of some kind. This is how our æsthetic urges come to be interpreted as attempts to regain an original state of “perfection”; everything created by a “perfect G-d” must of necessity be striving to return to “Him”. Likewise the scientist, trying all the time to improve his descriptions of experience, is only trying to “discover” a “Truth” which has always existed; he is not inventing it as he goes along - as I believe to be the case. In both cases the identification effects an a priori elimination of the possibility of an evolving Universe.
I think that Bergson's denigration of the “intellect”, which spoils his evolutionary philosophy, was also a consequence of his probably unconscious acceptance of this identification. Having accepted the ontological priority of “change”, he felt obliged to attribute ethical inferiority to mental activities which seemed to be entirely devoted to slowing it down. But this is at least partially mistaken; “some” change is æsthetically preferable to “none at all”, but “enough” is also preferable to “too much”. All our value-experiences, including those which many of us rate most highly, are associated with the structuring of our raw material, and notably with harmonious compresences of a variety of structures generated by “scanning” it quasi-simultaneously at a great variety of “tempi”. The incon-ceivably fine rhythmic texture of the raw material provides unlimited potential for the creation of such structures, to which we are constantly motivated by our innate æsthetic urge. These can be communicated, though doubtless far from perfectly, whenever we can find means of replicating them in visible or audible form, and because our highest enjoyments are always enchanced by a feeling that they are shared, this activity of “reason” is felt to be valuable in itself.
For example, it is quite possible that the structure of a Beethoven symphony, as it originally revealed itself to him in “thought”, was of a subtler quality than anything that he could commit to paper for the purpose of achieving its replication at the actual intensity-level of aural sensation, but he, nevertheless, was not content merely to revel in the ecstasy of his original “revelation”; he felt the urge to find means of enabling others to share it. This involved effecting an analysis of its structure to the best of his ability, then the using of “reason” to symbolise the “parts” on paper and to resynthesise them in such a way that the structure could be replicated publicly at the high intensity and leisurely “tempo” of musical sound. Doubtless the increased intensity of his experience of it served also to increase his own enjoyment. This motive could hardly have been operative near the end of his life, since he was deaf; yet he still continued to compose. He evidently took the view, which is strongly supported in this essay, that “manifesting” is superior to “unmanifest being”. It is this view that thinkers of the Pythagorean-Parmenidean-Platonic school were concerned to deny, and most “religious” thinkers have followed in their footsteps. The source of higher possibilities of manifestation is indeed to be sought in the unmanifest - we need to “dive back into the flux” - but their full value is not attained until manifestation is achieved.
Thus the interpretation of “reason”, in this essay, as the manifestation of a common æsthetic urge which is the genuine “a priori”, is not intended in any way to be depreciatory. In Hume's terminology, it is equivalent to maintaining that the “cogitative” part of our nature is a manifestation of the “sensitive” part. This in no way constitutes a departure from “empiricism” provided we accept the “sensitive” part as empirically given; and the behaviourists' reluctance to do so, being itself the expression of a “preference”, appears to be self-refuting. Hume was unwilling to accept this identification, since it involved regarding “knowledge” as merely an important sub-species of “belief”. He shared the rationalists' hearty respect for “knowledge”, but was contemptuous of “belief”, doubtless as a reaction to the way in which “religious” believers tend to claim the status of “knowledge” for many of their highly dubitable “beliefs”. He was therefore distressed to come to the conclusion that even the beliefs that he had regarded - and we regard - as “factual” were due to the circumstance that it “costs us too much pains to think otherwise”.
In this essay this conclusion is accepted wholeheartedly in so far as it serves to demarcate “reasonable” and “unreasonable” beliefs; a widespread gap-indifference between the phenomena that are accompanied by disvalue-judgments, especially in infancy, is what makes “reason” possible. But fear is only the beginning of wisdom; Hume has overlooked the possibility that there may be modes of “thinking otherwise” which lead to an increase of enjoyment. It is clear that every attempt to communicate such a mode will be suspected of unreasonableness, simply because it differs from “reason” as currently accepted: such suspicion, however, will remain without foundation unless and until it is corroborated by the actual occurrence of disvalue-experiences. In the absence of corroborative evidence, it is just as unwise to doubt as to believe, especially if the belief is a pretty one. This is why we prefer the heliocentric hypothesis and Kepler's laws to the geocentric one with its Ptolemaic schema; its prettiness has even persuaded us to doubt the evidence of our own eyes!
In any sphere of activity in which we are not concerned with the possibility of serious disvalue-experiences, there is no objection to discarding “logic” altogether, and making what use we like of words and symbols. Ambiguity of meaning may be a cardinal sin for logic, but elsewhere it can be a major source of enjoyment, as demonstrated, for example, by Professor Empson in his well-known “Seven Types of Ambiguity in the English Language”. The ambiguities with which he deals are mostly subtle; when they are cruder and more obvious, they are major sources of “fun”. The expressive richness of any word or symbolic expression actually increases with the multiplicity of its connotations, so that when we are using it simply for the purpose of trying to communicate enjoyment, there is no point in looking over our shoulder to make sure that we are using it “correctly”. We are no longer engaged in “language-work” but in “language-play”;7 we may find it more enjoyable if our game has some communal rules which we are expected to obey, but we are not obliged to take this view. Attempts to insist on the observance of rules which add nothing to the enjoyment of the game constitute what we call “pedantry”.
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7. Wittgenstein, as far as I am aware, never made this distinction, which I believe to be valuable, although the line of demarcation is not an exact one.
When William Webb Ellis, “with a fine disregard for the rules of the game as played in his day”, first picked up a football and ran with it, he was acting “irrationally”, but not “unreasonably”. So was De Moivre, or whatever other mathematician had the temerity to write the symbol /-1 for the first time, and play games with it.8 These symbolic games have since been incorporated into the technique of “reason”, although symbolic expressions which include the symbol are still called “imaginary”. On the whole, the practitioners of symbolic games prefer to play in accordance with rules which create certain difficulties and provide them with a sense of achievement in overcoming them. When the rules are such as serve to keep the symbolism in touch with arithmetic, they have the advantage that it can be used as a language by physical scientists; as we have seen, Brouwer objected to all “higher mathematics” that did not comply with this requirement. This seems to be excessively puritanical: “All work and no play makes Jack a dull boy”.
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8. But not the man who invented “zero”; this was simply a “space-filler”, a device for ensuring the clarity of the spacing of the integers in the Arabic numerical notation.
No improvement in the quality of individual human enjoyment can be expected from the employment of “pure reason” as it exists at any given time; this only comes from imaginative exploration of the vast and uncharted regions of the “irrational”. Admittedly, this only becomes possible when we are free from the fear of grave disenjoyment, and this state of affairs can only be assured by the continual use of reason in its “practical” aspect. But reason alone will not, as Plato believed, help his cave-dwellers to emerge into the sunlight; it will only help them to avoid disvalue-experiences which are liable to result from their misinterpretation of the “shadow-show”. Only a confirmed pessimist could regard this as an ethical optimum; an optimist, while willingly attributing a positive value to the exercise, will continue to strive for something better.
We have already seen that what appears on a television screen is, literally, a “con-fusion”, in the sense that it is a fusing together of a succession of discrete “re-creations” into an enduring “reality”. Every “discrete” entity which appears on the screen is a “confusion” of quasi-instantaneous changes which have been produced by “scanning” the minute ultra-rapid changes in the “carrier-wave” with the aid of a rhythmic faculty functioning in similar fashion to a “slow-motion” cine-camera, imposing “structural detail” on a flux which is initially too rapid to be detected by any of our senses.
Now in so far as we always locate “what” we see outside our own “immediate” experiences, all our vision is, in effect, “tele-vision”*, so that we may very well be functioning in the same way as a television receiver all the time that we keep our eyes open. The main difficulty about this notion is that the tempo of such a succession of discontinuous sections of our raw material is so rapid that it is difficult to contemplate it in relation to the kind of tempo in which we are ordinarily interested, which is that of bodily movement; such tempi are the only ones that can be ostensively defined with any confidence. But we are sufficiently familiar with differences of tempo to be able to imagine an indefinite extrapolation of such differences; the notion of an “infinite” tempo of change is beyond the range of our imagination precisely because of our inability to contemplate a limit to the extent of such extrapolation. It is in such circumstances that we use the term “infinite”; this should always be regarded as a negative rather than a positive term, as is clearly indicated by the negative connotations of its first syllable.
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Editor's note: i.e., seeing at a distance.
Now within our experience, it is visual “simultaneities” which constitute the most advanced stages of our progress in the direction of this unimaginable “absolute”. Since we can account for their character without having to make use of the notion, it is clear, a fortiori, that we can also dispense with it for the purpose of contemplating any type of “private” experience whatsoever.
We can now proceed to extend this train of thought by inquiring whether our intuitions of the “Universe” require us to retain the notion at all, or, in other words, whether a Herakleitan cosmology of “pure flux” must be fundamentally inconsistent with our intuitive rejection of a solipsist position, which, as Hume pointed out, is an ineradicable element in “human nature”.
We clearly do not require the notion whenever we envisage our relations with entities outside our experiences as “causal”, since we always assume in such cases that any activity on the part of an “outside” entity has anteceded its manifestation “inside” our experience, and vice versa. But the possibility of dialogue requires a temporal overlap between the existences of the communicants. Can we intelligibly combine this condition with the elimination of “absolute simultaneity”?
This can, in fact, be done. We have simply to postulate that our own “continuities” are in fact “confusions” of what, in the ultimate analysis, would turn out to be discontinuous series of “atomic durations”, separated by periods of relatively enormous length during which each of us does not exist, but which are “owned” by the entities which constitute “the rest of the Universe”. We have, in fact, to accept the possibility that the “continuity” of our own experiences may be as much an “artifact” as the continuity of an image on the television screen.
Once this possibility is accepted - and it would be difficult to refute provided that we reject the absurd suggestion that we could be “aware of our own periods of non-existence” - there is no objection to regarding the “Universe as a whole” as a unidimensional linear flux. This must divide itself into atomic durations, “confused” into cinematographic sections, or “monads”, in accordance with a principle that we can only think of as “rhythmic”. The monads never exactly co-exist, but their occasions of existence overlap within the totality of “duration”, and they can therefore all be connected by “causal” relationships. It is reasonable to suppose that each monad has power, within its extremely limited “occasions of existence”, to modify the flux before “passing it on” to whatever monad “owns” the next “atomic duration” that “comes into existence”.
There is no need for each monad to “mirror” the Universe, as in Leibniz' monadology, since each monad, during the extremely brief periods of its existence, is the Universe. We thus obtain a pluralist Universe of the type postulated by William James, consisting of interlocking passages of “pure experience”. I do not think, however, that James ever envisaged the possibility that these might all have been dissected out of a unidimensional flux, and occur entirely in succession; this view has the advantage of allowing them all to be causally related. We do, however, require the postulation of some unifying principle in order to account for the ubiquity of quasi-permanent structures which each of us in fact succeeds, without much difficulty, in imposing on, or detecting within, his raw material. The most obvious solution is that of a common æsthetic urge, operating through each of the monads, and motivating its attempts, or the absence of attempts, to modify the flux.1 This is a satisfactory replacement, from a monist point of view, of the “pre-established harmony” of Leibniz's scheme. Furthermore, if we regard all æsthetically motivated activity as a priori meliorative, we can look upon the Universe as “G-d enjoying Himself as many, instead of as one”. This requires the elimination of all notions of the activity of an “evil will”. Nevertheless, we need not follow Leibniz in regarding the Universe as “the best of all possible worlds”; but there will be no objection to regarding it as “the best - or the least objectionable - of all worlds that have been possible so far”!
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1. These are, respectively, the “resistance” and “prehension” of Whitehead's philosophy. They are not “opposites”; “prehension” is simply a negligible degree of “resistance”. Editor's note: A. J. Ayer's interest in Solomon's work is hardly surprising. For Positivists all experience is sense experience. Experience is passive in the sense that its occurrence is totally dependent on the activity of the object experienced, and it is physical in the sense that it is constituted by a special relationship of sense-contents in space and time without any experiencing subject distinct from such experiences and without any distinct efficient cause of such sense-contents. For Logical Positivists nothing has a meaning unless it can be understood by someone with a purely scientific outlook. Cf G. M. Gozzelino, La Filosofia di Alfred Jules Ayer (Zürich: PAS-Verlag 1964, pp.xii-199, especially pp.11.26).
This cosmology differs radically from all “religious” ones, which always assume G-d's “perfection”, idealise His “eternal invariance”, and attribute ethical superiority to the “One” over the “many”. Among nominally Christian philosophers, only Leibniz realised that the richness of an experience might be in direct ratio with the amount of variety that it embodied, and therefore postulated that G-d had created the maximum number of “compossibles”; the resulting richness was presumably enjoyed by the “One”, in the same way that each of us enjoys the rich compresence of the variety of forms that he succeeds in extracting out of his own raw material. But variation can be excessive; from time to time, each of us is confronted with some change which is felt with great intensity on account of its very rapid tempo and exceedingly short duration, which does not allow us to extract any structure whatsoever out of it. Whenever this is concerned with whatever analysis of our raw material it is that has furnished us with our internal awareness of “matter”,2 it becomes a major source of “shock” and “pain”. When such changes are intolerable, we simply stop analysing in this fashion, and “switch off”, much as we shut our eyes. In other words, we “faint”, or, if the trouble is severe enough, we “die”. If only we could scan such experiences rapidly enough to enable us to structure them - just as a “slow-motion” cine-camera enables us to discover structures in exceedingly rapid sequences of change - we might be able to “slow them down” sufficiently to render them tolerable.
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2. This mode of analysis, in the East, forms the subject-matter of “Yoga”. In the West, it is not regarded as suitable material for “science”.
The idealisation of “invariance” is, to a considerable extent, an understandable reaction against the disenjoyments associated with excessively rapid change. But it has been overdone; “absolute invariance”, and for that matter “perfect peace”, would be equivalent to “eternal monotony”. Indeed, if we are not prepared simply to accept the Universe as a “going concern”, and feel a need to postulate its “creation”, this could well be accounted for as G-d's reaction to His own boredom; he “exploded”, and the element of “randomness” present in the Universe may represent unforeseen and maybe unforeseeable events resulting from the “explosion”. Subsequent events would then manifest His efforts to alleviate the more unpleasant of the resulting experiences, replication of the pleasant ones being sought, while that of the unpleasant ones is avoided.
It is important to remember that in the cosmology postulated here, each of us is in a “cross-section of G-d”, so that the Thomist principle “Inasmuch as anything is pleasing to Man, it is also pleasing to G-d” must be applicable. So also is its converse “Inasmuch as anything is displeasing to Man, it is also displeasing to G-d”. But anything that we consciously seek or avoid must be a replication of something that has already been experienced; genuine novelties, which frequently arise, can only be judged directly on their æsthetic merits or demerits. Our experience of “will” is essentially one of “dissatisfaction” - but of a “divine dissatisfaction”, which is here postulated as the motive power of the Universe. Every desire to “achieve something definite” manifests such a dissatisfaction; the structure of the “something definite” must already be present in conceptual thought, and what is sought is an increase in the intensity with which we experience it, the low level of intensity characteristic of “conceptual thought” being less than satisfactory. Similar considerations are applicable to the “desire to avoid”; what is to be avoided is, likewise, an increase in the intensity with which we experience the conjectured structure.
There is, however, a considerable difference between the applicability of the Thomist principle and that of its converse. The use of the general term “Man”, rather than “a man” or “men” is only justifiable in the case of the converse proposition, since human opinion is virtually unanimous only in condemning certain types of experience as “displeasing”; there is no comparable measure of agreement as to what is “pleasing”. It is true that the whole of humanity appears to be “addicted” to breathing, eating, drinking and sleeping, but even these “addictions” originate as reactions against the unpleasantness of being deprived of these modes of experiencing. Newly-born infants do not always breathe spontaneously; a slap administered by the doctor or midwife is often needed in order to stimulate the crying reaction which in turn initiates the activity of breathing. Once any of these “addictions” are established, we can fairly assume that a serious deprivation will be accompanied by grave displeasure; We can also assume a unanimous dislike of the exceedingly abrupt or intense experiences of change that we call “shock”. But this is about as far as we can go in assuming human unanimity, and even in the case of “shock”, sensitivities vary enormously; we can, however, confidently postulate that there is, for every human being, an intensity level at which it becomes unpleasant.
Since we do not start with the “religious” assumption of an initial “perfection”, we have no grounds for taking a derogatory view of change, or even for regarding “chance” as ethically undesirable. We entirely reject Einstein's dictum “The Old Man doesn't play dice”, which expresses the view both of “orthodox” religion and “determinist” science. We can either accept the element of chance as the outcome of one colossal throw of the dice - the “explosion of G-d” - or suppose that He, through His creation, is throwing dice the whole time; in either case, we assume that He, through His creatures, only attempts to replicate the “throws” which have been pleasing, and to avoid replicating those which have been displeasing. Such a willing acceptance of chance and novelty makes it impossible to formulate a final ethical “ideal”, which all creation is striving to attain, but permits general agreement in respect of the types of experience which are best avoided.
We are here seeking an adequate basis for ethical agreement in the dislikes which are common to the whole of “humanity”. But we must remember that the Herakleitan Cosmos must also embody a vast multiplicity of sentient beings who cannot be expected to manifest in human or even in animal form. We have no clear indication whatsoever as to the nature of their individual “likes” and “dislikes”. Even in the case of human beings, we can only conjecture the æsthetic reaction of one of our fellows to the manifestation, within his or her experience, of some activity of our own; we generally judge in accordance with the pleasure or displeasure occasioned to ourselves by what we take to be a manifestation of that reaction. We can extend this kind of judgment to certain of the “higher” animals, but beyond this point it becomes impossible, since the reactions of individual sentient beings are no longer manifest within our experience. We conduct our own activities mainly with the object of ameliorating our experiences within the range of the limited selection of frequency bands that furnish us with our “sensations”, to which alone we tend to attach importance. We have no notion whatsoever as to what their relevance might be to sentient beings operating on altogether different frequency ranges. It is likely, however, that the higher the “orders” of frequency with which we “scan” the raw material of our own experience, the more likely we are to detect manifestations of activities at frequencies which are “factors” of our own scanning frequency. Thus a radical increase in this frequency is bound to increase our sensitivity, and may make us aware of the activities of sentient beings whose existence we have never previously suspected.
In India, the existence of such being has long been taken for granted, and the doctrine of “Ahimsa” - that we should refrain from occasioning any suffering or displeasure to any sentient being - is extended to include them. Its underlying assumption is that all discord, all disorder, all suffering is inherently undesirable; the ultimate religious ideal is the abolition of all dissatisfaction, but this, in terms of the cosmology with which we are here concerned, would be tantamount to complete annihilation.
Such an “ideal” is seriously discordant with our everyday judgments of experience. Many of us find the highest degree of enjoyment in the effort that we make to alleviate excessive degrees of suffering, and to resolve seriously unpalatable discord and disorder. But “complete order” and “perfect contentment” would also be complete stagnation. This is the “ideal” put forward by pessimists like Schopenhauer, who was much influenced by Eastern thinking. Some people might perhaps be content with it, but most of us find it impossible to accept as an ethical-æsthetic “optimum”. Gœthe in his Faust went so far as to identify such complacency with “damnation”, but this view is rather extreme; while it is not the “best”, it can hardly be the “worst”. The common-sense view advocated here is that the ethical-æsthetic “opposite” of “too much” dissatisfaction is not “none at all”, but “enough”, and that “enough” generally differs less from “too much” than it does from “none at all”. We are here concerned entirely with an intensive quantity, which language notably fails to express, so that the point has to be illustrated by means of simple “parables” or exemplifications. A fairly obvious one is that of the saltiness of food; some people will tolerate and even enjoy much more than others, but in no case is the “ideal” none at all.
This point is becoming increasingly important. In recent years, many discoveries have been made which strongly suggest that the activities of sentient beings are manifest in what we call “plant life”; although it is almost certainly a mistake to “locate” these beings in the plants themselves, it can no longer be regarded as “superstitious” to suppose that they are concerned with what happens to them. The question therefore arises as to how much attention we ought to pay to their “feelings”; cases have been cited of people who have given up mowing their lawns on account of psycho-galvanic reactions on the part of pot-plants to persons who have been “guilty” of such practices. Sir Jagadis Chandra Bose and others who have followed in his footsteps have recorded reactions by plants which suggest great sensitivity to human actions and even to human thoughts, and if we attach pejorative importance to all of them, every one of us must be guilty of extreme insensitivity, if not of “crime”, each time that we pluck a flower.
It is vital in such contexts to retain a certain robust sense of humour. Plants have also been found to register psycho-galvanic responses to intensely pleasurable experiences on the part of human beings who themselves, when monitored, also react in similar fashion. It is, in fact, impossible to certify whether the psycho-galvanic reaction of a plant manifests a favourable or an unfavourable response on the part of the sentient being concerned. The automatic attachment of pejorative significance to such reactions is a mistake which is the converse of the one already noted, namely, the assumption that the ethical-æsthetic counterpart of “too much” is “none at all”; in the present instance it is assumed that the counterpart of “none at all” must be “too much”. Our failure to give adequate attention to the intensity-relationships between value-judgments and disvalue-judgments can fairly be ascribed to the inadequacy of language in this field.
I am by no means advocating a total disregard of the findings of Bose and of men such as Washington Carver, Cleve Backster and many others who have worked in this field, and have made out a strong prima facie case for the operation within the Universe of sentient beings whose manifestations have not been adequately recognised. A sound ethic, based on sympathy, must advocate the avoidance of types of action which are liable to occasion them grave displeasure. Such action is generally intended to modify the environment of the phenomena embodying their manifestations, and if they find such modifications intolerable, they will cease to manifest. Conversely, they will intensify their manifestations whenever our modifications afford them extra enjoyment. We should regard them, like ourselves, as “cross-sections of G-d”, animated by “wills”, or “dissatisfactions”, with an æsthetic basis identical with our own, although operating on raw material which is so different from ours that direct communication with them is impossible at the level of sense-perception. But there are no grounds for supposing that the “Universal Æsthetic” excludes a reasonable sense of humour, so that a certain amount of give-and-take between us and them is entirely admissible. An excessively sensitive conscience in these matters would reduce us to the condition of the enthusiasts for the “Rights of Vegetables” in Samuel Butler's Erewhon whose diet had to be confined to windfall apples and decayed cabbage leaves.
Hindus, except perhaps for a few extreme pietists, do not carry their doctrine of “Ahimsa” so far as to include plant life; even so, they take it rather a long way. At the other extreme, we have the Old Testament view that Man was to be given “dominion” over the rest of the sentient beings in the sensible Universe. A sane, intermediate view is expressed by Jesus' “Ye are of more value than many sparrows”; human enjoyment and suffering may rank as most important within those aspects of the Universe normally disclosed to human perception, but the sparrow is likewise not “forgotten of G-d”, nor are the sentient beings whose activities are manifested in plant life.
When we pass beyond plant life to “inanimate” matter, we reach a point at which we cannot detect, within our experiencing, any manifestation of activity on the part of individual sentient beings. Any “habits” which we detect within our raw material - assuming that they are not entirely due to our method of “scanning” it - can only be attributed to the “public opinion” of the “Universal Society” as a whole. Our descriptions of these habits are what we call the “Laws of Nature”. The stability of these habits is no criterion of their “excellence”; it is merely prima facie evidence that they include none that have occasioned widespread experiences of intolerable displeasure. In a Cosmos constituted entirely of sentient beings, “natural” selection is, in effect, “æsthetic” selection; but it is only in respect of major disvalues that we can postulate a widespread measure of æsthetic agreement.
The “laws” are not final or binding and, if we dislike them, we may be able to discover ways of evading them without provoking any unfavourable reaction, such as would be likely to follow our widespread infliction of displeasure on the members of the “society”. Even the Hindus have not attempted to extend the doctrine of “Ahimsa” to this field; their activities within it are guided, like ours, by considerations of prudence rather than of sympathy.
Our supposition that the members of the “Universal Society” are all motivated by the “Brahma-æsthetic” does not preclude the possible existence of ethical hierarchies within that “society”. Only Brahma, speaking as the “One”, could make a definite pronouncement on the subject, and there is no evidence that He continues to manifest in this fashion. But there can be little doubt as to the basis of any such hierarchical order; the highest rank must be assigned to those through whom He has experienced the highest degree of enjoyment. If, therefore, we wish to suggest a hierarchical order within the “Universal Society”, or even within human society, we need to ascertain, or at least to conjecture, the nature of the qualifications which enable their possessors to enjoy in greater measure than their fellows. Furthermore, it is essential, in this context, to distinguish between “enjoyment” and “avoidance of disenjoyment”, since the latter could be fulfilled by self-annihilation, or some approximation to it, and we have already rejected this as an ethical-æsthetic “ideal”.
Let us start from Jesus' pronouncement “Ye are of more value than many sparrows”, which is hardly likely to evoke much dissent, even among Hindus, whose caste system manifests their strong sense of ethical hierarchy. We can proceed by asking: “What forms of ‘higher’ enjoyment are available to men but not to birds?” The answer would appear to be that human beings attach æsthetic importance to a far greater range of structures than do the birds.
We have seen that when “change” is regarded as the “Stoff-an-sich”, “intensity” and “tempo” are alternative descriptions of a single variable “quantity” of experiencing. This certainly attains its maximum in our internal awareness of “matter”, when its excessiveness is “pain”, while more or less unstructured “visceral” sensations of lower, but still high, intensity provide us with our most intensely experienced enjoyments - as, for example, sexual intercourse.* Smell, taste, touch and our internal awareness of bodily movement also provide enjoyment both for man and bird.
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* Editor's note: It is appropriate to distinguish between intentional and non-intentional pleasures, such as the pleasures of bodily sensations as such, and to notice that our awarness of physical stimulus during sexual arousal cannot ordinarily be detached in thought from our appreciation of who is doing what to whom. Cf Roger Scruton, Sexual Desire - A Philosophical Investigation (London: Phœnix 1994). This distinction is not incompatible with J.D. Solomon's basic position; indeed, it rather strengthens its appeal.
But there is no evidence that birds attach serious æsthetic importance to changes within the visual field, although, like us, they employ such differences as signs for the differences between more important future possibilities. Now the changes which constitute the field of vision are, experientially speaking, of relatively very low intensity, and we are therefore justified, conceptually, in regarding their “tempo” as low compared with those which constitute our inner awareness of matter, which are, in fact, much “denser”, i.e., of a higher order of “frequency”. We have already seen3 that the scanning of colour-invariance must be conducted at a more rapid tempo than that which we use for the scanning of shape-invariance, but even so, we have, on account of its low intensity, to treat all visual experience, conceptually speaking, as being of relatively slow “tempo” compared to that of our other modes of sensation. Its tempi are, of course, enormously more rapid than those of the “changes” that occur within the field of vision which we interpret as the movement of “physical objects”, including our own bodies. These changes are what furnish us with our “normal”, extremely leisurely, time-scale.
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3. In Chapter Three, above.
The indications are that among the individual sentient beings that we believe to be manifest within our experience, mankind alone obtains æsthetic enjoyment out of the scanning rhythms whereby he creates his visual field, and out of the colour-relations and proportions that he discovers during the process. He alone takes steps, which are often completely irrelevant to any practical considerations, to replicate such phenomena. Other sentient beings may possibly obtain some æsthetic enjoyment from certain types of colour-radiation, but hardly from visual shape. They certainly respond to musical sound, but this manifest itself in the shape of obvious changes of intensity within their internal awareness of matter, and must therefore be considered as change of a higher order of intensity/tempo than, for example, changing combinations of colour.
We must assign the highest “frequency” to the raw material of our experience, which embodies the whole of our conscious awareness, and a great deal more besides. This is beyond the range of linguistic expression, but is probably best regarded as a kind of non-conceptual, non-verbal “thought”. It is most nearly approached by our internal awareness of “matter”, which results from that primary analysis of our raw material which we call “incarnation”, and provides us with our most intense enjoyments and disenjoyments. We must be careful not to confuse this with our external awareness of the “surfaces” of matter; such “contacts” are merely those instances of our internal awareness of our own bodies that we conjecture to be “caused” by the external “objects” that we touch.4 Taste and smell are specialised varieties of “touch”, and need no special consideration. Vision is quite another matter; it is conducted at a minimum of three scanning “tempi”, which furnish us with our experiences of colour, shape and size. Very intense visual experiences, however, become “tactile” in character; a blinding flash or glare obliterates the structural features that are of paramound importance in normal vision, on account of the disenjoyment that is occasioned by such very great intensity.
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4. This assumption is expressed by Newton's highly metaphysical Third Law of Motion:- “Action and reaction are equal and opposite”.
Primary enjoyment/disenjoyment is occasioned by our internal awareness of matter. This is of predominant importance to infants, and probably also to animals, and is occasioned by visceral sensations, bodily movement, touch, taste, smell and sound. The so-called “primary” qualities of visual experience are merely those which are useful for the recognition of signs for the possibility of the fundamentally more important types of experience, especially that of touch. The “primary” qualities are shape, size and position within the visual field; colour is an “optional extra”, which is why it is called “secondary”. However, since our awareness of it is a comparatively high-frequency phenomenon, it occasions enjoyment and/or disenjoyment from a fairly early stage in childhood. An æsthetic appreciation of the lower-frequency cognitions of shape develops much later, and it is difficult to attach any intrinsic æsthetic importance to size or position, although relations between them are clearly involved in our appreciation of shape.
The slowest tempi that we can actually enjoy are those of our visual perception of movements with an order of tempo similar to those of our own bodies. These alone can be ostensively compared with the rhythm of the “second”. So-called “rhythms” such as that of the “year” and the “day”, and even those of the “hour” and the “minute”, are not apprehended directly. The “rhythmic invariance” of successions of phenomena such as eclipses, or the return of periodic comets, can only be purely conjectural, even when it has been repeatedly corroborated. Nor is there any reason to suppose that any non-human sentient beings, who manifest in the “public” universe of vision, have any awareness of these rhythms, although they may respond to some of the more rapid changes embodied in the “events” which are members of such rhythmically invariant sequences. It appears, for example, that certain manifestations within plant and animal life vary with the phases of the Moon. It would be stupid to attribute “causal” responsibility to the “changes of the Moon”, as manifested within visual experience; but the “causes” may reasonably be sought in the high-frequency radiations which are, possibly, reflected from its surface.
We neither “enjoy” nor “disenjoy” very slow rhythms; we merely find our conjectures of them useful for the purpose of predicting changes which are important to us. Their “tempi” have ultimately to be compared with those of visible bodily movements, or of music, which are the only ones that we can confidently define “ostensively”; such comparisons provide an extremely important function for “number”. Alternatively, we can construct visible models, such as the “planetarium”, which replicates their mutual relationships at a tempo speeded up to the order of that of bodily movement; this functions in similar fashion to the “time-lapse” camera, which makes visible the rhythmic structure of phenomena such as plant growth.
“Wisdom” has traditionally consisted of skill in the detection and the linguistic or symbolic expression of these extremely slowly-changing patterns of event-sequences. The priestcraft, in ancient times, preserved its power by virtue of its monopoly of the secrets of calendar rhythm, since only the priests could give reliable advice to cultivators as to when to sow and harvest their crops, etc., etc. Pythagoras and Plato, who between them founded Western science and philosophy, followed this ancient tradition. Thus it has come about that within this tradition, overwhelming importance has always been attached to the “invariance” of the slower repetitive rhythms. But their importance, that is to say, their value, is merely “instrumental”; it is entirely derived from the intrinsic judgments of value or disvalue which have respectively accompanied the agreements or disagreements between actualities and expectations that their formulations have stimulated.
Unfortunately, the “rationalist” emphasis on the slower rhythms, which mostly characterise series of visual events of very low intensity, has led to our neglect of the more rapid rhythms, within high-intensity phenomena, which are directly responsible for our enjoyments and disenjoyments. In this context we should remember that every “disappointment”, whether it be a failure to achieve an expected enjoyment or to avoid a conjecured disenjoyment, is itself a disenjoyment, so that since the importance of the slower rhythms is always the minimising of “disappointment”, it can fairly be asserted that their function is confined to the minimising of disenjoyment. It is only in this negative fashion that they contribute to an improvement of the æsthetic quality of experience, by permitting the operation of “human-natural”, i.e. æsthetic selection. But our preoccupation with them tends to render us insensitive to “mutations”, which alone can make a positive contribution to the enhancing of our enjoyment. For example, the over-valuation of invariances has given rise, among the “highly educated”, to an almost automatic disbelief in anything that smacks of the “miraculous”.
Attention to observed “invariances” has undoubtedly improved our ability to avoid those very grave disenjoyuments which lead us to “disincarnate” or “die”, i.e., to discontinue whatever analysis it is of our experiential raw material that gives rise to our “internal awareness of matter”. But in the process, we have almost forgotten how to enjoy ourselves; “intense” experiences - the “passions” - have come to be regarded with contempt in “higher” circles. We attach paramount importance to “survival”, which is, to a major extent, a prolonged repetition of familiar experiences, no matter whether these experiences occasion us intrinsic value or intrinsic disvalue.
Yet our most intense enjoyments are always concerned with our internal awareness of matter, which must be an extremely rapid tempo of change. It is quite likely that birds and butterflies, and perhaps many other “incarnate” beings, enjoy their inner awareness of matter as intensely as we do. Æsthetic enjoyment is always of the “present”, although this is admittedly “specious”; a certain minimum duration is required. But even when an intellectual sincerely claims to be “enjoying an eternal truth”, it is not its “eternity” that he is enjoying, but his repeated “present” experience of its actual formulation and of the harmonious relationship between his interpretation of it and the massive background of his beliefs.
In seeking to enhance our enjoyment, we should not confine our attention to the slow quasi-invariant patterns of change studied by the “intellect”, but should also take account of our most intuitive and non-intellectual type of experience, namely our internal awareness of “matter”. Our ability to “structure” or control this type of awareness is markedly defective, compared with our control of visual awareness, which we can “turn off” by shutting our eyes. Some progress has been made in the East, by developing the techniques of “yoga”, and there seems to be no reason why we should not ultimately develop techniques for turning our internal awareness of matter “on” and “off”, or even for “turning its volume up and down” as requisite.
The Hindu sages have unfortunately concentrated, for the most part, on “turning the volume down”, since they look upon this as progress in the direction of their ideal of complete “invariance”, or “absorption in the Infinite”. They have, somewhat pessimistically, concentrated on the removal of “suffering”, and since this is commonly associated with excessive intensities of our internal awareness of matter, they have, like many western “rationalists”, taken a relatively pejorative view of intense experiences in general, no matter how enjoyable they may be.
We cannot sufficiently stress the point that the ethical-æsthetic “opposite” of “too much” is, in terms of intensity/tempo, not “none at all”, but “enough”. Furthermore, if we take a Herakleitan view of the Universe, and regard its “stuff” as pure activity, or “spirit”, then the intensity/tempo of our internal awareness of matter is much more “spiritual”, that is to say closer in nature to our raw material, than are either visual experience, or the slow transitions between verbal and symbolised concepts, with which the intellect deals. There seems to be a persistent assumption on the part of all major religions that the creation of “matter”, like that of “time”, was a mistake on the part of the Almighty, and that our “dharma” or “duty” is to help Him to clear up the mess!
It appears altogether preferable to postulate that the purpose of the ethical-æsthetic urge is not only to enhance our experience of the beauty and subtlety of structure, but also to further its experience at the maximum tolerable level of intensity. And since the intensity of a beautiful experience is always enhanced by the feeling that it is shared, we should strive to express its structure, for the purpose of communication, at the greatest possible variety of tempo and intensity.
At this stage it becomes possible to adumbrate a pen-picture of a “Superman”,5 not with any intention of formulating an ultimate “ideal” towards which Mankind should strive, but in order to exemplify the qualitative direction of the æsthetic urge, or “divine dissatisfaction”, by indicating how he would differ from the rest of mankind. The nature of these differences may also suggest a basis for the establishment of an ethical hierarchy within the human race itself.
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5. Nietzsche's thinking had close affinities with that of Herakleitos, as Russell noted in his History of Western Philosophy. Thus there are bound to be important resemblances between my “Superman” and Nietzsche's “Zarathustra”. I have therefore thought it advisable to add an appendix to this chapter in order to pinpoint the differences between them, which are also very important. For the present I need only remark that my “Superman”, unlike Nietzsche's, does not exclude the possibility of a “Superwoman”.
My Superman is one who, although sensitive to the finest nuances of a wide range of experience, also displays the “heroic” virtues, and is able to endure great suffering; even when he cannot “laugh it off”, he can at least tolerate it. This ability will enable him to take great risks in widening his range of experience, not only in respect of its refinement, but also of its intensity. He will normally avoid disenjoyments, and his great sympathy for others will deter him from inflicting it on them, but he will not shrink from enduring it or from inflicting it should this appear to him to be a necessary step towards the attainment of a wider, deeper harmony.
He will rejoice in his greatness, he will not be “proud” of it, because he will realise that in the ultimate analysis it can only be accounted for by his “good luck”. Above all, he will not seek to be praised or rewarded for the luck which has brought him his superior ability to enjoy, but he will strive to enhance his enjoyment by trying to enable others to share it. He is bound to look down on his inferiors, but will not blame them for their inferiority, since he will say to himself:- “There, but for the Grace of G-d - the luck of the draw - go I”. Since he will regard all sentient beings, like himself, as “pieces of G-d”, he is bound to reject notions such as “sin” and “evil” as predicative of actions; he will, rather, regard distasteful actions as diagnostic of a backward ethical development on the part of their perpetrators. If he makes use of praise and blame, reward and punishment, it will not be because it is “deserved”, but simply as an incentive or disincentive to the replication of actions similar to those which have elicited it. His ethic, in effect, will be an æsthetic rather than a “morality”. Finally, he will not be complacent about his superhumanity, but will seek either to become a “hyperman”, or to further the development of such a being.
This last point is vital. In a pantheistic* Cosmos, in which all “will” is construed as meliorative, “damnation” can only consist of complacency, utter contentment. Gœthe interpreted this correctly in his Faust; the only souls who can be “damned” are those who have ceased to strive; they do not suffer, but the intensity of their enjoyment is negligible. Mephistopheles, the nihilist, “der Geist, der stets verneint”, is perpetually tempting them to take the “easy way out”. On this view, both the Christian “Heaven” and the Hindu-Buddhist “Nirvana” constitute “damnation”, while Einstein's “principle of least action” is the equivalent formula in the field of physical science. Since, however, we hold that a near zero intensity of experience can never constitute an æsthetic “optimum”, we may conclude that souls will not remain eternally “damned”, and that boredom will eventually induce them to resume activity. There is, however, a grimmer alternative in the possibility of a regrouping, by G-d, of their “atomic durations”; this is the function of the Button-Moulder in Ibsen's Peer Gynt.
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* Editor's note: Or, as Solomon agreed in conversation - and the difference is important, “panentheistic”.
I have a strong feeling that Jesus of Nazareth may have been the most complete embodiment of the qualifications for my notion of “superhumanity”. I am not thinking of the “sacrificial lamb”, the “Gentle Jesus, meek and mild” beloved of the churches, but of the heroic figure who strides triumphantly through the pages of the synoptic Gospels. He did not preach abnegation or abstinence, but “life more abundantly”; he came, as he himself pointed out, “eating and drinking”. He did not despise the flesh; the body was “the temple of the Holy Spirit”, and the “Kingdom of Heaven” was within everyone's bodily experience. The Crucifixion should not be interpreted primarily as an act of “atonement”, but as part of a deliberate performance of a script that had been written for the “Messiah”.6 He adopted the rôle reluctantly, because it appeared - correctly, as it turned out - that this was the best way of keeping his teaching alive. It involved a demonstration that it was possible for a man of the very highest sensitivity to endure a lethal form of torture and yet remain “incarnated”, that is to say, to continue to perform whatever analysis of his raw material was needed in order to generate his “inner awareness of matter”.
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6. Jesus himself stated this explicitly. See Mt 26:52-4.
I know of no comparable example, either in “history” or “fiction”, of such a combination of heroism with a degree of sensitivity characteristic of the greatest artists and mystics. Few “heroes” show any convincing evidence of high sensitivity - though Joan of Arc may be a notable exception - and conversely, few hyper-sensitives have been called upon to display heroic virtues. The saints and Avatars of India have concentrated on the avoidance of suffering, which always involves a diminution in the intensity of experience; they have make no attempt to “learn how to suffer”. Arjuna, the “hero” of the Bhagavad Gita, has clearly developed the heightened sensitivity of the Brahmin caste, and is reluctant to fulfil the heroic “dharma” of the Kshatriya caste into which he was born, and attempt to kill his kinsmen. The best advice that Krishna can give him is to accept his “dharma”, but to shrug off the whole affair as “maya”, that is to say, as completely insignificant and to retreat to the experiential nothingness of “Nirvana” - which, as we have seen, is actually an unstructured “fullness”. Socrates likewise seems to have alleviated hardships by his ability to “switch off” into a trance state.
A “Superman” must show the ability and willingness not only to decrease the intensity of his experience but to increase it as well.* In comparison with India, where the “escapist” ethic predominates, heroism, based largely on insensitivity, is in fairly plentiful supply in the West. Thus if we wish to look for examples of “superhumanity” in the West, we must look for them among the hypersensitives. And since it appears very difficult to find any extremely sensitive men who have voluntarily undergone suffering, we may have to accept, as a second best, those who have been prepared to take the risk of suffering by their refusal to repudiate the cruder, more intense forms of enjoyment. In general, they have treated the contrast between the structurally refined and the structurally crude as a source of fun. Obvious examples are Aristophanes, Shakespeare, Beethoven and Gœthe, and good claims can be made out for Michelangelo and Pieter Breughel. Most of the hypersensitives - Nietzsche's “higher men” - are disqualified by their inability to laugh! I do not think that it is far-fetched to ascribe this deficiency to two tendencies, endemic in Western thinking, which both stem from a belief in initial “perfection” - “Crosstianity” and the worship of “Absolute Truth”. “Higher men” who think in these terms are unable to ridicule their own earlier, cruder performances, which they have outgrown, and simply to dismiss them as “inferior”; they are bound to condemn them as “sins” or “falsehoods”, since their experienced inferiority stamps them, a fortiori, as falls from the original “perfection” postulated by their beliefs. The possibility of a universal ethical-æsthetic evolution is ruled out a priori.
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* Editor's note: St. Teresa of Avila, when writing about the prayer of quiet and the prayer of union in Chapter 18 of her Autobiography quotes certain words spoken to her interiorly about the soul by Jesus Christ that, like her own account of her experience of prayer, point to a paradoxical state Solomon appears never to have contemplated: “It detaches itself from everything, daughter, so as to abide more in me. It is no longer the soul that lives but I. Since it cannot comprehend what it understands, there is an understanding by not understanding.” Cf. The Autobiography of St. Teresa of Avila, translated by K. Kavanaugh & O. Rodriguez (New York: Book of the Month Club, 1995), p. 163.
Granted the ontological supremacy of change, as postulated by the Herakleitan cosmology, the only justification of a prayer for immortality, or “World without end”, is that “It is better to travel hopefully than to arrive”. Initial “perfection” would deprive the journey of any æsthetic justification, while the attainment of final “perfection” would annihilate the enjoyment to which it gives rise.
It is on these grounds that I suggest that we should reject the Parmenidean world view, which has dominated both religious and scientific thinking in the West since the time of Plato. The ethic appropriate to a Herakleitan cosmology seems to me to be a far more joyful one than any that is compatible with the notion of an existing “perfection”. Such a cosmology should therefore be welcomed provided that it is not irreconcilable with direct experience; I hope I have shown, by means of my hypothesis of “personal discontinuity”, that such a reconciliation can be intelligibly effect.
My ethic is entirely in agreement with Nietzsche's in respect of two of its major unorthodoxies.
Firstly, we both postulate an æsthetic motivation for all “creation” and “activity”. He expressed this view in his early work The Birth of Tragedy by the following profound aphorism:- “It is only as an æsthetic phenomenon that existence and the world are eternally justified”.
Secondly, we both agree in attaching positive value to the intensity of experience, as well as to the beauty of its structure, and reject that repudiation of intense experience which characterises both “official” Christianity and Hinduism. In other words, we joyfully accept the “Dionysian” element within our experience.
In terms of sense-experience, his “Apollinian” includes the highly structured, low-intensity field of visual awareness, particularly that of shape, and the world of linguistic concepts that is based on it. The “Dionysian”, on the other hand, includes everything that involves our inner experience of “matter”; this is of high intensity, but poorly structured. It includes visceral sensations, touch, taste and smell. Sound includes both Dionysian and Apollinian elements; structured sound, in the form of music, is a particularly effective link between them. What Nietzsche underrated was the importance of the fact that above a certain level, the intensity of Dionysian experience becomes painful, and that there is always, and for everyone, a limit above which it becomes intolerable. I agree with him that a “Superman” must be one for whom this limit is higher than for mankind in general - provided that this does not entail a corresponding loss in the fineness of his sensitivity. In Zarathustra's parable “Of the Sublime Men” Nietzsche regretfully admits that such a two-way extension of the ability to enjoy is a rare occurrence.
He might have been able to accept Jesus as a “superman” had he ever come across Blake's poem, “The Everlasting Gospel”, and re-read the synoptic Gospels in the light of that poem; Blake likewise took a positive ethical view of “intensity”. But it appears that he never envisaged Christianity except in the “orthodox” form into which he had been indoctrinated in his youth.
Unfortunately, he reacted too violently, both against this “redemptionism” and against Schopenhauer's oriental-style nihilism, and became too dogmatic a “Ja-Sager” or “affirmer”. Because he divined that there is, in existence, a surplus of joy over sorrow - that it has, in fact, an æsthetic justification - he accepted the whole of his experience, and ecstatically embraced the doctrine of “eternal recurrence”. In the concluding dithyramb of Thus spake Zarathustra he welcomes this Parmenidean virus into his otherwise Herakleitan cosmos in the following terms:- “Woe, says: ‘fade, go’, but Joy wants deep, deep, deep eternity".
It is, however, not “eternity” that can be “deepened”, but “intensity”. An antithesis to “fade” is lacking, so that “Joy” becomes static, and not essentially different æsthetically speaking from the Christian “Heaven” or the Buddhist “Nirvana”. It is not enough simply to say “Again!”; the only æsthetic justification of “World without end” runs:- “Again - ever more beautifully and more intensely!”
But in this case the fundamental expression of “will” cannot be the “will to power”, since structural novelty is hoped for, whereas power can only achieve an aim, which is always the intensification or avoidance of the intensification of some structure which is already believed to exist. A desire for structural novelty must be a blind urge, a purely hedonistic “Will to the structural enrichment of experience”. But Nietzsche's expression of utter contentment with the structure of life as it is leaves him nothing to “will” other than control over its intensity, which is “power”.
Another objection to power-seeking lies in the means which have to be adopted in order to obtain it. The ability of the power-seeker to fulfil his aims always depends on his obtaining the co-operation of a number of other sentient beings, and this requires that they shall be persuaded to take a sympathetic view of those aims. In the case of “material” power, it is the “Laws of Nature” - the “public opinion of the Universal Society” - which has to be considered; in the case of “human” power, it is the opinion of the group whose co-operation is sought. Once this is obtained, their combined strength may suffice to overcome any opposition to the achievement of the power-seeker's aim.
Any power-seeker who wishes to obtain widespread co-operation has to appeal to the “mob”. Now the sensitivity of the “mob” is no more than the highest common factor of the sensitivities of the individuals whom it includes, so that their sympathy has to be sought at a very low ethical-æsthetic level. It is quite impossible to enlist it for the purpose of fulfilling any very subtle purpose, although a power-seeker may be able quietly to achieve such an aim once the response to a cruder appeal has “conditioned” the mob into a quasi-automatic habit of co-operating with him.
This is why most men who have gained great power have been markedly insensitive; a highly sensitive individual has always to demean himself for the purpose of obtaining it. This consideration would appear to rule out the “Will to Power” as the fundamental expression of any æsthetic urge.
The Hindu recipe for progress is, essentially, the development of hypersensitivity to the point where all intensity is regarded as intolerable. Nietzsche's reaction to this is by no means unjustified, but he goes to the opposite extreme, condemning all hypersensitivity as “decadence”, and effectively glorifying “insensitivity”. My contention is that the fullest enjoyment of life requires a combination, or contrast, of the widest possible range of sensitivities. I agree that the Hindu recipe is free from risk, and that it can, perhaps, almost completely eliminate suffering; but it emasculates experience by removing joy as well!
- Shalom & Welcome! - 
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