Making sense in music
An enquiry into the formal pragmatics of art (part 6)

by Jos Kunst (1978)

4. Winding up

4.0 Art vs. non-art


In 0.5.0 we mentioned the theoretical problem of the "family-likeness" purported to distinguish art from non-art, and we promised that our line of ideas on well-formedness and UNLL processes would prove, in the long run, in some sense enlightening with respect to it. We will now bring together the separate strands making up our argument.


During all of our waking life, and surely not only then, the physical world impinges on our sensory apparatus. If we take this last expression in a large enough sense, it will comprise, among other things, submechanisms for dealing with well-formedness problems: admitting well-formed data, assessing and possibly working on ill-formed ones, in order to make them well-formed, and rejecting irretrievably ill-formed material. (We do not prejudge here on the role of consciousness.) Part of the transformation of ill-formed to well-formed material takes the form of the processes we have subsumed above (0.5, 0.6) under the UNLL label. Now we are undertaking to argue for the view that a subclass of UNLL processes, viz., those which are captured by BivFs under a certain interpretation of them, can play a crucial role in providing a definition of art, at least if we urderstand by that term art users' art. What will thus be characterized by such a definition will be the activity of those who recognize art as such.


Certain problems beset such an undertaking. If, by providing a definition of P, we understand providing some set of conditions each of which is necessary and vvhich are jointly sufficient for something's having P, the case of the imaginary planet where all trees stand upright and only trees stand upright might inspire some disquiet. Having upright position as a necessary and sufficient condition for being a tree, and thus as a definition of the concept of tree, does seem arbitrary and counterintuitive. However, chances are that to the natives of that planet the definition would seem entirely satisfactory, especially to those among whose possible worlds is not one akin to, e.g., our own, in which so many counterexamples are to be found against both the necessity and the sufficiency of upright position as a condition for something's being a tree, such as, e.g., fallen trees and standing humans, respectively. This being so, it is clear that those of my readers who are uneasy about my proposals must not only express this feeling, but also search their stock of possible worlds and come up with the relevant counterexamples, so that their qualms can be assessed as fully and as rationally as possible.


Then there is another problem, which, despite its being clearly distinct from the preceding, is liable to complicate it, I think, to a considerable degree. Whatever way one wants to philosophize on definitions, or construct them in practice, if the concept to be analyzed existed already within the ordinary language, any definition consitutes a proposal to make the concept undergo an in principle once-and-for-all precise fixation, to force it away, in a sense, from its natural language origins, and to make it into a specialized technical term. In the meantime, the natural language word lives on. And that may mean fuzziness of borderlines, variations from person to person, and certain basic liberties in its use, e.g., in metaphorical discourse, or in the general case of "trying out" words in ill-understood contexts. Thus, once the definition is in operation, two homonymic words exist, one the "living" word, and the other the technical term.

I think that this is a rather tendentious picture. By simplifying things in a certain way, it glosses over the fact that a definition may set itself the task of capturing important conceptual features of the natural language word, that it may actually be successful, and thus, in important ways, keep in touch with the natural language word. If so, enlightenment is gained on the natural language concept.

Here again, counterexamples are the appropriate way of contrasting some reader's "living" word with the newly created technical term.


Despite these obvious and unavoidable difficulties, we are going to try our hand on a definition of art. As we have seen, decisive proof of its validity is beyond anyone's reach: even an idealized common-sense use of a concept can never be simply equated with any technical use. Nevertheless, what is both possible and fruitful is to look into existing theories. Given the fact that there is, as yet, no successful one on music (if we thought there were one, we would not be engaged in the present enterprise) what might be interesting is 1) a successful theory on a subject in some sense closely related to ours, and 2) and unsuccessful theory which tries to account for a number of interesting facts our own theorizing addresses itself to also. In the first of these roles we cast modern psychological theorizing on emotions, as represented in Mandler 1975, and in the second an early and highly intuitive "cognitive" approach to music, that of Claude Lévi-Strauss.

4.1 Theories on emotion and cognition


Somehow bound up with the idea of art is that of beauty; somehow bound up with the idea of beauty is that of pleasurable emotion. Therefore psychological theorizing on emotion might well prove to be of essential interest to our enterprise. Thus if we find among the informed contemporary literature a specialized book on emotion, such as Mandler 1975, which in its turn gives some attention to aesthetics, we will do wise to compare the two approaches.


Key concept in Mandler's treatment of pleasurable emotions is that of the sense of mastery the individual has with respect to the situation confronting him (cf in particular p. 150). This sense of mastery is based in his evaluation of his ability to cope; coping reactions may consist not only in concrete transactions with the environment, but also in reevaluating it, restructuring it. Thus, on p. 106/7, Mandler says:

"The coping reactions (described by Lazarus et al., 1970, J.K.) are of two kinds. One is direct action, with its effect on the environment which, in its turn, affects the appraisal of the situation. The other coping process is cognitive in that it involves further evaluations or reappraisals. In our language, a coping reaction would be a reaction to a particular situation that may be executed and have certain effects as a result of the structures invoked, or it may result in a change of the structures themselves, whereby cognitive or mental restructuring (or reappraisal) may result."

Even relatively invariant, involuntary, "primitive" reactions such as the startle reaction to sudden loss of support (connected to the fear of falling), may become "positive" and pleasurable, as is shown by the roller coaster paradigm (p. 71/2):

"(...) even here the action of the cognitive interpretive system may be important. For example, loss of support has just been considered as an instinctive condition for an essentially negative emotional reaction, yet it is a condition foreuphoria for many people when it is experienced on a roller coaster. The interpretation of the roller coaster as a positive event and the autonomic reaction that takes place at the same time produce a positive emotional response in this particular case. The roller coaster effect also illustrates another important aspect of meaning analysis. One of the imputs that is analyzed for the "meaning" of a particular situation is our own behavior. If we see ourselves in control of a particular situation the emotional reaction is more likely to be positive than negative. Thus the seeking out of autonomic stimulation, as in the case of the roller coaster, is a condition for positive rather than negative evaluation. Contrast this with the child who does not want to go on a roller coaster but is forced to do so; the reaction is likely to be negative. With the increasing observation of his own control of the situation, that he can "choose" to go on the roller coaster, the situation changes from negative to positive."

In a general way, one of the chief releasers of emotion, viz. interruption, may be entirely pleasurable, depending on the evaluation of the situation that arises (p. 159):

"The prime example can be found in play behavior, particularly in that of children. Given the proper attitude or situational definition, children may be safely interrupted in the midst of organized sequences and find that such interruptions are pleasant, even delightful. A toddler laboriously climbing stairs may cry when suddenly snatched off them; however, he may also cry in delight when the snatching is done by a smiling parent in the spirit of play."

It seems plausible to say that in such situations the child is being trained in using its intelligence in reevaluating situations, and developing the "feel" of its sense of mastery: after all, it is only applying what it already knew (p. 159):

"It should be emphasized that the conditions of interruption that lead to positive, or any other, emotional expression must be the previously acquired evaluations appropriate for these emotions."


The internal reevaluation transforming a possibly threatening situation into a controlled, a "mastered" one, as exemplified in the roller coaster paradigm and other related ones, certainly involves UNLL processes. To someone who objects that in many cases no very new concepts arise, and that therefore the word "learning" may be felt to overstate the case, our answer will be threefold. In the first place new concepts are, of necessity, built up out of old ones (see 4.1.1 end), and one must take a sufficiently close look at exactly what concept is produced by the UNLL process. In the second place the impression of oldness may be due to the fact that many UNLL processes are in fact re-occurring: concepts are then being rediscovered, re-learned (cf 3.2.1). In the third place, the laughter of the children being manhandled by their parents or shaken up at fairs may be taken to prove that some UNLL processes remain, through many repetitions, in a very real sense unexpected (cf Mandler p. 173): what is well-known to one, say, verbally, may be repeatedly surprising if experienced on other levels. We might then have a subcase of the foregoing: that of superficially well-known concepts being re-discovered, re-learned at other, "deeper" levels (possibly also thought through to "deeper" implications, which would mean UNLL processes proliferating).

This brings us to the problem of how UNLL processes are related to consciousness. At first sight, they seem, by nature, part of the consciousness' "trouble-shooting" task (cf Mandler p. 57). Moreover, "(...) practically all novel relational orderings require that the events to be ordered must be simultaneously present in the conscious field. (...) Once relations (...) have been established and stored, subsequent evaluations are frequently unconscious" (ibid. p. 55). We may therefore assume that whereas novel UNLL processes will naturally take place within the field of consciousness, the conceptual orderings that result from them, once safely established, may be used in unconscious evaluational activities. But we will also note that it is, for the moment, unclear where we ought to locate the UNLL processes which are neither utterly new, nor so old as to have yielded well-established results: those through which concepts are being repeatedly "re-learned".


It is now clear how we may go about explaining the emotional appeal of music (and, generally, art). Music, if at all understood along the lines explicated in our theory, will afford the listener a sense of mastery: specifically of cognitive mastery. Each time one successfully goes through the cognitive restructuring process characterized by a BivF, one has avoided remaining 'stuck' at a world in which no law is asserted any more, a world whose only formula is of the form ¬□A∧◊□A, a world in which one says: I have ceased to understand, – a world of cognitive helplessness, of failure. Instead, faced by the cognitive crisis provoked by the music's anomalous behaviour, one has been able to successfully cope with it; through adequately reorganizing one's interpretation of the music, revising one's way of hearing it, one has gained new insights in it, and thus, you might say, succeeded in maintaining one's cognitive 'grip on things'.

Concomitant pleasurable emotions give no problem in this context. A BivF's left column, together with the A-world, contains interruptive, disruptive, or even threatening (the threat involved being disorientation, 'loss of contact') information. Thus interruption of a cognitive "organized sequence" may provoke automatic stimulation. Meanwhile, the situation is reappraised and the transition to the BivF's right column is made; thus mastery is reaffirmed. The autonomic activity is pleasurable in the new interpretation of the situation.

The quality of the emotion being precisely in its cognitive content, what is given in our BivFs may rightly be said to be the quality of the musical (or, generally, artistic) emotions.


We will now turn to some interesting borderline cases.

FUMU (Functional Music) is music originally designed to keep factory workers happy (or, rather, functioning at maximum efficiency) and regulate their tempo; dating back to the world war two industrial war effort.

Muzak is purportedly non-entertaining music designed to protect humans from anguish, fretting, worrying and the production and/or exchange of unwanted ideas, in factories, offices, supermarkets, dentist's waiting rooms, lifts, anywhere. "Muzak" is a trade name; other providers operate under other names.

I think it is reasonable to assume that these musics do, at least in part, what they are purported to do. In order to make some headway toward explaining that, it is wise to consider the following two passages from Mandler 1975:

"autonomic nervous system responses are very slow and their slow speed, in the order of 1 or 2 seconds, would suggest that emotion should not occur within shorter intervals. Introspection and some observations seem to suggest that such long latencies are not typical of emotional reactions." (p. 96)


"(...) after extensive experience of autonomic discharge (and its perception), autonomic imagery may develop. There is no reason why the phenomenon of imagery need be restricted to the visual or auditory systems. Just as extensive experience in these areas may lead to the perception of objects and events in the absence of external stimulation, so can past experience lead to the perception of autonomic discharge in the absence of actual discharge. Thus visceral events are necessary for the acquisition of emotional states but apparently are not necessary for their future occurrence. Such occurrence may take place because of structures that directly relate environmental events to emotional behavior. The actual arousal is bypassed (...) the perception of arousal may occur without the actual presence of arousal." (p. 97/8).

Let us note first of all that these remarks are of central importance in our general dealings with musical emotions: surely what we call our emotional reaction to music does not systematically occur with 1 or 2 seconds delay, and certain musics do "change emotions" in a tempo hardly compatible with any time lag of that order of magnitude. (But let us not forget that all these cognitively changing emotions might very well make do with just one continuous arousal state.) It must be the "image", the perception of arousal which, bypassing the arousal itself, precedes it or even supplants it.

To go back to our two borderline cases: the second, that of Muzak, seems the most extreme of the two. According to its manufacturers it is meant to be non-entertaining, and even "not-heard": in order to do its work, it ought to remain below the consciousness threshold. An explanation of the fact that, within limits, it is effective can be given on the basis of our theory if we assume for those who are subjected to it a) a sufficient previous acquaintance with music, and b) no special preoccupation with it.

Condition b) is only there to ensure the possibility of its remaining subliminal and is of no specific interest. But it is a necessary condition, because interested listeners might be annoyed by the platitude or, possibly, intrigued by the strangeness of a music which is a systematically toned-down version of musics as common-place as possible.

This common-place character of the musics that provide Muzak's raw materials brings us to condition a). And on condition a) our explanation essentially rests. Extensive experience of music, in which the appropriate (musical) UNLL processes have, as a rule, led to arousal and the (at first ensuing and later also preceding) emotional sense of mastery, is assumed to have "conditioned into" the listener's cognitive structures the direct link: music ⇒ sense of mastery. Then, whenever he finds himself in, e.g., a possibly claustrophobic situation like a lift, if also Muzak is piped into it and its surroundings, a continuing sense of mastery will make him more impervious to his tendencies in that direction. Also, personal insecurity, anguish and despondency, be they due to his working situation or to private circumstances, will be counteracted by the sense of mastery Muzak, unbeknownst to him, injects into his system. The ego is thus buttressed on an unconscious level. – Our own dislike of the whole thing is thus mostly based on the fact that, because of these psychological and sundry obvious concomitant physical facts, the people subjected to it are offered simply no choice with respect to it. –

Let us note in passing that this explanation allows us to bypass the need of actual UNLL processes going on in people's unconscious. But neither are they explicitly excluded. Non-novel UNLL processes may, in as far as we are concerned, take place in the centre or in the fringes of the conscious field, or also altogether out of it. Should the latter case be possible in reality, even Muzak might admit of actual UNLL processes taking place, albeit necessarily non-novel ones.

FUMU, in contrast to Muzak, is meant to be occasionally stimulating, and is thus, in all probability, not dependent on its remaining "not-heard" for its functioning. On the other hand, it does, just as, for that matter, all "listened to" music does, all the ego-bolstering things Muzak does in its more underhanded way. Moreover, the manufacturers' pretensions notwithstanding, it would probably be very unwise to try defining any sharp practical boundary between Muzak and more "normal" musics. Not only does Muzak, in practice, crop up sometimes into the middle of one's awareness [1], but we may also safely assume that people subjected to FUMU have often to really concentrate upon certain tasks, their foremen, their colleagues, etc., and that this will drive the music that helps them through their days to the fringes, or altogether out of their conscious field. It may then be the case that, coming out of these difficult (and possibly even interesting) parts of their work, the music, in some sense, cushions their relapse into routine and dreariness. However this may be, it is certain that FUMU manufacturers have experimentally evolved a "best daily energizing and relaxing curve" guaranteeing workers' quiet and optimum efficiency. – Here again, their prospective customers are not the workers themselves. –

Therefore, and in a way that is strongly listener-determined, there is, we take it, a continuum of musical effectiveness, as approximated in Fig 31 (where the "musical awareness threshold" roughly corresponds to an imaginary borderline between what we called the "centre" and the "fringes" of consciousness), and, given this listener-determinedness, what is unobtrusive for one listener may very well be disruptive to another. Also, I tend to think, even Beethoven symphonies have become, in some real sense, unobtrusive to many of their users.

[Fig. 31]
Fig 31 (cf Fig 21)


Claude Lévi-Strauss, from his 1955 (Tristes Tropiques) onward, and notably in his 1964 (le Cru et le Cuit) and 1971 (I'Homme Nu), has developed some rather daring (and risky) notions on the functioning of (western classical) music which have been fairly influential, especially since the French/Canadian so-called "semiological" enterprise got started. Nevertheless, this influence has been an "ideological", a "background-forming" one rather than a concrete and specific methodological influence, mainly because of the highly speculative and rather imprecise character of his ideas, which for more than a decade constituted something like the height of fashion in France and elsewhere. For a clear and adequate introduction to them, the anglosaxon reader may profitably consult, e.g., Ph. Pettit 1975.

In a first perspective he presents music and the modern novel as dividing between them the heritage of myth. Listening to music then becomes essentially an adventure, isomorphic (homologous) to some (?) "real life" adventure, but, in contrast to it, successfully completed (cf 1971, p. 589/90). We will have more to say about this in 4.4.7, and will refrain from going into it now.

In a second perspective (which is clearly related to the first) understanding myth, or music, is represented as essentially akin to the resolving of a homonymy, a pun (calembour); he adds that "this type of transformation constitutes the foundation of all semiology" (1971, p. 581). He talks then about "conjuring up in a word or sentence, as on a photographic negative, the other meaning (his italics) that, within a new logical context, the word or the sentence could also have" (ibid., our translation). This sounds somewhat like the key idea of our BivFs (cf, e.g., 2.5) and indeed, earlier in this book we have been looking into some reasonably pun-like cases (cf. 2.4.1, but also 2.3.2 and even 2.3.1); one might even be tempted to argue that UNLL processes generally should be classed as essentially based on homonymy, in some suitably extended sense of that term.

Now as to Lévi-Strauss' claim that such processes "constitute the foundation of all semiology", we do not feel very confident about it. Naturally, semiology is a rather ill-defined concept, but Saussure, who after all created the term, meant it to include, among other things, linguistics in all its current senses. And surely, puns do occur in natural speech, perhaps inevitably so; but to say that they constitute its foundation seems unwarranted, to say the least. Conversely, there is a large class of human activities that are clearly based on the resolving of homonymy, and which have, for as far as we know, not yet all of them been claimed by semiology as its objects: we refer to things like asking riddles, like puzzle and maze solving; to all sports involving tactics, and in a general way to all those contrived situations in which a secret is, or can be, discovered or disclosed, in most cases in a step by step manner; in short, to what we will call cognitive puzzles.

The relations between such cognitive puzzles and the phenomena called languages are complex, and partly open to conjecture. Thus it seems reasonable to think that cognitive puzzles have a decisive role to play in one's first learning of a natural language, and possibly also in its historical genesis [2]. Now clearly, not only do they not vanish with the acquisition of language (they do even, in a sense, in their turn parasitize on it) but they also remain with us in many non-verbal forms.

Philosophy has, up till now, mainly concentrated upon the allencompassing cognitive puzzle formed by "the world" as it is conceived of by scientific investigation. But cognitive puzzles are virtually omnipresent, and occur in all shapes and sizes. Humans propose them to each other in many forms, and they come in all degrees of complexity and subtlety. We will be defending the view that what we call art rightfully belongs to their kind, and thus, once again (cf 0.2.1, 0.2.2) have reason to reject the linguistic paradigm (as does, for partly parallel reasons, Pettit 1975).


The standard crossword puzzle may be said to be based on homonymy of (sequences of) letters with respect to words. There is only one solution, which may be found in part only. In the standard whodunit the plot is homonymic with respect to more than one way of solving the murder case. An essential difference with crosswords is that you do not know which pieces of evidence are relevant. (In crosswords you may have uncertain evidence, but its relevance is clear.) Another, and related, difference lies in that until the end, and in the (often arising) case of an unsatisfactory author's solution even after it, you can never claim to have solved even part of the puzzle. If you find the solution before the end, the story has failed you: its lasting ambiguity is essential to its charm. – And now for serious literature. A literary metaphor is understood in two ways. First one understands the sentence it occurs in: both tenor (comparé; see 2.4.2) and vehicle (comparant; ibid.) are identified. Second one understands the "reasons" for it (represented in Fig 19 by the letter e): the "effect" of the metaphor, those parts of the signifié of the comparant which it brings into contact with the signifié of the comparé. Now the first way of understanding is relatively easy to talk about; but trouble arises with the second, which is, in many cases, extremely difficult, if not downright impossible, to specify satisfactorily. Nevertheless, people do agree that many (nontrivial) metaphors "work", i.e. have a good effect. They seem to know what those metaphors do, without being very good at specifying it: if they try to, the irremediable slowness of their efforts, and the wrongness of emphasis produced already by that slowness alone, vitiate their attempts.

To sum up. The three cases reviewed here essentially differ in the "accountability" of their results. The standard crossword puzzle admits of definite partial results. The detective story does not; but its results are easily explained; discounting specific literary merits, purely as a whodunit, its solution could have been arrived at by different routes. This it has in common with the crossword puzzle. The literary metaphor, finally, seems to have its result determined precisely by its way of producing it, so much so that alternative routes (equivalent ways of describing its result) are not readily available.

However, this does not mean that it is not open to investigation. Useful partial insights may be gained into its workings, and specifically into our common understanding of them, by asking definite questions. Thus the fact that eagles reproduce by laying eggs is probably for most of us not relevant to the usefulness of the word "eagle" for /Napoleon/, whereas their power, their mercilessness, or the use of their images in heraldry might very well be.


Our taking cognitive puzzles rather than languages as a paradigm for art might suggest some questions to be answered. In the first place one might think of the relations obtaining between cognitive puzzles and UNLL processes. One might consider the two following questions: a) are there cognitive puzzles which do not give rise to UNLL processes? and b) are there UNLL processes which take place outside cognitive puzzle situations?

Question a).
Metaphors are obviously out (cf 2.4.2). Detective stories, with their emphasis on carefully laid false trails, surely give rise to UNLL. And even crossword puzzles, where words, first designated by their semantic content, are to be selected on the basis of specific letters occurring at specific places in their written form, involve UNLL. We will have to look somewhat further afield. The best we have been able to come up with is the following. If I am a spectator at a race, and I see two runners coming up and nearing the finish, their chances may be exactly even, for as far as I can see. I may then try to foresee what will happen, and thus propose myself a cognitive puzzle. But whoever wins, I cannot very convincingly say afterwards that I went through an UNLL process: I did not unlearn nor learn any concepts.

Some will say that, as cognitive puzzles go, the example hardly constitutes a central case [3]. Others might want to object that in such situations one's mind is operating in a definitely two-track manner: the two conflicting (and equiprobable) hypotheses: A wins, and: B wins, are entertained side by side; but then it is also true that one of them will have to be falsified. Now this falsification was, naturally, foreseen as a possibility, and had thus, in a sense, "been through" in imagination. My objector might now want to say that what happens involves an UNLL process, a very non-novel one, and weakened still by the fact that "on the other track of my mind" there is simple hypothesis confirmation. I do not know whether all this carries any conviction, and will leave the question open. After all, it all depends on the strength of the notion of puzzle you are prepared to endorse, and I wouldn't, off-hand, reject even such weak ones as those constituted by foreign language texts occurring in their native country, and that I would ask an interpreter to translate for me.

Question b).
All UNLL processes involve two interpretations, two "readings" of the same material (cf, for the more restricted case of our BivFs, 2.5.1), and thus essentially satisfy the condition of homonymy "in some suitably extended sense" (4.1.5). Now in order to prevent the whole world and everything that is in it from immediately acceding to the status of a cognitive puzzle we have in 4.1.5 also introduced contrivedness as a necessary condition. We might therefore try to look for UNLL processes taking place outside any contrived frame. However, our use of the word 'contrived' must certainly not be construed as requiring the presence of human artefacts (such as metaphors, whodunits and crosswords) nor that contriver and prospective problem solver always be separate persons. 'Contrived' will thus be, roughly, 'meant to be taken on by somebody (as a problem to be solved)'. Now if, totally by surprise and in no way "framed" by anybody else, I suddenly find myself in a situation which forces me to reorganize my conceptual apparatus, I still must, if I am not to reject the whole event as irretrievably ill-formed, take it on as a puzzle, propose it to myself as such. If our sense of the term "contrived" admits of such cases (as I think it must), question b) must be answered in the negative. On the other hand, non-novel UNLL processes might be handled, and thus "taken on" by my mind, in such a way that little or no conscious decision making is going on; but then the puzzles are old ones as well.

We thus see that there probably is a strong positive correlation between UNLL processes and cognitive puzzles. Especially it seems that all central enough UNLL processes may safely be described as occurring in cognitive puzzle situations.


Finally, current psychological theory (and introspection, for that matter) may lead us to expect a strong positive correlation between arousal and cognitive puzzles. These will, as a rule, give rise to interruption of cognitive "organized sequences" (cf Mandler ch 7 and 8) and therefore to arousal. But it entirely depends on the promptness with which they may be if not solved, at least thought to be amenable to solution, whether the emotion-felt be pleasurable or not.

4.2 A definition: its "only if" part


Making use of such specific properties of cognitive situations as are expressible by BivFs under our intended interpretation of them, we will now argue for the idea that those properties, and through them our BivFs, enable us to construct a useful definition of the way art users recognize art as such.


When I perceive something as being art, the sole applicability of the concept "art" sets that something apart from all instances which are non-art. I am understood to agree with other members of the same linguistic community that it is recognizable as such, that it involves a special way of perceiving it, of "reading" it. In this "understanding-something-as-art" the notion of convention plays a crucial role: if understanding involves, as we assume, the perceiving (construal) of law-likeness, the law-likeness, in this case, typically depends on conventional laws.

In 1.2.3 and 1.2.4 we have introduced convention as an essential element in the interpretation of the n.n. worlds in our models, and we have there linked up the logical properties of n.n. worlds with 1) the arbitrariness of all things true in them, and 2) the possibility that these arbitrary facts be used to interpret as law-like things true in other worlds which have access to them. Now this arbitrariness-cum-availability for lawconstruction is not enough to guarantee the conventionality, in a philosophically interesting sense, of the laws so construed. For that to be the case more is needed; what exactly is needed has been the subject of some controversy in the last few years, notably since David Lewis 1969. In this seminal book the author puts forward a theory of convention based on a simple gametheoretical idea: viz, that conventions are solutions of coordination problems: game analogues in which the interests of the participants are not pitted against each other, but in which the gain of each of them depends on all (or almost all) others gaining as well; he defines them as (cf 1969 p. 24) "situations of (1) interdependent decision by two or more agents in which (2) coincidence of interests predominates and in which (3) there are two or more proper coordination equilibria". (A proper coordination equilibruim is a combination of choices that, once implemented, each agent prefers to any other combination he could have reached, given the others' choices (p.22).) "We could also say (...) that they are situations in which, relative to some classification of actions, the agents have a common interest in all doing the same one of several alternative actions". A time-honoured example (it is from Hume's Treatise of Human Nature) is that of the rowers in a boat, who have to coordinate their actions in order to get anywhere at all.


Lewis' account of convention has been challenged by various philosophers. Not all attacks are equally serious – thus B. Rollin's idea (cf his 1976, p. 68) that, e.g., laying a wreath upon the grave of a dead soldier is not a case of interdependent decision, but an instance of "the behaviour of individuals acting in isolation" seems somewhat superficial, to say the least. More serious, but, according to us, still mistaken, is S. Schiffer's criticism (in his 1972) concerning the conventionality of language and meaning, a criticism that is simply taken over by W. Kummer 1975 (p.144). As the issue is of central importance to our enterprise, we will look into it somewhat more closely. At Schiffer's p. 151, we read:

"Conventions of meaning provide the best examples of conventions that are not solutions to coordination problems. (...) (H)ere one does what (...) one is expected to do to secure that a certain inference is made, not to secure that one co-ordinates one's action with the actions of certain other agents. What is common to a convention to drive on the left and a convention to utter x only when one means thereby that p is that in both cases one does what the convention prescribes because everyone expects everyone to do so, but the cases differ relevantly in the way that others' expectations serve as a reason for doing what one does: in the former case one does what others expect one to do in order to co-ordinate one's action with the actions of certain others, whereas in the latter case one does what is expected in order to secure that a certain inference is made in the surest possible way."

I think that Schiffer has a rather bewilderingly cavalier way of just positing x, and utterance, it seems, in some miraculous way available to some person, uttered by him, and thereby (?) present in the addressee's mind as a given from which a state of affairs may be inferred. This, I suggest, is quite unacceptable. Not only here, but in some other places as well (cf p. 153 top, p. 153) he seems to make the assumption (sometimes suggested by Lewis' own wording: cf, e.g., p. 180 of his 1969!) that conventional behaviour must be conscious, or at least open to introspection. Once brought to light, this assumption is seen to be quite unpalatable. Conventional behaviour, once learned and reinforced over time, in many cases (among which there is, quite conspicuously, that of verbal language), becomes automatic and in no need of conscious attention. It does not become any less conventional for all that. People who unthinkingly drive on the right (which is the case, to be sure, of the overwhelming majority) still conform to a convention. I think that this error on our authors' part is related to the crucial fact that they tend to forget that a convention, once established, represents a coordination problem solved, and not being solved.

What we want to get at is this. It may very well be the case that someone, in uttering x, and meaning thereby that p, acts as he does in order to secure that a certain inference is made in the surest way possible. But how are inferences made? On the basis of givens. How does the addressee come by his givens? Through understanding x. What does "understanding x" mean ? It means reconstructing x and mapping it into an interpretation, viz., p. Now this is an extremely complex, and almost totally unconscious piece of behaviour. And surely it constitutes a coordination problem solved. Speaker and hearer, utterer and addressee, coordinate their actions so as to produce the same mapping from syntax (utterance) into meaning [4]. It may be true that the actual behaviour of speaker and hearer (utterer and addressee) greatly differ, that producing a map and a sentence (utterance) is not at all like reconstructing them, one just cannot escape the fact that these two activities will have to be relevantly coordinated in order to make communication at all possible. We will therefore maintain that convention, in the full game-theoretical sense, governs essential parts of all linguistic and equally all culture-determined non-verbal meaning behaviour.


In order to make true also the last part of this claim we will have to come up with a suitable generalization of Lewis's "truthfulness-and-trust-in-L" convention (cf his 1969, pp. 148/9 and 177 ssqq; but also his 1975, passim, but notably pp. 7 ssqq: 1975 modifies some of the views contained in 1969, e.g., "truthfulness-in-L" is replaced by "truthfulnessand-trust-in-L"). We cast in that role the convention of C-traditionality, of traditionality with respect to cultural heritage C. Let us explore the way in which Lewis's "truthfulness-and-trust-in-L" convention is just a special case of our "C-traditionality" convention. We will assume that the language L is part of the cultural heritage C, and we take up again the three conditions quoted in 4.2.1. The coordination problem, as it was before it had been solved, can be described as follows.

  1. Participants are the members of a community evolving a cultural heritage, and a language as part of it. Their situation clearly was one of "interdependent decision", for
  2. their interest in coordinating their decisions was in effective communication, both by verbal and non-verbal behavioral regularities, and
  3. a great number of alternative coordination equilibria was open to them, not in the form of being untruthful/untrustingin-L, but in the form of being truthful/trusting in L', L'', ... etc.; and in the same way, not in the form of being non-traditional with respect to C, but in the form of being traditional with respect to C', C'', ... etc. Indeed, other communities can be observed to have evolved other cultural heritages, and other languages as part of them.

This generalization of Lewis' account of the conventionality of language enables us to achieve some substantial grip on the conventionality of art also. We begin by returning to music. Earlier (from 0.6.5 and 0.7.4 onwards; for the logical form of it, cf 1.1.1) we have said that we considered a musical behaviour as law-like iff it conformed to some precedent [5], and we have constructed our models accordingly. I think we can safely take this to be a necessary condition of musical perception, because once some auditory construct ("event heard") is classed as musical, it is within the class of possible musics that we must try to "place" it, that we must construe its lawlikeness.

Conforming to some precedent: this is one of the simplest ways in which a convention may get started (cf Lewis p. 36), and it is perhaps its natural way of growing well-established. Conforming to precedent consitutes the solution to a coordination problem: in trying to construe a music's law-likeness I am actively searching through my own musical past, my own set of possible musical behaviours, for a precedent to which it (or, if you prefer, the musician) may be conforming, and to which my reconstruction of it may conform in its turn. The musician, on the other hand, if he wishes himself to be understood in our sense, will have the task of looking through his set of possible musical behaviours (precedents) for one which he may expect to be (potentially) sharing with me.

To state in a somewhat more precise way the relevant parallel between verbal language behaviour and musical communication, we may say that what both speaker and hearer have to come up with in a coordinated fashion is the "same" map from syntax into semantical interpretation; whereas what musician and listener have to come up with in a coordinated fashion is the "same" map from musical event into precedent. Then, and only then, they identify in the same way the conventionality of the music, the perspective in which to "place" it.

I think that no really important problems are created by the possibility that our musician should be performing a pre-composed work, or that one should be listening to a recording, etc. Equally, we take it that the other arts, mutatis mutandis, give no problems here.


But our claim is stronger still. BivFs essentially involve the changing-over from one perspective of conventionality to another. And the second one incorporates a change exactly where the first one became untenable.

In Fig 32 we give a (purely notational) variant of Fig 9: the capital letters will serve, in the following pages, as labels for the argument-places to be filled, or, alternatively, as names for the precedents/conventions (or parts of them) that are being invoked.

[Fig. 32]
Fig 32

The essential thing is that my having to exchange my original perspective of conventionality (precedent) P for another (Q∧R), which is a reformulation of (part of) it in the sense that we must have P→(Q∧R), is not due to any strictly personal error of mine, but to a change of behaviour introduced by the artspecimen in question (as always, as I understand it). Then and only then can appropriate arguments be formulated for P, Q and R.

THEN: for an art behaviour incorporating a change can only be understood with respect to a precedent both acknowledging the change and allowing for it (viz., Q∧R). For it is reasonable to assume 1) that I consider the post-change art as still lawlike, and therefore have access to (know of) a precedent R; and 2) that I understand the change, in that I know of a possible pre-change way of listening which specifically differentiates the pre-change understanding from the post-change one, a way of listening, that is, involving a precedent Q∧R.

AND ONLY THEN: for if the change is not introduced by the art-specimen in question, but is entirely due to some "external" factor, I can never explain it by making use of a BivF's right column, which, in reinterpreting the past on a sounder basis, still explicitly attributes a change to the art-specimen itself (¬Q).

Our claim now is that at least all central cases of what we call art (i.e., as always, art as it is perceived) involve such changes of behaviour; in consequence we should look for cases which are clearly art but do not involve them.

First of all let us dispose of an easy one: the idea perhaps cropping up in some readers' minds that, e.g., paintings have no "beginning" and no "ending", no time elapsing between these points, and therefore no change occurring in them. Understanding a painting, just like any other piece of behaviour, takes place in time, draws upon our knowledge of precedents, and, we claim, in at least all central instances of pictorial art, gives rise to UNLL: incorporates some reformulation of (part of) the precedents.

Then, there is art without any originality. Let us note that precisely because it is without any originality, it repeats what other art specimens have done before it; and they must then be looked into: if the originals involved UNLL processes, so do their imitators, viz., the same ones, older now and more well-worn.

I think that our simplest, and clinching, argument is the following. Given the results of 4.2.3, we have it that processing art essentially differs from processing other information, in that I may be said to have understood, in a normal sense, my pen before me, if I have classed it as such, if I have recognized it; as regards its uniqueness, there is no further understanding it. In contrast, with an art specimen the processing characteristic of it only begins with the "mapping into precedent" specified in 4.2.3. Then either of two cases will occur. It may happen that the processing in question classes the art specimen as unique, and then it brings at least one decisive change with it; or it may happen that the processing, perhaps through being superficial, classes the art specimen as belonging to a certain group of such, which will then share the change they bring with respect to their common precedent(s).

Now imagine the case of no change at all. Then my processing would class the art specimen as belonging to a group of such, which in their turn would be not differentiated from any further precedent; in consequence, there would exist one and only one indefinitely reproduced specimen of art. Now this is clearly false, inconsistent with what I know to be the case. We will conclude therefore that the processing of any specimen of art involves UNLL as representable by BivFs in our intended interpretation of them. (Clearly, we disregard some uninteresting ways of identifying art as such which are wholly external to it, such as its occurring in a gilt frame, or in a museum, etc. Nevertheless, the gilt frame or the museum may become part of the specimen.)

I do not think that our claim is really very risky. Also, I would like to warn the reader against thinking too easily that we are dealing with a very specifically occidental and modern conception of art. If this were the case, our definition would still be interesting. But I do not believe it. Even extremely ritualized art, such as Japanese Gagaku music, makes use of (well-worn) musical UNLL processes; after all, no intelligent ritual will be above using some moderate and well-canalized arousal, and, as we have seen, the appropriate non-novel BivFs can provide it.

4.3 A definition: the "if" part


We will now investigate the claim that any object or event the understanding of which requires activities representable by BivFs in our interpretation of them actually is what is commonly called art. As this claim may seem more daring than the foregoing, we had better get a few caveats in at an early stage.

In the first place, we admit of art-forms that cannot easily be accomodated within the framework of well-established genres: so-called "happenings", to quote an example, are art. Second, our initial, and throughout our enterprise fundamental starting point is that we are interested in the perceiver's activity. Therefore, exactly in as far as the perceiver is the master of his own mental processes, he is able to permit arbitrary objects or events to suddenly achieve the status of "art"; he may transform into art (that is, for as long as he can keep it up) anything he pleases. Our definition thus also in no way prejudges on what is valuable, useful, or good art.


We will now review a number of cases in which a change-over is made from one perspective-of-understanding to a new one, cases of change being understood, in order to find out just how could possibly work the discriminatory power BivFs need for their role in our projected definition of art.

First let us take the case of a scientific theory being exchanged for a new one. Certain aspects of such cognitive restructuring are reflected in BivFs, notably the falsification of the first theory and the fact that the new theory must, in some sense, explain our adherence to the first up to a certain moment, viz., that of the falsification. But the conventional aspect specific to BivF situations is not found in the case of scientific theories, for in the case of a scientific theory being replaced by another, neither of them has in its past a moment in which certain things were true, in accordance with its laws, but nevertheless not law-like. A scientific theory asserts its truths as law-like for all cases which form the domain of the theory. The behaviour of nature is not conceived by science as conforming to precedent. Neither, I take it, is the behaviour of scientists. The naive view (and some others as well) considers it an essential part of scientific behaviour that it looks for some confirmation for theories beyond just falling in with colleagues. And even if scientists' behaviour were purely conventional, theory dynamics could not be successfully represented by BivFs. What would then have to be represented, would be something like the spectacle of scientists in the throes of theory dynamics. A more or less suddenly anomalous behaviour of some or all of them would arise. And precisely in as far as this behaviour would really seem anomalous, precisely in as far as I would be proved wrong in my previous understanding of scientists, the situation would represent a subcase of the more general one of errors corrected in convention-determined fields; it would, as we are now going to show, be impossible to formulate a suitable Q∧R precedent.


We now turn to the case of errors corrected within a convention-determined cognitive field. Suppose I am a very naive young man who always believed that when someone, say A, tapped his head with his forefinger, he meant thereby to praise me as a clever boy. Suppose that that is the gesture's meaning if it is executed on the side of the head; suppose further that when executed on the forehead the gesture means that I am an idiot. A always uses an intermediate region. Now some day I meet him again and again he comments on my intellectual powers by tapping his head. I would have read this gesture as I always did, but for the fact that he now audibly mutters: "What an idiot". Now, can a BivF serve to represent the cognitive framework of my revising of my ideas?

P may be something like: Someone's tapping his head where A does means he thinks the other clever. In that form, P gives rise, in my mind, to the convention-determined law □P, and this is seen to yield an acceptable left-hand BivF column. As for the right-hand column, my new and definitive interpretation of the gesture may fill the R place. But what to do about the Q place ? Using the same proposition as for P (and thereby making the BivF into a 2-place one) would yield a right-hand column in which, along with □R, before w12A, □P would still hold, which is clearly unacceptable. We need something new by way of Q, something which always held, up till the falsification of my idea that P. One might think of some decisive lack of effective communication with A, which is remedied just as P is found out to be false. But clearly, this faulty communication can never itself have been a conventional fact. It will not do. We will need something which, in conjunction with R, forms a convention, is falsified at w12A, and then permits □R to go on alone as a conventional law.

That is why, for Q, something like: If someone thinks another an idiot, he will not tell him so in his face, will not do either. Q∧R, in that case, is not the solution to a coordination problem. Q is, and R is, but Q∧R is not. This is because, clearly, the two coordination problems involved do not merge into one. For read R as: Someone's tapping his head where A does means he thinks the other an idiot. (I keep being naive, but this does not affect our argument.) This may be taken to represent a mapping from gesture into meaning which has to be produced in a coordinated fashion by utterer and addressee. The common end to be achieved is the transmission of certain ideas. Now Q is convention of a quite different sort: one which aims at mutual comfort and easy relations between humans, the solution to a coordination problem involving an indeterminate number of humans over time.

Now someone may say: let Q∧R represent the solution to A's problem of letting me know he thinks me an idiot without telling me so in my face. A tactful intimation, so to speak. I might, in some way, unconsciously expect this, and want the impact of the message to be cushioned. Do we then have one coordination problem between us ? If so, it is one to which A's actual behaviour ¬Q destroys the solution. (We must have ¬Q at w12A.) So we get, in our right column, a coordination problem not solved; and that is what right columns just do not admit of. They are designed precisely to show how coordination could have been successfully achieved: before w12A on the basis of Q∧R, after it on the basis of R.

It is clear that Q remains present in the situation as a separate problem, and simply refuses to "merge into" Q∧R. The reason for that is that R is a convention governing part of a semiotic system whereas Q is not.


Nevertheless, there are fields outside art where a change-over from one convention to another can be made and where the conventions actually are related as in BivFs (we are indebted to J.J.A. Mooij for this point). These are fields like, e.g., jurisprudence, or the quasi-improvised working out of constitutional law practice by creating new precedents on the basis of old ones, and so on.

Now, whereas in the foregoing example the BivF's row zero, the topmost one, displayed its discriminatory power, we will now see that also row 2, the bottom row, has its contribution to make. Consider, for example, the following case. Before March 1977, it had never occurred that a Dutch cabinet, after seeing its resignation accepted by the acting head-of-state, proceeded to dissolve the parliament. March 1977, this happened, and it has been, for as far as I know, taken in good part by almost all concerned. That is to say, notably, this created no conflict between cabinet and parliament: what happened was what the parliament itself wanted.

If now we write, for P: only a fully empowered cabinet can dissolve the parliament, for Q: the same thing as for P (the BivF then becomes a two-place one), and for R: in the case of a not fully empowered cabinet the parliament's will prevails, we obtain a suitably interrelated set of conventions.

Clearly, (1) the situation was one of interdependent decision. These jurisprudential cases are describable along the following general lines. Someone involved in it, as a rule someone in power, someone at the very top of the political or legal hierarchy, faces an unprecedented case. He sets himself the task of creating precedent. In view of that, he must act. That is why his situation is essentially analogous to that of the natural language speaker, as opposed to the hearer. Finding himself in an unprecedented situation, he has to do something analogous to inventing (part of a) language: filling a gap, risking a neologism – and he knows that his invention is intended to become part of the accepted common fund. This makes his situation a delicate one. He will have to weigh 1) the acceptability of his possible decisions for his contemporaries, 2) their use as precedents for the future, and 3) the judgment of his contemporaries with respect to 2).

Clearly, (2) coincidence of interest predominates. All people mentioned in the last paragraph are concerned with maintaining and suitably extending the system of conventions which not only fends off social chaos, but also safeguards their power.

Clearly, (3) there is more than one proper coordination equilibrium. Precisely, the situation is a delicate and ambiguous one. And just as the whole political, or legal, conventional system was once evolved as part of the culture's C-traditionality, forming the solution to a coordination problem, so now the point at issue, felt as it is to be a gap in the culture's political or legal conventional system, forms an unsolved coordination problem on its own. We are witnessing part of the culture's beginning.


The situation described does not belong to art; neither, we contend, is it adequately representable by a BivF, the abovementioned "suitable interrelatedness" of conventions notwithstanding. For consider the situation of the person perceiving it, and whose cognitive behaviour the BivF is supposed to describe. Two relevant cases arise. A: he is only a witness to the situation (being, say, an uninterested foreigner), and B: being, e.g., a dutch politician, he is a participant in the situation: his behaviour, be it action or inaction, counts in it.

We want to argue that in case A the BivF's w12 is no necessary condition for the solution of the coordination problem at hand; whereas in case B the state of affairs described by the whole BivF, including w12, is no sufficient condition for the solution of the coordination problem. For in case A the problem may well be solved without the person's understanding its solution, whereas in case B he might, after having perfectly well understood the proposed solution's claimed justification, still (try to) block it; for a course of action that leads to serious trouble may well lose its value as a precedent, and he might succeed in making such trouble.

A BivF is supposed to describe a coordination problem solved. But it describes only a way of (re)understanding a situation, and it is just that which has to be its subject's contribution to solving the problem involved in it. Therefore a coordination problem adequately represented by a BivF will not require overt action (or inaction, for that matter) on its subject's part, but it does require the way of understanding specified by it.

It may be wise to note in passing that the purely cognitive part of Mooij's political coordination problem does not, in itself, constitute a coordination problem in the Lewisian game-theoretical sense, for there is no independent mutual advantage to be gained for the parties involved in it. If they fail to reach practical agreement, any successful cognitive communication will have been to no avail for at least one of them.


Using BivFs for formalizing non-art situations turns out to be somewhat less easy than we might have thought at first. Let us for a moment reflect on this. What exactly are we going in for with BivFs?

You are understanding a situation by mapping it into some precedent P. It so happens that at a given moment this way of understanding breaks down because there is a change in the situation not allowed for by the precedent P it was up till then being successfully mapped into. The cognitive problem this poses is solved in the following way. Two interrelated new precedents are found, of which one (R) is simply unaffected by the change: it permits the situation before the change and the situation after the change to be mapped into it with equal ease. The other (Q∧R), like P, does not allow for the change; like P, explains the situation leading up to it; but unlike P, contains a proper part (R) which is in itself also a precedent, viz., one allowing for it, as specified above.

Why does this description constitute such a tall order to fill, outside art?

Take for instance the conventions regulating good manners. Infringements against them do occur. If they are understood, it is as a rule along the lines of some natural (i.c. psychological) law explanation. (Sometimes it happens that traditional art is naively understood as a form of good manners. Deviations then get an analogous treatment – with concomitant punishments added.) There do not seem to exist many fields where unconventional behaviour is easily re-thought as conventional. These fields must have been so structured as to have layer upon layer of interrelated different precedents ready to serve for understanding situations occurring in them. But, given that conventions, being solutions to coordination problems, have to be evolved, layers upon layers of interrelated different conventions must have taken much time and much coordinated special attention of people to have become at all available. Their existence is plausible only in specialized fields, where no practical constraints, such as in the simple case of Hume's rowers, operate on the genesis of conventions; special playgrounds, one should perhaps say, set apart from the harsh practicalities of life by the fences and hedges of "good manner"-like conventions of a practical nature (such as concert and museum rituals, the ritual linking of specific musics to specific moments (times of day or year, social occasions), etc. ...). This might go some way toward explaining the fact that parts of art itself, as remarked above, are sometimes understood as a form of good manners. For if we accept as true this picture of art as a field of layers upon layers of non-rigid conventionality (let nonrigid conventionality be conventionality infringements against which can be re-thought, and therefore understood, as conventional, but differently so) surrounded and isolated from the rest of life by a structure of rigid conventions (let rigid conventions be conventions infringements against which can only be understood as anti-social, otherwise pathological, or just stupid: i.e. along the lines of natural law), it would not only account for the possibility of (parts of) art fossilizing and becoming part of rigid conventional structures, but also for the possibility of art invading, as it were, the surrounding rigid structures, and annexing parts of them to itself – even if only temporarily, and with respect to certain art-forms only. Most interestingly, I suggest, it offers the means of describing more ritualized and less ritualized art-forms in one unified gamut of possibilities. Here again we may thus refuse to let Western art be separated in any trivial way from art practices in other cultures.


Even if we can make it plausible that the "homeland" of BivFs is art, we have not shown that they find no application outside that field. And I think there is some headway to be made to wards doing just that. Consider again the sort of understanding BivFs describe. It is a mapping into precedent. By the BivF description it is meant to break down at a given moment. I think that this is a very common risk we incur in using such a way of understanding things. I have to come up with an alternative. Now either the new precedent just " allows for " the change, and then it does not even mention any aspect relevant to it, or it describes some relevant aspect(s), and then the change has been re-described as a no-change. In either case the change has been annulled, so to speak. In either case my own (changing) cognitive behaviour has become, in the new perspective, uncomprehensible, unaccounted for. It is the elementary "Have I been stupid!" case, a very common one, and ruled out in BivFs by the Q∧R precedent.

Now the Q∧R precedent is proved wrong, just as the P one was. (At w12A we have ¬Q, and therefore ¬(Q∧R), just as we have there ¬P.) Nevertheless, from the vantage point of superior "post-change" knowledge I need to have it in the right column of my BivF. It is a way of being wrong I cannot do without in my alternative and "better" past. I would have been entirely right, I could not have been more right than by being wrong in that specific way.

Two comments impose themselves.

  1. Obviously, a world where being wrong is somehow superior to being right cannot be a world of immediate practical relevance. The information it imparts cannot be immediately related to things like human survival. Somehow that world is not the real one.
  2. If being wrong is somehow more adequate than being right, I ought to, indeed I must permit myself to be framed into being wrong. A world in which this is the right thing to do is a contrived world, an artificial one, a labyrinth in which taking a pre-programmed wrong turning is doing better than just unerringly hurrying through it. I think we may say with some confidence that such a world, contrived, conventional, devoid of immediate practical relevance, in which pre-programmed error is somehow the right thing, that such a world belongs to what we call art, and to no other field.


This completes what will, for the moment, have to do as our proposal for a definition of art. If it is leaky still, I hope subsequent discussion will pinpoint the leaks, so that we may look into the problem of whether and how to seal them. At any rate, something has been defined, call it *art*, and I think it is overwhelmingly clear that *art* is interestingly related to art. In a field of enquiry that has for so long been suffering from illdefinedness, that in itself constitutes a substantial gain.

Music, or *music*, we take it, may then be defined as a sub-field of art (*art*), viz., the one we process, wholly or in part, through our non-verbal auditory channels.

To sum up: we stake out the claim that *art* as we defined it ("we perceive something as *art* iff our perception of it can be adequately represented by one or more BivFs") actually is art and nothing else. Counterexamples thus regard the relation between *art* and art (*music* and music) – and, if successful, should teach us a lot both about the areas of their origin and about the art concept we in fact use.

4.4 Musical meaning revisited


It is now time for us to go back to this book's very first subject (cf 0.0), and to take up again the basic problem of musical meaning. This time we will be starting out from verbal language.


If you say to me; It's raining outside, that sentence may be said to be meaningful on two different levels. In the first place (granted that I "follow" your meaning) we come up with the same mapping of syntax into semantical interpretation: the same truth conditions of your sentence. In the second place (granted that I believe you and that your information is new to me) you have changed my cognitive relation to the world (cognitive in the sense of specifiable by my knowledge, beliefs, hopes, fears, etc. ... any propositional attitude may be involved). The first meaning is called semantical meaning, the second pragmatical meaning.

Now it is interesting to note that most people who maintain that music is meaningless contrast it with verbal language, report the absence of truth conditions for given musics, and rest their case. This is interesting because responsible philosophers who have investigated the concept of meaning and have consistently oriented themselves on the natural language use of the word, have always come up with pragmatical, and not purely semantical, definitions (for a survey of the literature, cf Schiffer 1972). I think this just goes to show that naive people have naive views about how verbal language does its work.

Consider the sentence: It is raining outside, occurring within a literary work. If I understand it, truth conditions are found: there is a mapping into semantics; but the sentence is not believed as the other one was: i.e. not about the real world, but about a fictional one. A special sort of restricted pragmatics is at issue. Still the story does not stop here. This is so because the full understanding of a literary work, be it a novel or a poem, has pragmatical relevance to my world view. This effect on my propositional attitudes with respect to the world is produced indirectly: no sentence of the text need be about it, and yet, somehow, the whole is (cf below, 4.4.3).


Consider sounds. Can truth conditions be associated with them in any systematic way? I think they can, if we relate the question to some person's, say A's, auditory competence: with respect to the conceptual system A has evolved for understanding sounds, the sound S carries true information iff the process/state of affairs A associates with it actually takes place/obtains. (What we have here is an analogue of Tarski's "truth-in-L".) I also think that we may safely assume that for most persons A and B who have grown up in the same sonic environment, and therefore have been "accultured" to some common soundscape (cf 0.6.3 note) these systems are, at least to a degree permitting effective communication between them, the same ones. Just as with the verbal sentences, the existence of "truth conditions" depends on the sound's (sentence's) being well-formed (within A's system (in L)) (cf 0.5.1). Therefore we may legitimately speak of sounds' syntax and semantics (cf also the Preface). – One important contrast between verbal sentences' truth conditions on the one hand and sounds' "truth conditions" on the other is that in some "conventional-natural" meaning spectrum (cf Bernard Rollin's important 1976) the former occur on the "conventional", the latter on the "natural" side.

Next, consider sound S occurring within music. (It may be the sound of middle C on an oboe in traditional music just as well as the sound of rain outside in some tape composition.) In the first place, it still has the same "truth conditions" as always. But, in the second place, its relevance, its pragmatical aspect, is changed. It is now "played", and part of an "act", just like the verbal sentence was in the literary work. In consequence it is now understood in a different way, we will say: within the framework of a different logic (cf Appendix I), viz., the one which, in our enterprise, has served as the BivF's underlying logic, and which reflects the "mapping into precedent" [6] our description of understanding art rests upon. It is thus taken to share this logic with the understanding of verbal sentences within literary art.


We now return to the way understanding art might possibly affect my notions of the world. Consider, e.g., the novel. Within a restricted perspective, a new novel, by making me reorganize my set of precedents for novels, may affect my notions of (propositional attitudes with respect to) that part of the world we may call the set of possible novels. (We permit ourselves to include in the world the set of all possibles (potentialities, virtualities, etc.): as such, they "are the case".) Now obviously, in a wider perspective, my set of possible novels ("stories") is bound up with my verbal (and non-verbal) notions of the world generally, and in this way my world view may be affected by reading some given novel.

Let us now see how far a parallel treatment of music will take us. All goes smoothly within the restricted perspective: obviously, a music can profoundly affect my set of possible precedents for music, and thereby my set of possible musics. But in what way (apart from being a part of it, that is) is my set of possible musics related to my notions of the world generally?


But how, for that matter, is my set of possible novels? It is not over-bold, we presume, to make the following two assumptions.

  1. At least part of all information on the world, be it verbal or not, can, in being processed, go through (parts of) channels (or combinations thereof) prepared in me by my previous novel reading activities.
  2. This possibility is directly related to the fact that, in reading novels and processing the fictional information they contain, I continuously draw upon both verbal and non-verbal knowledge derived from my experience of the world.

As the reader may recall, we already made for music an assumption parallel to assumption b), viz., in 0.6.4, where we introduced the term "sound comprehension", and described its intended meaning. (Sound comprehension concepts are concepts used in understanding music which I could have had at my disposal even without knowing any music – they therefore embody precisely that "experience of the world" we are talking about.) We now want to warn against certain preconceptions perhaps existing in some readers' minds, according to which the set of concepts usable in music should be, in some important sense, particularly limited in its range. In the first place, we have very little reliable knowledge about it. In the second place, what knowledge we have strongly suggests that it would be unwise to exclude from it even the prima facie most unlikely fields of human experience. Therefore, assuming that 1) all auditory concepts can become musical, and that 2) concepts of any kind can (in principle) be associated with auditory experiences, we will suggest that there are, in fact, no reasonable bounds anyone can impose on the range of concepts usable in processing music.

Moreover some of them are indeed important, and cover quite interesting areas of meaning-content. For example, whenever I hear music, whatever kind it is (including electronic music), I hear people doing things, and thus my notions of people and their possible actions (in all more or less "deep" senses of those terms) may be affected by it.

But the class of concepts used in music that provides perhaps the greatest number of links with other fields of human experience is, I take it, the class of abstractions: as we had it in 0.6.4, not only the totality of a sound, all its aspects taken together (which will, inevitably, lead us back to the "human activities" mentioned in the foregoing paragraph), but also some aspectts) of it on its (their) own may give rise to the use of a (possiblyj non-musical concept. Often these abstractions are expressed in metaphors, but presumably more often still they just remain unexpressed by listeners.

Let us, in order to ensure at least some practical grip, stick to the top of the iceberg, and concentrate on the class of metaphorical statements on music. Metaphorical discourse, in this case, is no mere ornament, no luxury; it is a matter of dire necessity. Talk on music often takes place on the uneasy boundary between non-verbal and verbal concepts, and forces our verbal system to emergency measures. Metaphors then occur as short cuts to verbalization.

In this context it is important to note that our distinction between verbal and non-verbal concepts is not meant to sharply separate them. Let a concept be a recognitional capacity. Then we will take a verbal concept to be one which, in being activated, has concomitant verbal activity matching it. A non-verbal concept is one for which this is not the case. The attributes "verbal" and "non-verbal" are thus seen not to characterize the concepts themselves, but their (normal) use. For it might well be possible to verbalize any concept; in practice, however, many of the concepts we daily use remain non-verbal in the sense just described. But these are philosophically deep waters. The issue appears in psychology and in philosophy in (or uncomfortably close behind) a variety of problems, such as the knowing that vs knowing how distinction (cf the psychologists' propositional vs procedural knowledge, e.g. in Anderson 1976 p. 117), the knowledge by description vs knowledge by acquaintance issue, certain problems surrounding proper names, those concerning the "language of thought", etc. Psycholinguistics ought to be able, in the future, to clarify at least the part the verbal vs non-verbal knowledge issue plays in (or behind) these problems.

For the moment, theories assigning to verbal language only a marginal role as compared to non-verbal knowledge are just as difficult to disprove as theories doing the exact opposite. It seems wise to assume neither to be marginal with respect to the other, and, most of all, to stress their enduring interrelatedness.

Therefore, if our understanding of music, in principle, starts out from non-verbal concepts [7], this does not mean that (possibly) verbal concepts have no role to play in it.

Metaphors on music may tell us still more. To most people, they do not come easily, and if they come, they are felt to be very risky. The precision and complexity of music prohibit any easy isolation of one of its aspects. Musical understanding organizes concepts to form complex conceptual structures which are lost in the metaphor, but which remain foremost in the mind. This very strength, richness and precision of musical conceptualization make it plausible that also assumption a) above has its parallel for music: just as novels do, music may prepare in me specific channels, (parts of) which (or combination thereof) can be used in processing incoming information on the world generally, be it verbal or not.

Let us probe this matter somewhat further.


The suggestion of the foregoing paragraph has been that combinations of concepts arising in the understanding of some music may come to compete with combinations of concepts produced by a metaphor, and that we might therefore be tempted to say, somewhat loosely, that some music and some metaphor may come to cover, albeit in different ways, the same field. Happily, the theory of metaphor has been rather better studied than the theory of music – but then, many subjects are – and therefore we will now turn to it, in order to try and find out just how metaphors are about the things they are about.

J.J.A. Mooij 1976 is a well-informed and eminently sensible book specifically centered upon the problem of metaphors and their reference. Obviously, the "about-ness" of metaphors can be mediated, as it were, by neighbouring non-metaphorical descriptive words. But on p. 24 the author touches upon the special case of larger, and even independent, bodies of sentences which are wholly metaphorical:

p. 24: "(...) a series of two or three sentences can be metaphorical, at least in the sense that all or nearly all of their specific descriptive words are metaphorical. But what about larger (and even independent) bodies of sentences? It all depends on how to specify the notion of "aboutness" if larger units of text are involved. For instance, if one should wish to say that a certain literary work is about what normally would be called its symbolical content (or, that the symbolical content determines its subject), then this work would be wholly metaphorical in the above sense. (...)"

Mooij is somewhat reluctant to admit this possibility:

p. 25: "(...) I, for one, would be less inclined to consider the symbolical content to be the subject-matter of a piece of discourse, according as this symbolical content is more ambiguous (and ambiguous it often is!) and according as more sentences are involved. But there certainly is room for discussion."

Availing ourselves of this room for discussion, we will examine why it is so unsatisfactory to admit that, e.g., Kafka's Castle just is about someone arriving late at night at a village buried in snow, etc. etc. ...

A comparison with proverb-like metaphors (cf Mooij p. 172/8) is instructive here.

p. 128: "Proverb-like metaphors can be marked off from some other types of metaphor by the fact that a literal interpretation of all the worlds in the sentence will not result in nonsense. It is only the larger context or the nonlinguistic situation, or even general considerations as to what, in any case, may (and may not) be said, that makes it clear that the purely literal interpretation will not do, and that most of the descriptive words in the sentence have to be interpreted metaphorically. Consequently, they resemble a class of proverbs of which "As a tree falls so must it lie" and " greatest barkers bite not sorest" are examples; for if all the words in such proverbs are interpreted literally, this will not result in an impossible reading, though it will not lead to an adequate interpretation of the sentence. But, as I have argued above, it will not do either to eliminate from proverb-like metaphors the reference to the literal extension altogether."

Proverb-like metaphors are identified as metaphors because of the wider and possible even non-linguistic context in which they occur. One who would try to understand such a sentence, reconstruct the speaker's meaning, and restrict himself to the literal sense' would be forced to think: yes, that might well be true; but why on earth should he be saying it?. In our terms, he would then again have to search through the class of concepts mobilized by it, in order to find more general ones which could perhaps apply to the given situation also; and he might be forced to enlarge that class.

Parallel to proverb-like metaphors we can construe cases like Kafka's Castle. There also, the reader may say to himself: yes, all those things about someone arriving late at night, etc. etc. ... they do form a story; but why on earth should the writer have told it? Important contextual clues as to the non-triviality of the author's meaning might be, e.g., the high standard of writing, knowledge from other sources, etc. The reader would then have to identify, within the class of concepts used in understanding the book, such more general items as: being excluded from a community, and/or: the functioning of bureaucratic power-structures, and so on; the network of all these concepts as they interrelate in the book could then be taken to be something the book is also about.

Nevertheless, it will not do to say that a book is about all concepts the reader uses in understanding it. In the first place, in reading Kafka I use concepts enabling me to identify printed letters; but the book is not about them. Let us therefore also stipulate that the concepts the book is "about" be affected, or changed, by it. In the second place, the natural language use of "about" relates it to things like books and not to readers. One might therefore propose to define, on the basis of the book, a class of readers who are just able to follow it: then, if we take for example a book on some mathematical subject, the thing the book "is about" is seen to correlate with the set of concepts used and changed in that class of readers. Now, for literature, it is best to take the whole literature-reading community as the intended class of readers. Then, one could propose the Castle to be "about" all things it uses-and-changes the concepts of in the class of its readers. Here again, as in 0.6.2, some consensus condition may come in useful.

Now as an account of "aboutness" this may have some limited virtue [8], but it can never claim to reflect natural language use of the word "about". No account along these lines can, for, in a dishearteningly trivial way, natural language refuses to speak about specific non-verbal concepts: it just hasn't got the means. I do not think we need any other explanation for the fact that we do not say that a piece of music is about anything. But it is a relatively uninteresting explanation, and the fact explained by it might be, in that sense, uninteresting as well.

More interesting, in our view, is the possibility of generalizing our concept of "about-ness" from books to paintings, musics and the like. For then, if we also accept the conclusions reached in 4.2.4, it becomes plausible to say that assumption a) above (4.4.4) is actually entailed by assumption b), so that both assumptions would have to be made for novels and musics alike.

Part of assumption a) for music is relatively trivial: the part concerning the understanding of music itself: it will always be influenced by earlier musical experiences. But, given our stance on "sound comprehension", assumption a) also claims that previous musics, in having also been "about" many things not only musical, may co-determine the processing of incoming information of a non-musical nature.


In this way, the meaning of a work of art is seen to be a pragmatical meaning, just as we already claimed in 0.0.2 and 0.0.3. Semantical meaning has its role to play in the production of this pragmatical meaning, but it is, in the case of music as in the case of verbal arts, only through the pragmatical meaning that it comes to function at all with respect to the world. It is now also seen that BivFs, precisely because they aim at capturing processes of conceptual change, must be taken to reflect a work of art's meaning as well as the emotion it may give rise to (cf 4.1.3). Networks like the Fig 30 one thus become a work of art's" pragmatical map", and reflect what it may do to one. Also, L.B. Meyer's views on the interrelatedness of understanding and emotion are vindicated.

For these reasons, we will propose to describe art perception situations no longer as a subset of the situations schematizable by the traditional

sender ------> message --------> receiver

schema, but as a subset of the situations represented by

cognitive puzzle -----> cognitive puzzle -------> cognitive puzzle
designer                ________________          solver

and, clearly, we have replaced an essentially semantical approach by a pragmatical one: after all, even if the meaning of messages can, at least in part, be specified by truth conditions, this is simply not the case for puzzles.


We are now in a better position to assess Lévi-Strauss' intuition concerning the music – real life adventure homology we first mentioned in 4.1.5.

In the first place we will allow that understanding a music, in itself, constitutes a real life adventure successfully completed, as any solving of a cognitive puzzle would be. But this is clearly too trivial for him.

In the second place we will specifically allow that the understanding of a music makes use of concepts, of knowledge derived from past experience – that, e.g., a given melodic profile, in being understood, vvill borrow the structures I assign to it from my own (musical and non-musical) past experience. But this is still not what he means.

What he means we are not going to allow.

(1971, p. 589/90, our translation:) "(...) And if, at the end, tears of joy flow, it is because this adventure, wholly lived through in a much shorter time than any possible real life adventure, has been successfully completed as well and thus ends in a bliss real life adventures seldom have to offer. (...) (The) musical work provides (...) a matrix of relations which filters and organizes lived experience, substitutes itself for lived experience and produces the pleasurable illusion that contradictions can be overcome and difficulties resolved."

What he means is that music, availing itself of the very stuff of life, produces a substitute for it, creates an illusion of success, and that this explains our delight in listening to it.

I think this constitutes something uncomfortably like a pornographic view of music. The user of pornography employs such reading matter in the general strategy of his life as a means to help him attain a self-induced "illusion" leading up to the sexual stimulation he needs. It will be generally impossible for him to integrate the "world of possibles" provided by pornography into the fabric of his life-at-large. That is why one has a right to talk here of an "illusion" of sorts.

Factory girls at seven o'clock in the morning, having to ride for twenty minutes in a bus to their work, which will occupy them all day long with the task of packing sweets in plastic bags, may also need, at that hour in the morning, some sort of reading matter about strong and powerful doctors and their nurses, about high life, the aristocracy, successful artists, and so on. Some sort of self-induced "illusion", forming part of their general strategy for staying alive, may be at issue here. Integration of the worlds they read about into the fabric of their life is at best problematic.

Now, I take it that the more one is able to realize that integration of the world of possibles presented in a book into the fabric of one's life, the less any one has a right to speak of an illusion. Possibles are, as such, part of the world. And I think there is a sort of gamut of literary products, ranging from pornography at one end to, say,serious literature on the other, of which the satisfactory use requires, at one end, self-induced "illusion" states, and at the other end, no illusion at all, but simply the construal and exploration of possibles.

There is no reason to conceive of music as a form of pornography. Our theory seems, on the other hand, quite capable of explaining, in an interesting sense, that Lévi-Strauss should have had the ideas he has had each of them can be traced back to something real and important on our account; but it does not vindicate them. Music, as we see it, is something real, and is "about" real things, according as I am at all able to integrate it into the fabric of my cognitive life. That it should be so satisfying can be explained by invoking pleasant facts. Music does not impose any illusions; as we described it, it provides knowledge of (know-how with respect to) the world.

His interest in interpreting music as one of the "heirs of myth" has led Lévi-Strauss to the interpretation of music as a metaphor of sorts. Given the variegatedness of theory on metaphors this is probably a defensible viewpoint; at any rate it will not be easy to disprove. But it is distressing to see that the metaphor's "tenor" really should be nothing but a story – and a story with a happy end at that [9].

4.5 Theoretical status of our enterprise


In the different sections of this chapter we have been freely availing ourselves of a number of claims central to our theory of music, and the disceming reader may have noticed, here and there, that we added to them from what we took to be the stock of generally available knowledge. In such a way, a theory may find applications. These may be important theoretically, in that they may take the form of explanations, and thus be booked on the theory's credit side, or in that they give rise to predictions, and thus, possibly, to experiments. We will now briefly look into the confirmation/falsification problem we face.


Even where a theory has as yet predicted no specific thing, and so does not yet incur the risk of falsification through experiments, it can rationally be reflected upon, viz., by comparing it to competing theories. One may then compare their "costs", expressible in the theory-specific assumptions each has to make which are not made by the others, and one may compare the "returns" they bring in, by comparing their explanatory powers: by taking stock of the facts explained by each which are left unexplained by the others.

Our theory does fairly well at this test; however, this is a rather trivial fact because of the theoretical deficiency of competing approaches. It is even difficult sometimes to find out in what way exactly they are competing. In many respects, our theory just is the only one, which is a sad but essentially honourable way of being the best. (The worst theory is always no theory, because for every fact to be explained it has to make a special assumption. Because it cannot recognize any facts, this is trivial; but it is true all the same.)

Let us now work our way through some relevant cases.


In many respects, Meyer 1956's theory is not a competing theory, because so much of it is incorporated in ours. Our Bivalence Function could be described as a formalization/specification/generalization of some key ideas contained in his book. His Gestaltist vocabulary has been dropped. This was only to be expected: in psychology also, the "cognitive psychology" approach has become, in a sense, the natural heir of Gestalt theory (cf Hilgard & Bower 1975 p. 280). It is to be hoped that such new departures in philosophy as Eliott Sober's 1975 (Simplicity) will help elucidate what was behind Gestalt ideas. In that form, our theory easily accommodates them.

Our treatment of both emotion and meaning is, for particular cases, more specific, and, thanks to the generalizing power of BivFs, at the same time more general than his. Thus nothing prevents motor and image concepts, connotations and moods, just as the so-called "biological" aspects mentioned in Ruwet 1975 (p. 33), before which also current brands of structuralism, on their own admission, remain powerless, from occurring in columns of Fig 30-like networks, and entering into logical relationships with each other and with other concepts to form compound formulas (complex concepts). In this way they are not only integrated into networks on an equal footing with traditionally more accessible concepts, but they will also become better defined, viz., in terms of these. Thus it certainly makes sense to admit statements like the following:

(This music is "like marching") (it is characterized by rhythmic periodicity)
(This Schubert piece is "sad") (it has the characteristics specified in Scruton 1974 p. 123/4)

etcetera [10].

Thus, with few assumptions more, and even some dropped, we explain many more facts than Meyer 1956 could.


Moreover, all conventionalized meanings, such as often studied in ethnomusicological research, are easily accomodated within our networks. As Bernard Rollin 1976 has, I think, convincingly shown, tne conventional-natural distinction for meaning, however valid as a distinction, does not imply the separation of conventional and natural meaning cases into two isolated categories.

The verbalism-centered semantical research of Francès and Imberty (cf 0.2.0) remains innocent of all general theorizing about music: it offers no competition. Conversely, however, I think that their type of research could gain immensely in (musical) scope and precision by adopting pragmatical maps as proposed here.


Nattiez must have a lot of theory somewhere – but I have been utterly unable to dig it up from between the cluttered-up 448 pages of his 1975. (One specimen of his theorizing: he defines meaning as follows (p. 158, my translation): "Something takes on meaning, for someone perceiving it, if (! J.K.) it becomes related to the lived experience of his past" (– how on earth could he even perceive it, if it did not?? .. J.K.) "More pithily, one may say that there is meaning whenever an object is related to a horizon" ... Etc.) On the other hand, essential parts of the Ruwet-Nattiez analytic practice receive some justification from our theory.

I take it that the "generative" theory of music is the only seriously competing one. For it is a theory on semantics, and it tries to explain facts of comprehension of and communication through music. Ruwet, when assessing theories about music along Popperian lines, explicitly recommends it in his 1975.

The two theories are really at odds. Ours makes a crucial assumption that the generative theory does not make, viz., that of the Bivalence Function. The generative theory makes a crucial assumption that ours does not make, viz., that of the applicability of linguistic theory on music. We say that that assumption in unwarrantable. As argued throughout Ph. Pettit 1975, it introduces into musical theory the idea of well-formedness, as definable by a finite set of rules, and it is thus syntax-centered (cf 0.0.2 note, and 0.5.1 note). Generative theory tries to find out the conditions of a music's being "right".

In our terms, this would mean: a music's being "recognizable for what it is", a Fig 21-like cognitive situation. It is now interesting to note that our theory enables us to explain the triviality (witness Ruwet 1975 p. 17) of the musics studied by generativists (Tegnèr's nursery tunes!) and to predict that no non-trivial musics can ever be successfully tackled by them (cf above, 0.2.2). For if generativists are interested in (in our terms) only Fig 21-like situations, it is something like Muzak they are interested in (cf Fig 31). If they take on Mozart, it is Mozart reduced to Muzak. I, for one, have still no complete competence with respect to Mozart, and I should like to meet the guy who has. I am still learning (UNLL) Mozart.

Our theory has it that understanding music consists in insight-based learning-processes (re)occurring. There is no point of closure of any musical competence. What the generativists study is – if it is at all there to be studied – a music amputated of its central portion, which is the learning of it; that is what makes it at home in the central parts of our consciousness; that is what gives it its emotional presence, and its capacity to evolve under our eyes (which a natural language, in principle, cannot (cf 4.6.0)). What generativists study would have to be Muzak, were it not that this is obviously a late by-product, a bastard offshoot of music itself, and characteristically dependent on it.

I take it that the generativist, unrepentant,will say that this is just as it should be. For he must refuse to distinguish between music and Muzak. Those facts-to-be-explained which determine the difference in interest separating music from Muzak and for which our theory offers a general explanation plus the framework of a special one for each specific music, all aesthetical and emotional facts the generativist must leave unexplained. Conversely, I know of no facts explained by the generativist that our theory would remain powerless to tackle.


Many assumptions our theory makes are not specific to it – they are borrowed from standard cognitive psychology. In that way, our theory already profits from whatever confirmation has been experimentally gathered for cognitive theories in general. It is also seen that the relation musical generativism – linguistic generativism is fundamentally different from the relation between music theory – general perception theory. In the latter case, the more general theory already existed in its own right when we specified our theory within its framework, whereas in the former case the more general theory (the Saussurian "sémiologie générale") is only postulated with a view to accomodating within it both linguistics and its twin, the "generative" brand of theoretical musicology. It thus cannot bring with it any constraints, nor any confirmation either. Indeed, it is hard to see what constraints general semiological theorizing, such as presented in, e.g., L.J. Prieto 1972, can bring to bear on music that ordinary perception theory does not bring with it also. Ordinary perception theory is clearly the more basic one. The generativists' main fault is, we believe, in the fact that they behave as if linguistics itself were the more general theory – as if Saussurian "general semiology" and linguistics were, by and large, the same theory.


Clearly, the confirmation derived from our adherence to established cognitive psychology is not enough. Our theory must itself be open to falsification by experiments. The crucial problem is how to find ways of making observable the listener's behaviour, if possible without the detour via verbal language. Ideally, activities ought to be captured and recorded in protocols. Laske 1977 proposes to do that by defining a compositional task, and letting his test subject work away at it. This involves, in his use of BivFs, some rather drastic reinterpretation of, e.g., the nn worlds.

If, as we did in 0.3.0, we define the composer as the designer of the listening situation, an adequate modeling of his activity is apt to turn out rather more complicated than that of the listener's. But at the same time, there is an obvious, and presumably in many ways rigid, link between the two. Also, I believe it will be possible to use possible worlds models to integrate the activity to be designed, the listener's, within the designer's, the composer's. Especially the different modelings of counterfactual logics (cf Lewis 1973, Åqvist 1973, Segerberg 1973) and those of deontic logics (cf Hilpinen 1970, von Wright 1972) may admit of such use. But there is still much theoretical work to be done here. When it has been done, however, it may be experimentally tested on composers, and it may even allow for verbal and non-verbal testing-procedures being used in parallel.


The best short term chances our theory has to be tested are via some micro-theory defined within its frame; a micro-theory that could,e.g., be the theory of some definite piece, of which different versions could be made to order. Predictions concerning the listeners' to be elicited overt behaviour could then be made, and tested upon a group of them, on more than one group if possible, where each of the groups ought to be in some way independently defined for its musical "background" (here is where sociomusicology could profitably be "plugged in" into our enterprise, as it would seem, to mutual profit; for it might then itself become somewhat more precise musically than it is nowadays). This last setup would specifically enable us to do justice to the essentially genetic character of our theory, according to which understanding music is going through a learning process.

4.6 Rationale


Indeed, in all theorizing, criticizing and testing it ought always to be borne in mind that the sort of competence we are dealing with is not a simple sign-interpreting competence. Our central contention is that humans can communicate not only by signs and languages made up by them, but also by puzzles (cf 4.1.5 and following sections) occurring in the messages they exchange. Puzzle-solving competence is then to be defined quite apart from sign-reading competence, but presupposing it. A puzzle many times solved wears out, and may collapse into the language (as metaphors are apt to do in verbal language). It then becomes a simple sign (cf Fig 21), and we may come to "read" it unconsciously (consciousness, in its trouble-shooting role, is not needed; cf Claparède's "law of awareness" (Mandler p. 171)). It has become unproblematically well-formed.

Art, as we describe it, characteristically demands conscious attention: it is essentially marked by the occurring in it of puzzles, of ill-formed elements which, in a different and to be construed new perspective, or, if you prefer, on a (well-defined) "higher" level, become well-formed. That is the process of understanding it, and its being a conscious process brings the problem of freedom and human responsibility to the foreground. We are responsible for our art as we never are for our natural languages.

From the very beginning of my life, when I first learned to understand my mother playfully making a face at me, to the most sophisticated and "difficult" art-forms available in my adult life, I am undergoing continual and pleasurable training in puzzle solving behaviour, in adequate cognitive coping with the world. Making that possible in an intelligent, appropriate way, in such a way that commmunication goes on in and through it, communication such that all those engaged in it may take full responsibility for it, that is the business of art.