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“The Universe as ‘Pure Activity’ ”
“On ‘Seeing a Chair’” (1)
“On ‘Seeing a Chair’” (2)
“On ‘Seeing and Hearing an Aeroplane’”
“On the So-called ‘Heterological Paradox’”
“On the So-called Velocities of ‘Light’ and ‘Sound’”
“On the so-called ‘Velocity of Light’”
“The Epistemological Status of the Physical Constant ‘c’”
“The Internal Velocity of ‘Illumination’ and the External Velocity of ‘Light’”
“The Temporal Function of Microscopy”
“The Empirical Experience of ‘Time’, and its Symbolic Expression”
“Spatio-temporal Relativity within the Visual Field of the Individual - an inference from the everyday use of written words”
“Should Zero be regarded as a number?”
“The Semantic Function of ‘Zero’, the ‘Logically Null Class’, and the ‘Meaning of Equations’ ”
“The Statics and Dynamics of Meaning” (1)
“The Statics and Dynamics of Meaning” (2)
“The Meaning of Meaninglessness”
“The Fundamental Nature of ‘Meaning’” with an Appendix: “The substitution of symbols - the use of ‘mean’ in dictionary definitions”
“The Basic Assumptions underlying Symbolic Communication - The Limits of Meaning and Truth”
“The Epistemological Primacy of Difference - Introduction”
“The Epistemological Primacy of Difference”
“The Epistemological Priority of Error”
“The Empirical Origins of Geometrical Concepts”
“The Empirical Origins of the ‘a priori’ elements in Geometry and Physics”
“The Experiential Origins of ‘Number’”
“The Origin and Basic Function of Concepts”
“The Relation of Verbal and Symbolic Expression in Direct Experience” including an Appendix: “The Solution of Three Classical Paradoxes”
“Self-referring Expressions, and the Paradoxes arising therefrom”
“The Limits of the Ethical Value of Truth”
Some Related Research Documents & Concluding Note
In this essay, the term (meaning) will not be treated as a substantive, but as the present participle of the active transitive verb (mean). This is used indiscriminately to denote and refer to two distinctive sequences of mental transitions, each of which relates a word-symbol with an extra-linguistic mode of experiencing; the problem of the meaning of 'meaning' arises from the circumstance that the temporal order of one of the sequences is the reverse of that of the other.
A writer's 'meaning' is whatever he intends to signal by means of the symbols that he employs, while the reader's 'meaning' is the outcome of his interpretation of the symbols. The reference of the substantive term (meaning) is therefore seriously ambiguous. There is no serious difficulty about resolving this ambiguity; we already dispose of the term (interpretant) as a synonym for the reader's 'meaning', and (significant) is a natural choice where the writer's is concerned.
In what follows, the use of upper-case letters will fulfil an unusual semantic, or more accurately, anti-'semantic' function. They warn the reader that he is intended to confine his attention to the visual aspects of the symbols, suppressing, as far as he can, his awareness both of their spoken equivalent and of any extra-linguistic interpretant. The point of this procedure is that standard practice provides no method of mentioning the symbols in isolation from their connotations; a word-symbol can only be shown, and as soon as it is recognised by a literate English speaker, he immediately and quasi-automatically endows it with an acoustic/phonetic interpretant, and in most cases also with an extra-linguistic one. Utterance of its acoustic/phonetic equivalent is never treated as referring to the symbol; its interpretation is always referred back to its supposed extra-linguistic significant.
It is hoped that this difficulty will be overcome by the present ad hoc use of an unusual but simple symbolic device, and that readers will be able to overcome their interpretative 'reflex'; only so will it become possible to discuss the word-symbols independently of their quasi-inseparable concomitants. Thus, for example, RED and red, HETEROLOGICAL and heterological, etc. etc., are not to be treated as strictly synonymous, as is usually the case.
Double inverted commas (" ") will not fulfil their function as 'quotation-marks', since the essay contains no 'quotations'. The function that they will fulfil is the quite common one of concentrating the reader's attention on the audible connotations of the included symbols, at the expense of any extra-linguistic ones. Were the essay to be delivered as a lecture, the symbol "red" would be replaced by a markedly ostensive demonstration of the word-sound.
Single inverted commas (' ') will also be restricted to one of their usual functions, namely, that of a synonym for 'so-called', which is most often used when the expression concerned is somewhat out of the ordinary. It can be shown that when employed in this manner, its tendency is to accelerate reference to the significant of the enclosed word-symbol.
In the almost unique case of the word sound "red", the transitions occurring during signification and interpretation can be unambiguously and quasi-instantaneously shown, as follows:-
Thus the tendency of (' '), when interpreted as 'so called', is to encourage the hearer to transfer his attention immediately to what, for him, is the usual significant of the included word-symbol. In practice, this is our standard method of conjecturing the interpretant of any word-sound; we start from an implicit premise that the communication will be successful, in which case the utterer's significant will be gap-indifferent with the one that we ourselves would have expressed by means of the word-sound.
We will now examine just what happens when attention is drawn to a familiar verbal symbol. By the use of plain brackets, I draw attention to the symbol (red). If I now point to it, and ask "What is that?" I will be prepared to accept no fewer than three answers, differing from one another radically in character, but none of them false. Two of them are interpretants of (red) rather than descriptions of it, but I am confident that they will be approved by everybody who shares the usual assimption that the marks were made for the purpose of signalling something that was in the writer's mind at the time; this is one of the criteria which distinguishes symbols from visual phenomena in general.
The three answers to our question "What is (red1)"? are approximately as follows:-
1. Ostensively demonstrated.
(i) A group of marks adjudged to be gap-indifferent with R, E and D, scanned rapidly in an approximately invariant direction, in that order.
Here we need to remind ourselves that in standard practice, r is actually adjudged to be gap-indifferent with R, e with E and d with D, in spite of their obvious differences in appearance.
R E D will hardly be acceptable. Nor will D R E, since the scanning order is not clear; the three marks might be signals for the vertices of a triangle in a geometrical drawing, or for places on a map.
It is clear that this answer is concerned with properties which must be predicated of the group of marks before it is accepted as a word-symbol. They are the essential ('est-se-ens') features needed to ensure its recognition. Only a little reflection is required to arrive at the realisation that no visual phenomenon can possibly function as a 'sign' until it has been recognised; but once we are thoroughly familiar with it, interpretation follows recognition so rapidly that we mentally 'telescope' the succession, and think of it as a single process. This is misleading, since the stages differ from one another in certain important respects, as will presently become apparent.
(iia) Any speech-sound adjudged to be gap-indifferent with "red" - as defined ostensively.
This condition explains why R E D and D R E have to be ruled out; their spoken equivalents would be symbolised by something like "ah" "ee" "dee".
It is clear that this answer cannot express any logical predicate of (red), since it is contingent, and will only be given by a speaker of English, or of some other language with similar phonetic equivalents for the alphabetic symbols.
(iib) Any colour-experience adjudged to be gap-indifferent with •. Using the symbolic convention described earlier in this essay, • could be signalled by 'red', and this method would have to be used to signal the extra-linguistic interpretant of almost any other word-symbol. The symbol RED plays a major rôle in the present discussion because its virtually unambiguous significant/interpretant can be exhibited in almost immediate temporal proximity to the symbol, within the visual field of a single observer. The complementary transitions signalled by the verb (mean) can be symbolised as • ---><--- RED, when the visual transitions can be effected quasi-instantaneously. This is actually a little misleading, since signifying by means of written symbols is a great deal slower than their interpretation, because it involves writing.
At this point it is advisable to consider certain groups of marks which might be expected, on cursory inspection, to fulfil the full function of a word-symbol, but which have in fact only one interpetant, namely, the phonetic/acoustic one. These include the so-called 'nonsense words', and can be excellently exemplified by Lewis Carroll's VORPAL. No English-speaker has ever doubted that this symbol was intended to signal an acoustic significant and to prescribe a phonetic/acoustic interpretant, namely, "vorpal", but even Carroll himself, whose powers of imaginative association were quite outstanding, was unable to discover any extra-linguistic significant for that 'word-sound'.*
* Editor's note: During the 1980s a central-London shop serving the needs of users of the then popular Commodore-64 computer offered for sale a proprietary 5¼"-diskette known as "The Vorpal Drive" containing several useful and ingenious programs, one of which was able not only to diagnose the presence of, but also quasi-instantaneously actually to remedy any irregularities in the performance of the notoriously less than 100% reliable Commodore-64 computer's disk-drive.
It is open to question whether such groups should be included within the reference of the term 'word-symbols'. But if we decide to exclude them, we shall be faced with a similar difficulty in the case of 'proper-names', which are basically speech-sounds used for 'calling', i.e. signalling, and not for description. For this reason, it is probably better to retain them, since no word-sound ever provides any indication as to whether its acoustic significant expresses an extra-linguistic one.
This essay is only concerned with languages in which the script is wholly phonetised, so that any purely visual connotations of the alphabetical shapes can be disregarded. This would obviously be illegitimate if we were considering Chinese. In several ancient languages, the phonetization of originally pictographic scripts was initially confined to proper names and terms borrowed from other languages, which otherwise could not have been visually represented. But as its greater convenience became obvious, it gradually spread to the rest of the language.
We are now in a position to formulate definitions of 'word-symbol' and 'word-sound', in the following terms:-
2. The vocal equivalents of alphabets and syllabaries are always classified in phonetic terms, never in acoustic ones.
These definitions serve to distinguish the communicative 'verbal' function from the visible and audible phenomena that we produce in order to perform it. This effectively destroys the substantive status of (word), which will henceforth be used exclusively as an attribute.
Assuming that "red" is generally accepted as a word-sound, with RED as its descriptive/prescriptive symbol, a complete communicative sequence of 'meaning', from the utterer's significant to the reader's interpretant, can be symbolically exhibited as follows:
I do not think that any writer will seek to deny that the occurrence of the first "red" stage is a necessary condition for the writing of RED. The reader's "red" stage may well be eliminated when the transition from RED to • has become quasi-automatic, although this is certainly not the state of affairs while it is being learned. I am not asserting that it is impossible to establish a quasi-automatic association between RED and •, but this is not how it is commonly done in practice.3 The eventual skipping of the intermediate stage is not a particularly difficult matter, because the structure of the scanning of a word-symbol has to be identical with that of the word-sound that it describes; its sequence has to be the same as that of the muscular efforts that it prescribes, since these serve to replicate the word-sound whenever this is required.
3. It is clear that some such associative techniques have to be used in order to teach deaf and dumb children to read.
The 'identity' of structure is in respect of the temporal sequence of a limited repertoire of 'sames' and 'differents'; it is'melodic' in character, corresponding to the succession of notes in a tune, but with 'pitch' alone taken into account in assessing 'sameness' and 'difference'. No account is taken of musical qualities such as variations of tempo and intensive quantity. The following three parallel examples, which embody the same melodic structure, should serve to make its 'essence' perfectly clear:-
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(i) |
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+ |
- |
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! |
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? |
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+ |
- |
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(ii) |
.- |
-... |
.-. |
.- |
-.-. |
.- |
-.. |
.- |
-... |
.-. |
.- |
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(iii) |
a |
b |
r |
a |
c |
a |
d |
a |
b |
r |
a |
It is extremely unlikely that anybody would ever attempt to translate line (i) directly into speech. In the case of line (ii), an extremely skilled Morse telegraphist might just possibly manage it without first transcribing the message. But in the case of line (iii), unless the wide spacing needed in order to demonstrate structural correspondence has actually destroyed the 'verbal' appearance of the symbolism, an attempt at phonetic interpretation will be quasi-automatic. This particular word-symbol is highly suitable for illustrating the structure involved, since it is not in common use, and will therefore not be immediately recognised; since it is purely a 'performative', with no extra-linguistic significant, no attempt will be made to seek an extra-linguistic interpretant. Furthermore, it includes five 'differents', some of them repeated, while others are not, and there is an unusually close correspondence between the alphabetic symbols and their phonetic interpretants.
Once a scanner of written symbols has grasped which of them are intended to be regarded as 'the same' and which is 'different', and has adopted the habit of scanning them unidirectionally, it is literally 'child's play' to memorise this elementary form of structure. The present writer suffered from a defect, possibly psychological, which almost completely inhibited him from speaking until the age of 2½. But he had meanwhile been taught by his 'nanny' to distinguish the upper-case letters of the alphabet, and to point to the appropriate one when its name was uttered. Looking around him, it soon became clear that general importance was attached to the melodic structure of their horizontal sequences, and he began to memorise them. As soon as he was able to speak, he began to come out with questions like "Mummy, what does M-E-T-R-O-P-O-L-I-T-A-N stand for?" The visual equivalent of melodic structure had clearly been quite easy to remember, and although the conventional names for the alphabetic symbols are not the same as their phonetic equivalents, the degree of correspondence between them was sufficiently close to make the eventual correlation of word-symbols and word-sounds quite an easy matter; actual reading instruction was not needed.
It is clear that the meaning-transitions within language, that is to say, between speech and writing, relate phenomenal sequences which are structurally as similar as it is convenient to make them, although this clearly falls far short of structural 'identity'. We want communication to succeed, and are glad to overlook discrepancies as long as the hearer/reader's reaction to the audible/visible language shows that his interpretants do not differ importantly from the utterer/writer's significants. The intra-linguistic stages of the process are within our conscious control, and we keep them as stable as we can, in the interests of communicative efficiency.
This is the static aspect of 'meaning', the proper sphere of 'logic'. But no 'rational' grounds can be attributed to any initial act of 'signifying'. This is not intended to deny that some form of psycho-physiological causation was operative on the first occasion when somebody reacted to the sight of • by uttering the sound "red", but the association cannot nowadays be regarded as more than a 'coincidence'. There is no conceivable structural association between the colour and the sound; one can only suppose that the utterer found the association pleasing, and repeated it. If he was a highly respected or influential person, his example would doubtless find imitators, so that "red" would become a standard signal for •. This is a 'humanised' version of the explanation of 'naming' given in the Book of Genesis; whenever Adam was confronted with some novelty, God noted the sound that he uttered, and that became the 'name'.
This aspect of 'meaning' is purely dynamic, since no recognition is involved. The only limiting factor involved is the psycho-physiological one that the sound can hardly be emotionally inappropriate to the circumstances under which it was uttered. This is well illustrated by the case of the onomatopœic words, where the utterer can approximately 'show' the significant; nobody would easily accept that the significant of "bang" was a whisper.
Every written communication starts from the writer's significant and terminates at the reader's interpretant. It is held to have been 'successful' when the reader's reaction is such that it indicates that his interpretant does not differ importantly from the utterer's significant. A definitive judgment in the matter could only be given by the utterer himself, but he is rarely in a position to give it, since the written symbolism constitutes a stasis within the 'meaning' process, which may last for many centuries. The 'correspondence' which gives value to 'correspondence-truth' is between the writer's significant and the reader's interpretant, but logicians have treated it as a correspondence between the symbolism and the reader's interpretant, overlooking the circumstance that the speech-based structure of language generally rules out any close measure of correspondence between the utterer's significant and its linguistic expression.
Consider, for example, a simple subject-attribute phrase such as "green grass". In this case my significant - and I assume, by analogy, other people's as well - is the memory of a synchronicity, or temporal overlap, of a distinctive mode of colour-awareness with a visual structure which I interpret as a sign for the proximate possibility of a tactile experience of 'grass' type. But I cannot express the synchronicity! Were I to superpose the symbol GREEN on the symbol GRASS, the result would be confused. I obviously cannot achieve a synchronous vocal utterance of "green" and "grass", and were I to arrange for the synchronous mechanic reproduction of those sounds, the outcome, once more, would be confusion.
Of course, this is unimportant in practice, since the juxtaposition of words is the closest possible approximation to their synchronicity, and therefore effects a minimum of falsification. Each of us therefore discovers, quite early in life, that it is employed, as the least of evils, in order to express synchronicities.
Sometimes the interpretation of a juxtaposition in terms of synchronicity turns out to be impossible, as in the case of "green red", which puzzled Russell. This only occurs when the words express significants which belong to the same 'dimension' of experiencing, which was what W.E. Johnson called a 'determinable'. In this case the fundamental incompatibility is between two rhythmic frequencies, both included within the same 'order' of perceptual 'tempo'. Such instances provide us with our empirical experiences of 'logical falsehood'.
The main function of 'grammar' and 'syntax', of which 'logics' are conventional schemata, is to enable us to avoid such utterances, and in general to ensure that the syntax of our linguistic utterances is not importantly at variance with any implicit or explicit syntactical relations between the significants for which their components stand. Each of us will, of course, interpret the individual word-sounds or word-symbols in terms of the significants that we habitually 'mean' by them.
Consider, for example, the sentence (He will arrive yesterday). In the absence of any counter-indications, we will attempt to interpret (will arrive) and (yesterday) as synchronous attributes of (He). Our attempt fails, for basically the same reason as it does in the case of (green red); we are confronted with incompatible 'qualitative co-ordinates' within the same dimension of experience, namely temporal succession. Similarly, (this office opens Monday, Friday and Wednesday) is 'wrong'; it is analogous to writing RDE instead of RED. It is melodic structure that is fundamental for language, whether the unit is a word, a phrase, a sentence, or a 'logical' sequence of sentences. And in view of the a-rational character of associations such as that of • and RED, it appears to be the only aspect of language that we can keep under 'rational' control.
The illusion that 'irrefutable proofs' are possible is clearly the result of a failure to distinguish between the several significants of (is). In (RED is RED) and ( • is •) it signals gap-indifference, the gaps being about the shortest that are publicly communicable. In (RED is red), provided that the arbitrary one-one correspondences between R and r, E and e and D and d are accepted, it signals a gap-indifference of melodic structure. This gap-indifference extends, subject to the corresponding provisos, to the word-sound "red". But the (is) of ( • is red) and (red is •) signals what is no more than an arbitrary, conventional association; any 'logical' relation between two word-symbols can therefore only represent a necessary syntactical relation between their customary significants. The persistence of such logical relations is therefore entirely dependent on the maintenance of quasi-permanent conventional relationships between individual word-symbols and their significants'(interpretants). These relationships constitute the dynamic aspect of meaning, which is purely arbitrary. Unlimited experiments in this field, such as those undertaken by poets - and nowadays, for that matter, by scientists - are perfectly in order, and may even reveal unsuspected and possibly valuable relationships between the significants of the words.4 They are only seriously undesirable in cases where any uncertainty in communication is liable to jeopardise the success of widespread human cooperation aimed at the fulfilment of a common purpose.
4. e.g. Einstein's E = mc², which states that the energy which constitutes, i.e. 'is' a gramme of 'mass' amounts to c² ergs, where c is expressed numerically in terms of centimetres per second.
Whenever attention is drawn to any visible phenomenon which customarily functions as a sign, 'standing for' something other than itself, the question 'What is that?' permits of two utterly different types of answer, neither of which is likely to be rejected as 'false'.
In one case, the answer is ontological and predicative, since it describes a set of circumstances which necessarily anteceded the 'dication'. In the other, it is semantic and attributive, i.e. 'postdicative'. In the first case, it refers to the sign-phenomenon itself; in the second, it names or describes one of its customary interpretants.
This generalisation is applicable to all visual signs, but is most easily exemplified in the case of verbal symbols, which are man-made 'tools' used for communication purposes, and very seldom show any discernible structural relationship with their extra-linguistic interpretants.
Consider, for example, the word 'red', to which I am now drawing attention. Were I to ask 'what is that?', any one of the following answers would be acceptable, although one of the second group would be somewhat more likely:-
Since no visual phenomenon can function as a 'sign' until it has been recognised, the answer (i) is self-evident; it simply states the conditions necessary for recognition, which constitute the 'essence' of the symbol itself. Its 'tautological' character is the very reason why it is unlikely to be chosen; it is 'too true to be any good'.
The answers in the second group are contingent and 'postdicative', since they will certainly not be produced by anybody unfamiliar with the English language or perhaps, in the case of (iia), of a language in which the phonetic equivalents of the symbols are similar to the English ones. For an English reader, they are both so familiar that they virtually function as 'conditioned reflexes', and the tempo of such associations has generally become much more rapid than that of the actual recognition of the written word, with the result that their repeated occurrence, on every occasion when the written word is recognised, tends to be overlooked.
Since the self-evident answer (i) seldom occurs to the mind of the responder, but is of great importance when we are discussing the problems of 'meaning', the comparatively rare case where the answer refers to the symbol itself needs to be distinguished in some way from the usual one in which it refers to one of the interpretants. This will be done by the use of capital letters, which, it is hoped, will inhibit the reader's normal tendency to transfer his attention quasi-instantaneously to the interpretant, by giving him a forceful reminder that the symbol is still 'THERE!' Similarly, the 'ontological' use of the copula will be written as IS, so as to distinguish it from the more usual semantic or attributive use, where it will remain unchanged.
The impossibility of indicating these distinctions within the 'ordinary' practice of written language has been one of the major obstacles to the formulation of a satisfactory description of 'meaning'. As Wittgenstein pointed out, we mean, but do not say 'I laid three examples of the meaning of "slab" to-day'.
Indeed, were we to insist on expressing our experience as fully as possible, we would have to say:-
"The meaning of 'I' the meaning of 'laid' the meaning of 'three' … etc. etc." Such a prolix procedure is ruled out by the signalling requirements of language, which are often urgent. By the use of capitals, we could shorten it to "The meaning of (I LAID THREE SLABS TO-DAY)". But in practice, readers will have discounted the 'inaccuracy' in advance, so that in what follows, capital letters will only be needed for the specific and unusual purpose of discussing the symbols in isolation from their interpretants.
The trouble is that the symbols have no names of their own, and can only be mentioned by 'showing' them; yet so soon as this is done, they are quasi-automatically assumed to be functioning as 'names' for one of their interpretants.
Acoustic interpretants such as (iia) are partly symbolic and partly 'iconic' representations. The correspondence between each pair of individual written and individual acoustic elements is conventional and completely a-logical, but the sequences of the paired elements have to be identical, since the series of symbols is designed to be interpreted by a series of corresponding muscular efforts, and these will only produce a sound that is gap-indifferent with the one originally symblised if the order remains identical throughout both transitions. The obvious analogy is with a composer's use of musical symbols in order to achieve a publicly audible representation of his sound-thought. The correspondence between individual notes and individual symbols is clearly 'symbolic', although in music a second 'dimension' allows a certain degree of structural correspondence between the 'height' of the pitch of a note and the height on the 'stave' of the corresponding symbol; nevertheless, the horizontal order of the symbols is an 'iconic' replication of that of the notes.
We will now proceed to examine the distinctive functions of the copula as it occurs respectively in the 'major' and 'minor' premises of Aristotle's archetypal syllogism, namely:- 'All men are mortal; Socrates is a man; therefore Socrates is mortal'. If we regard Aristotle's major as his attempt to express a 'necessary' intensional relation between the meanings of MAN and MORTAL, we can eliminate the semantically dubious 'all', and rewrite it simply as 'Man IS Mortal', while retaining its logical force.
The 'necessity' of this particular relation is doubtful, but it is easy to cite instances, as for example 'crimson IS red', or 'red IS coloured', where it would be unlikely to be questioned. The word CRIMSON was clearly invented for the purpose of differentiating between a variety of colour experiences which had previously been adjudged to be sufficiently gap-indifferent to merit the attribution of the single symbol RED. In this case, the experiential basis of the so-called 'illative relation', 'if x then y' ('when x then y' is better) was 'unless y, not x'. This relation is the natural outcome of the pre-verbal development of concepts by progressive differentiation. Each stage of the process effects an exclusion - 'omnis determinatio est negatio' - which results in an extensional relation between the 'y-class' and the 'x-class', although it is the intensional, semantic relation which should be accorded experiential primacy.
It should be obvious that a class-concept must be determinate and recognised before the corresponding 'class' can be assembled; but many determinations have taken place so early in life that their occurrence has been forgotten, so that they are taken for granted and do not need to be named until much later, when we begin to 'philosophise'. This is obviously the case where the distinction between 'colour' and 'shape' is concerned; the words COLOUR and SHAPE are normally learned much later than those associated with their 'determinates', such as RED and ROUND. This is why W.E. Johnson called COLOUR a 'determinable', but the 'future' connotation of that word is misleading' 'determinant' would have been more appropriate.
We can now return to the 'minor', 'Socrates is a man'. Since 'Socrates' is a 'signal', and effects no description, it should be written SOCRATES. Furthermore, the 'is' asserts no intensional relation between the meanings of SOCRATES and MAN, since SOCRATES has no determinate meaning. The minor should therefore be written:- 'SOCRATES is man'.
Thus the premises should be written 'Man IS mortal: SOCRATES is man'. From this there is no passage to Aristotle's conclusion that 'Socrates IS mortal'. It would be valid if we could assert 'unless x is MAN, it is not SOCRATES; but there are no grounds for negation 'x is DOG' or 'x is RAILWAY ENGINE'. For Aristotle, SOCRATES doubtless functioned as a descriptive reference, but unless this is the case, no phrase embodying a 'proper name' can have any logical function. The 'form' of a syllogism is quite insufficient to guarantee its validity irrespective of semantic considerations.
The contrasting uses of the copula are also evident in Russell's analysis of his favourite stalking-horse, 'Scott is the author of Waverley'. He analysed this into two components, as follows:- 'One and only one man wrote Waverley: that man was Scott.'
The first part of the analysis does actually express a recognisable intensional relation between two meanings; it can be written as 'the author of Waverley IS unique man'. But SCOTT, in the second part, is simply a 'signal', unassociated with any attributes, and can only have intensional relations with its essential visible components and with any collection of symbols of which it forms an essential part; it IS bot SC and OTT, since these components are necessary for its recognition. Similarly, SIR WALTER SCOTT IS SCOTT. Thus the relationship between 'unique man' and SCOTT must be written 'is'. Were we to substitute UNIQUE ANIMAL for SCOTT, we could write 'Unique man IS unique animal', in which case, 'the author of Waverley IS unique animal' would be a valid deduction, though not, of course, 'unique animal IS the author of Waverley'.
The 'logical' IS expresses a transitive, one-way relation, whereas 'is' only expresses 'synchronicity', which is symmetrical, two-way. If there had been any appreciable semantic difference between "Scott 'is' the author of Waverley" and "The author of Waverley 'is' Scott", the inversion actually performed by Russell for the purpose of his analysis would clearly have been out of order.
It would be 'folie de doute' to deny the 'existence' of SCOTT or, for that matter, of Lewis Carroll's VORPAL; they 'show themselves'. On the other hand, all that can be predicated of them are the visual characters essential to their recognition. Unless some distinctive extra-linguistic modes of experiencing have been habitually associated with them, 'Scott' and 'vorpal' do not 'exist'.1 In Lewis Carroll's view, this was the case as far as VORPAL was concerned. But the widespread acceptance of SCOTT as a 'verbal sign' implies the existence of 'Scott', although nothing else can be predicated of it. If 'Scott exists' is bad syntax, it is merely because it is redundant. Scott is recognised as a 'name', but the procedure of naming is completely a-logical, at any rate at the 'conscious' level of experiencing.
1. I am here disregarding their acoustic/phonetic interpretants, which are always treated as 'synonymous' with them.
It is clear that no 'name' can occur in any expression that is suitable for use in a logical argument. But every word is merely a 'name' when it is first uttered, and it is quite possible inadvertently to endow it with an attribute which actually negates its sign function. This occured in the case of HEROLOGICAL, to which Grelling attributed the meaning 'not predicable of itself'. In any assertion of this association, the small 'is' is clearly in order; it should be written "HETEROLOGICAL 'is' not predicable of itself". But in order for HETEROLOGICAL to function as a verbal sign, it IS, necessarily, HETEROLOGICAL; it must be recognisable, and therefore 'predicable of itself' in all significant respects. Thus it IS, equally obviously, not heterological - assuming that Grellings's attribution has commanded general acceptance. It 'is', of course, anything that you like to associate with it. Grelling effectively said that it 'is' a 'not-word' - which is permissible, but rather silly.
It has long been realised that most of the well-known paradoxes arise when an expression is consciously used for the purpose of self-reference. What is no longer obvious is that the recognition of any sign, which is a form of 'self-reference', necessarily antecedes any attempt at its interpretation. In childhood, when we are learning to read, there is generally an interval between the two processes, but the sequence becomes so accelerated that this virtually disappears, and the whole process comes to be regarded as a 'unity'. Since it is interprtation in which we are chiefly interested, the prior necessity of recognition has virtually eluded the attention of linguistic philosophers.
Peirce's description of a sign 'standing for' something other than itself effects a Hegelian-type synthesis of the two processes. 'Standing' expresses the 'invariance' of the sign which renders it recognisable, while 'for' expresses the transition to the interpetant, which occurs in the mind of the interpreter. Since most writers on 'meaning' have, like Peirce, been logicians, their attention has naturally been concentrated on the invariance aspect.
But a complete communication by way of writing involves the series of transitions:
The alternative interpretations of the alphabetic symbols correspond to answers (iib) and (iia) above respectively.
The only stage at which 'standing' can be publicly perceived is at that of the alphabetic symbols. Logic, at intra-verbal level, is only concerned to ensure the 'iconic' replication of the temporal succession of the writer's individual sound-thoughts by that of the succession of alphabetic symbols, and of that of the alphabetic symbols by that of the reader's speech-thought and/or his phonetic efforts. It is not concerned with the initial or final transitions, which are a-logical.
'Perfect' communication would require the reader's transitions to be a temporal 'mirror-image' of the writer's. The writer's RED stands for his sound-thought "red", which in turn stands for •. The reader's memory of •, on the other hand, stands for speech-thought "red", which in turn stands for RED. The order of the 'stations' in the export-import 'journey' is reversed as between the two communicants. For all practical purposes, it is the end of the journey which is most important, i.e. 'meaningful', so that from this point of view, it is the most suitable interpretant of the substantive 'meaning'. On the other hand, it is almost bound to differ in some respects from what the writer 'meant' to express, which may also be called 'meaning'. The beginning and end of the journey should be differentiated, and this is quite easy; we already have the term 'interpretant' for the end, and 'significant' seems highly appropriate for the beginning.
Of course, the agent of the 'meaning' process is always a human mind. Peirce recognised this when he defined the 'sign' as 'standing to somebody for something else'. What actually occurs can well be described as 'stimulating somebody to recall something else'. If we replace 'stands for' by 'recalls' in the foregoing account of the complete process, it appears in transitive order; the writer's • stimulates the writer, if he wishes to express it, to recall his sound-thought "red"; if he wishes to write this, he recalls the symbol RED. The reader's recalls, on recognising the symbol, are quasi-automatic; if he is reading to 'himself' he recalls his sound-thought "red", which leads to the recall of •. If, however, he is reading aloud, he will recall the appropriate muscular efforts, which will generate the actual sound "red".
The writer may be in a position to check that the structure of the reader's sound does not differ importantly from that of his speech-thought. 'Hi-fi' correspondence is altogether superfluous; both reader and writer want the communication to work, and will overlook or allow for speech defects and dialect variations in order to arrive at an extra-linguistic interpretant which will 'make sense'. For example, my tutor at Cambridge, who had a speech impediment which deprived him of gutturals, used to wish me a "dood vat" when I went to say good-bye at the end of term, although he would certainly have written the words as 'GOOD VAC'. This involved my acceptance of a 'dental' as gap-indifferent with a guttural, which would have been highly inadvisable apart from the actual context.
Similar considerations apply to correspondences between extra-linguistic 'significants' and 'interpretants'. The ultimate purpose of the writer is always to obtain a sympathetic response and possibly co-operation from his readers, but there is no point in the strenuous expenditure of effort required to try to establish a degree of correspondence much higher than the situation demands.
In written communication, the actual correspondence required is between the writer's 'significant' and the reader's 'interpretant'. Logicians, however, have ordinarily treated 'truth' as correspondence between the written symbolism and the reader's interpretant. They seem to have overlooked the circumstance - probably owing to its excessively tautological character - that every attempt to interpret a passage of written symbolism is based on an assumption that it is the outcome of a previous effort at expression on the writer's part. The symbolism is no more than a particularly stable interlude which occurs in the middle of the process. The treatment of a symbolic expression as 'absolutely invariant' presupposes that it expresses a corresponding 'invariance' in the writer's 'significant', and this entirely ignores the extent to which a writer is often obliged to falsify the character of his experience for the purpose of expressing it at all in terms of words and symbols.
The most blatant falsehoods are in respect of temporal structure. We are constantly trying to express synchronicities which occur within our experience, by just such expressions as 'white snow'. This expression of an experienced synchronicity by means of a succession is an obvious falsification, which can be augmented, in a manner that can actually be experienced, by writing it WHITE,SNOW: WHITE. SNOW: and even WHITE
SNOW. It becomes progressively more difficult to think the synchronicity of the interpretants of the individual words. An immediate juxtaposition of the word-signs effects the closest possible approximation to synchronicity, so that it is interpreted, whenever possible, as the outcome of an attempt to express it.2 An alternative to juxtaposition is the use of the attributive 'is', as in 'snow is white', which expresses the writer's intention of drawing attention ot the 'synchronicity'. The emphatic, ontological IS might be interpreted as "is at all times", but seeing that 'all times' are decidedly beyond our purview, this is better modified to "is at all times up to the present", and recommended as a useful rule of language. Thus 'red IS coloured' asserts that red, as far as is known, has never been used except when the meaning of RED was intensionally related to that of COLOURED; the use of IS recommends that this practice be continued in the interests of linguistic stability.
2. There are empirical limits; notwithstanding that RED BLUE is perfectly easy to write, 'red blue' is uninterpretable.
Since 'is' asserts synchronicity, it is clear that when snow 'is' white, white 'is' snow as well. In both cases, the 'logical subject' of the whole 'proposition' is an extra-linguistic synchronicity of visual 'snow--shape and white-colour. In such cases the grammatical 'subject' always denotes a remembered attribute that is the furthest removed from immediate experience; it is commonly associated with shape, since that is generally the first visual property to be recognised, on account of its frequent value as a sign for functional importance of some kind. The 'significant' of the attribute is nearer to experiential immediacy. But the usual grammatical relation between the words may, on occasion, be inverted. When viewing a mountainous region from a long distance, or when looking at a layer-shaded contour map of the region, we may very well say 'that white is now', since the 'white' is the first to be recognised. Here it is particularly clear that the function fulfilled by 'is' can only be 'semantic'. A similar inversion occurs in the use of the word-pair houseboat/boathouse, where both halves of each word would usually be regarded as 'substantives'. The visual meaning of the first will normally be recognised as boat-shaped, that of the second as house-shaped; it is the meanings of their 'attributes' which come nearer to expressing the individuality of the actual occasions.3
3. This seems to be an inversion of the 'semantic' relation between Russell's 'propositional functions' and their 'arguments'. It is a likely consequence of considering them from the point of view of 'expression' rather than from that of 'interpretation'.
On some occasions, vocal emphasis alone can indicate which of two attributes should be regarded as 'subject', especially when the extra-linguistic 'subject' is actually shown. A Biblical example is the reported utterance which accompanied the Baptism of Christ, namely, 'This is my well-beloved son, in whom I am well-pleased.' Should the emphasis be placed on the grammatical 'subject', 'son', or on 'well-beloved'? The text, being a mere inert 'fossil' of the spoken word, can give no indication; the Church tends to place it on the 'son', with a view to stressing his uniqueness. But in view of the circumstance that Satan is elsewhere recorded as being one of the alleged utterer's 'sons', an emphasis on 'well-beloved' would be far more appropriate by way of commendation.
Seeing that 'significants' often have to be blatantly falsified during their translation into written language, it is clear that a corresponding counter-falsification must normally be afected by the interpreter, in accordance with certain fairly general conventional methods, which can only have developed by means of 'trial and error'. The proper function of 'logic' is to try to ensure that they continue to function satisfactorily. Any attempts to maintain 'Truth' - with a capital T - throughout such a process is an absurd waste of time and effort, but it IS worth while to try to prevent the inadvertent transmission of serious falsehoods on account of defects in the technique of symbolic communication. The intentional transmission of falsehood, i.e., lying, does not come within the purview of logic, although logic might still concern itself with the technical efficiency of such transmission.
The 'value' of truth and the 'disvalue' of falsehood are alike almost always 'instrumental' rather than 'intrinsic' in character; an exception is the æsthetic enjoyment which frequently accompanies the discovery or invention of a subtle improvement within the field of symbolic communication itself. The discovery of grotesque defects, as in the case of the 'heterological' paradox, can also be a source of considerable amusement; unimportant falsehoods are a prolific source of 'value-experiences'. But it is also essential to be aware of such defects, since their importance may be anything but negligible when they affect the linguistic expression of extra-linguistic material.
In this essay, attention has so far been confined to verbal signs, 'symbolically' associated with their interpretants merely by virtue of long-standing conventions, and not because of any structural correspondence.
In infancy, it is empirically obvious that our primary means of expression and signalling are vocal. But as we grow up, we take an increasing interest in the highly complex synchronicities of structure encountered within the field of vision, and wish to communicate and discuss them with others. Our interest is primarily 'instrumental', since the 'natural' function of bounded images within the field of vision as signs for important tangible surfaces is established early in childhood, well before we learn to 'speak'. Manual exploration, conducted within the field of vision, repeatedly leads to the synchronous experience of a 'contact', i.e. a sudden increase in the intensity of tactile manual sensation, and an abrupt interruption of the visual signs of manual movement - which have in turn been established by repeated experiences of synchronicity. The visuo-tactile associations themselves are 'symbolic', not 'iconic', although, as in the case of the associations between written and spoken words, there is a relation between the temporo-spatial structure of their sequences.
Now complex visual structures cannot be adequately communicated by means of language, on account of its slow tempo. Even were it possible to give any kind of adequate description of the contents of the visual field experienced when viewing a landscape, it would be so lengthy that a hearer - or even a reader - would have not the remotest possibility of re-constituting a mental 'synchronicity' of the whole of it. Consequently, there has been a widespread development of 'iconic' signs for the purpose of effecting such communications.
These are light-reflecting or luminescent surfaces, approximately flat in most instances, which the icon-maker covers with colours and shapes in such a way that the structures generated within his own field of vision adequately replicate those generated by the 'significant' that he wishes to communicate. Because the 'significant' - his own visual experience - is in the majority of cases itself mainly important as a sign for tactile possibilities, the structures of the images replicated are, as a rule, those which he regards as characteristic of 'external objects'. There are, however, many exceptions. An artist may wish to communiate the enjoyment that he obtains from a visual field resulting from the 'visualisation' of non-ocular material, as for example in dreaming; the resulting 'icons' will be difficult to interpret in 'realist' terms.
When an icon is designed to replicate the visual sign for an 'external object', its name is almost invariably associated with its shape. Colour-contrasts - using the word 'colour' in a general sense to include variations of brightness as well as hue - are a necessary precondition for the 'existence' - i.e. the 'standing out' - of shape, but the colour qualities are irrelevant to it; they are a kind of 'optional extra'. But the shapes of the great majority of visual images have no names of their own; they are nearly always 'called' by the names associated with the most important function of their tactile interpretants. The word 'chair', for example, is applied indifferently to a 'this' - the sign-shape within the field of vision - and to the 'thats', namely, the tactile functions of its object-interpretant, and to the iconic replication of its shape on a flat surface. It is not surprising that it is difficult to formulate a satisfactory account of vision, or a coherent theory of the visual arts. It might perhaps help were we to write CHAIR when wishing to express the 'sign' - the 'sense datum' of realist philosophy - without referring to the interpretant.
'Ontological' descriptions of most sign-shapes are almost impossible on account of the poverty of any wisely accepted shape-vocabulary. In general, it can only be effected when the shapes can be fairly accurately replicated by the structured synchronisation of instances of those few which can be reliably named. Such descriptions are primarily of use to the makers of icons; we meet them in the 'perspective' researches of Uccello and Piero della Francesca, in Cézanne's doctrine of the 'cylinder, sphere and cone', and in the 'cubism' of Braque and Picasso.
The available vocabulary is in fact confined to the terms generally classified as 'geometrical'. There are, however, no grounds for supposing that these shape-concepts, or at any rate the names for them, antedate our acquaintance with their tangible interpretants. The name STRAIGHT LINE is a modification of STRECCAT LIN, which denoted a tightly stretched thread, while CIRCLE is derived from KUKLOS, a wheel. But the tactile interpretants of these shape-signs were of such great practical importance, at any rate in many parts of the world, that the shapes were being constantly replicated, and the degree of gap-indifference of replication was exceedingly high - much greater than that of the word-sounds and verbal symbols used for signifying them. Thus the significance of the 'names' of the icons became detached from that of their original tactile interpretants, and became associated solely with the visible shape.
The 'circle', in any case, is probably always with us, since it is the shape of the pupil of the eye, and apparently of the monocular field of vision - though the nose somewhat spoils its 'symmorphic' appearnce.4 it is, in the most literal sense of the word, the 'frame of reference'for the position of images within the visual field. The widespread attribution of 'divinity' to the Sun and Moon doubtless helped to increase its importance.
4. 'Symmorphy' is preferable to 'Symmetry' in exclusively visual contexts, since the quality is a purely visual one, prior to and independent of metrication, which always requires visuo-tactile synchronisation.
Now the 'ontological' description of a man-made sign is a prescription for its replication, as we have already seen in the case of verbal symbols and pictures. The 'ontological' descriptions of the spoken 'interpretants of the letters of the alphabet, which in their turn function as 'signs', are not in acoustic, but in phonetic terms. If there are any ontological descriptions of their 'significants', they can only be in terms of 'frequencies'.
The 'ontology' of a 'circle' can be taken for granted, since the rough 'compass' method of construction used by Africans to-day for drawing hut-circles has apparently been in use since Mesolithic times. The straightness of the 'plumbline' is likewise almost universally familiar, although the drawing of 'horizontal' straight lines is much less widespread among 'primitive' peoples. Euclid, however, could confidently take it for granted, and simply gave instructions for the construction of his diagrams out of straight lines and circles, without stipulating how they were to be drawn. In the present writer's youth, it was still an accepted 'rule' of the 'geometry game' that only ruler-and-compass constructions were permitted.
Replications of these shapes could be achieved with an extraordinary degree of gap-indifference, so that the meanings of 'straight line' and 'circle' could safely be treated as 'invariant', or at any rate as varying so little that the difference between them was 'indiscernible'. Leibniz' principle of the 'identity of indiscernibles' is an application of that of 'Occam's Razor'; whenever we use different symbols to express significants which it is not worth while to distinguish, we impose an extra burden on the memory, since the introduction of each new symbol requires the superfluous memorisation of an additional a-logical semantic correspondence.
This explains why there has been comparatively little proliferation of shape-names, the shapes are of little intrinsic interest, their importance being mainly their function as signs for likely tactile possibilities.
Since the time of Descartes, the algebraic formulæ of co-ordinate geometry have furnished an inexhaustible supply of 'ontological' prescriptions for the construction of shapes, by joining up a series of 'points' ('punctus', a prick, here denotes the sharp point of a stylus) by the shortest available route. Each 'point' is defined by the ratio between its distances from two symmorphically intersecting straight lines, one of which is customarily the 'visual axis of symmorphy'. The definition of the 'points' by means of 'polar' co-ordinates is more suitable for the purely visual aspect of the shapes, where linear metrication is impossible. In this case each point is defined by its distance from the centre of the field, which can be estimated by its ratio to the total length of the 'fixed' diameter of the circular 'frame of reference', and by the 'angle' - a proportion of a complete rotation - reuired to turn the 'axis of visual symmorphy' into the position of the actual diameter concerned. This latter procedure is the one we employ when estimating ("telling" requires metrication) the time from the position of the clock hands.
It is hardly surprising that C.G. Jung found that the circle appeared to be almost universally employed as a symbol for 'totality'; it is indeed very difficult to try to imagine the 'Universe as a whole' without subconsciously envisaging its shape as spherical.
The 'verifiability' of geometrical 'truths' was a natural consequence of the high degree of gap-indifference with which the icon-interpretants of the verbal expressions could be replicated. The expressions functioned, in effect, as symbolic prescriptions for the standard methods of replication; they wold have been completely meaningless in 'primitive' societies, where the construction of such icons is rarely, if ever, undertaken.
The notion that a comparable invariance of 'meaning' could characterise any other verbal symbnol is an unthinking and altogether unjustifiable generalisation, which resulted in Socratic idealism, in the adulation of 'universals' and in a superstitious belief in the possibility of 'rigorous' logic.
Until the Renaissance, the most influential of Plato's writings was, unfortunately, the Timæus, in which it is even suggested that two geometrical 'forms' - to wit, the shapes of two types of right-angled triangles - might be the ontological foundation of all 'existents'! If only attention had been paid to his eventual repudiation of the Socratic 'ideas', wich are ridiculed by 'Parmenides' himself in the dialogue named after that philosopher, the wild-goose chase which constitutes a great deal of subsequent philosophy might well have been avoided.
In conclusion, we should not overlook the fact that images in our internal 'visual fields of illumination' are predominantly experienced as 'natural' signs for tactile possibilities. It is not usually suggested that we have made them, and they assuredly have no 'names' that are independent of their interpretants. But an 'ontology' of our visual images is by no means out of the quesion; images within the 'field of luminescence' of the television screen are undoubtedly abstracted from the purely sequential flux of electromagnetic intensity which constitutes the structure of the 'carrier-wave', and it is by no means out of the question that our visual images originate in a similar fashion.
Whitehead, in the chapter on "Relativity" in his Science and the Modern World, realised that his line of thought was leading to the conclusion that the raw material of experience might be purely sequential, but proceeded to reject this possibility out of hand, 'in order to satisfy the present needs of scientific hypothesis'. The evidence now available from television suggests that this may have been unjustified, although we are bound to accept that a raw material of this kind would preclude the possibility of recognition, and hence of expression by means of signs. But a sequential ontology is perfectly tenable provided that we are prepared to admit that the 'raw material' of experience must fall outside the purview of 'science'. In the case of the televisual field, such an ontology would doubtless be formulated in terms of 'rhythms', for which the images are 'signs'; and it would certainly be very difficult to suggest anything more 'basic' as the substratum of experience in general.
It is the very reasonable conclusion of the physicists that our interactions with the 'outside world' could theoretically be analysed into 'atomic energy transfers'. 'Simple impressions' were likewise the basis of Hume's epistemology of the 'empirical' world. But the necessity of recognition before any idea can be formulated requires the expansion of Hume's classical formula to:-
Judgements of 'gap-indifference', however, are æsthetic in character and can hardly be considered as other than 'internal'. Thus it does not seem at all far-fetched to identify Kant's 'transcendental æsthetic' with the basic methods of 'cookery' that are common to all mankind, at least in infancy; and its obvious manifestation, which appears to be fundamental for all perception, is what we call the 'sense of rhythm'.
Language, being a linear, one-dimensional temporal succession, is completely incapable of properly expressing the rhythmic structure of any temporal succession which may be embodied in its stimulus-content. This becomes immediately obvious when we compare the written symbolisation of language with that of muic, in which such expression is unconditionally necessary.
Language can indeed ensure that some indication is given of any distinct temporal order in which discrete elements occur within its stimulus-content, but it cannot in any way exhibit the tempo of such a succession, and is even constrained, on account of its linear structure, to denote 'compresences' by predicative word-sequences. Musical notation, on the other hand, easily expresses them by means of the simple device of vertical superposition. The second dimension is unavailable in written language, because this has to be speakable.
Nevertheless, the temporal proximity of the word-sounds, in a phrase or sentence, is always used to represent a certain degree of proximity between the elements of the stimulus-content that the separate word-sounds are intended to express. To this extent a limited degree of correspondence is expected between the temporal structure of the word-sequence and that of the corresponding elements within the stimulus-content.
A verbal sequence becomes 'meaningless' when this condition is not fulfilled. There are two distinct types of meaninglessness, corresponding to the two distinct ways in which the mode of temporal association of the word-sounds is felt to differ intolerably from that of the corresponding elements in the stimulus-content.
The first occurs when we attempt to express a degree of temporal proximity which is too close to be expressible by any succession of words; this is 'logical' meaninglessness, or 'self'contradiction'. The second occurs when we construct a phrase or sentence from words which separately express elements which are so widely separated in thought that the transitions between them cannot be effected with a speed comparable to that at which we effect the transitions between our 'recognition' of the word-sounds themselves. This is 'empirical' meaninglessness, or 'nonsense'. The first type includes all compresences which might be considered to be 'absolute' or 'near-absolute'. As an example, we can take 'simultaneously red and green' or even 'simultaneously red and not-red'.
Such statements are 'logically' meaningless because they ignore an assumption which is basic to all symbolic communication, namely, that the invariance or gap-indifference of utterances and/or acts of awareness of a symbol represents a corresponding invariance or gap-indifference in the acts of awareness of its stimulus-content.
A consequence of this assumption is that the verbal expression of an 'instantaneous' transition between two different types of awareness is impossible, since a minimum 'quantum of duration' must be required to generate a judgment of 'invariance'. In the case of transitions such as that from 'red' to 'green' such a requirement is obvious. In the case of the transition from 'red' to 'not-red', an invariant memory of 'red' must be a constituent of the judgment'; 'not', however, never represents a persistent invariance; the gap-indifference of the symbol represents a gap-indifferent psychological characteristic of certain transitions or events1 which are too brief to permit of an internal judgment of 'invariance'.
1. I think that their empirical archetypes are sudden discrepancies between expectation and actuality.
This explains why the archetypes of 'logical impossibility' are always compresences occurring within a restricted, closely defined mode of experience. Transitions between awareness of 'red' and 'awareness of green' can be made so quickly as to be quasi-instantaneous, but it is clear, on reflection, that a certain minimum of duration is required. Einstein's principle, that distant simultaneity is unobservable, so that all 'interval' includes a temporal as well as a spatial element, is applicable to 'private' visual space just as much as to the 'public' variety, although the 'interval' between adjacent parts of the visual field must be regarded as angular rather than linear, the motion required to pass from one to the other being rotation rather than locomotion.
A compresence of 'green' and 'red' amounting to quasi-absoluteness is therefore verbally inexpressible. On the other hand, although experiencing 'squarely' differs more than experiencing 'greenly' from experiencing 'redly' a 'red square' is felt to be perfectly in order. This is because 'red' expresses a mode of awareness of an area enclosed by a boundary, while 'square' expresses a mode of awareness of the boundary itself. The transition between the two modes of awareness is nothing like instantaneous, and is therefore temporally compatible with the successive recognition of the two words. In the case of 'red book', the transition is even more leisurely, since the object only looks red from the outside, and has to be opened before the black marks on a white background which constitute 'experiencing bookly' can be perceived. The transition is generally from a sensation of red to a memory of book-experience, but this is quite slow enough to include the quantum of duration needed to permit the second judgment of invariance - a quantum which, although extremely brief in terms of our ordinary time-scale, can never be 'zero'.
As an example of the second, 'nonsensical' type of meaninglessness we can very well make use of Russell's 'quadruplicity drinks procrastination'. We have no difficulty in rapidly assigning each word-sound to its appropriate gap-indifferent series, but if we attempt to make a comparably rapid transition between their individual interpretations in thought, the effort is quite a painful one, and we correctly assume that nobody is likely to want to make use of such a sentence in order to express a thought-sequence.
We cannot, however, condemn the expression as unconditionally meaningless; 'Quadruplicity', like 'Felicity' might be used as a christian name, and 'procrastination' like 'White Horse', might be used as the name of a beverage.2
2. N.B. Capital letters disappear when a sentence is spoken.
Moreover, if we interpret 'drinks' in the wider, figurative sense of 'is nourished by', the expression, as it stands, could seve as a paraphrase of 'A stitch in time saves four'.
Neither of these interpretations can be ruled out as 'impossible'; what they are is 'far-fetched' - an epithet which is a very accurate expression of the above exposition of 'nonsensicality'.
I think that the two categories of 'logical' and 'nonsensical' meaninglessness cover all cases in which a juxtaposition of meaningful words gives rise to an expression which is felt to be extremely unsatisfactory.
It is clear that the reason for such unsatisfactoriness is not to be sought in the words themselves, but in the character of the transition between them. Since this transition is temporal, the obvious place to look for it is in a discrepancy of tempo between the transition between the word-sounds and the transition between their equivalents in the stimulus-content.
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