Jos Kunst home page: Nederlands | English
by Jos Kunst (1978)
| << 1: Preface, Summary, etc. | Contents | 3: Some mathematical aspects >> |
We will begin by proposing something in the way of a Gedankenexperiment, to which we will be referring in the future as our "stairs" example, and which is meant to serve as a non-musical paradigm exemplifying a number of interesting and essential aspects of musical communication.
The story runs as follows. Suppose that you and I are going down a flight of stairs. Suddenly I stumble and
threaten to fall. You get hold of my coat, but, in trying to stabilize me, you almost lose your own balance, which
I, in my turn getting hold of you, am able to restore. We reach the bottom of the stairs in safety, but at the same
time rather shaken.
We will now want to proceed in two steps: in the first step (0.0.2) we will show that certain activities mentioned in episodes (A) and (B) of our "stairs" example are laden with meaning, in a well-defined and philosophically respectable sense of that term, and in the second step (0.0.3) we will work out in what way this meaning aspect carries over into the parallel case of musical communication.
Your mimicking a stumble in (A), and our exchanging smiles in (B) may both be said to qualify as meaningful, in the sense of Schiffer 1972. In this book the author works out the concept of what he calls "S-meaning", claimed by him to be logically prior to all other semantic notions (pp. 6,7), and assimilable to the notion of "a person's meaning something by doing something". Perhaps the most important single ingredient used by him in concocting his definition of S-meaning is that of "mutual knowledge*", a concept originating with him, and introduced in his book by the following concrete example (p.31): "Suppose that you and I are dining together and that we are seated across from one another and that on the table between us is a rather conspicuous candle. We would therefore be in a situation in which I am facing the candle and you, and you are facing the candle and me. (...) I submit that were this situation realized, you and I would mutually know* that there is a candle on the table."
The relevant ingredients of the situation meant, those which make up the "mutual knowledge*", are the following. We are both of us supposed to be "normal" people. Then (1a) I know, and (1b) you know that there is a candle on the table. Furthermore, (2a) I know that you know, and (2b) you know that I know that there is a candle on the table. Moreover, (3a) I know that 2b, and (3b) you know that 2a. Next, (4a) I know that 3b, and (4b) you know that 3a. And so on, indefinitely. (The infinitistic character of this definition is not crucial to our enterprise; and not even, we take it, to Schiffer's own: in practice, he only needs the (finite) number of steps that guarantees the elimination of certain counterexamples to his definition of the S-meaning. But he himself regards the regress as harmless; cf. his p. 32 ssqq.)
He argues that this is a "very common, ordinary feature of our everyday life, one which has to do with interpersonal knowledge, and which (is) a necessary condition for performing (any) act of communication (...)" (p.30). In fact it would seem that it is what in ordinary language can be referred to as a consciously shared knowledge; it will therefore, and of necessity, be involved in any consciously shared understanding.
So far so good. Now, Schiffer's definiens for meaning (S-meaning) is instantiated whenever a PERSON performs an ACTION intending thereby to realize a STATE OF AFFAIRS having the following properties:
(Warning: Our rendering of Schiffer's definition is relatively pedestrian and untechnical, but, I think, essentially adequate, and rather easier to read than his. Interested readers are referred to his pages 63 and foregoing ones (notably 62, 57, 53) for full philosophical paraphernalia.)
We now need to show how our "stairs" example satisfies the definition, for episodes (A) and (B). In case (A) the PERSON is you, and I am mentioned in clause 1), 3) and 4) as "some other person", and the "audience", respectively. In case (B) we are both cast in both roles. The ACTION is in case (A) the mock stumble, in case (B) the smile with its implied pointing at the screen. All this is straightforward. Now for the various properties of the STATE OF AFFAIRS as it is intended to be by the PERSON:
I think that no one will have serious problems with our claim that such elements in (A) and (B) as we have been talking about do effectively carry meaning. But we have also claimed (0.0.1) that our "stairs" example can be made to correspond in an interesting way to musical communication. Let us now see how this can be done.
The reader will have guessed that I have deliberately tailored my "stairs" example to fit the parallel with musical communication I had in mind. First of all, no use is made of words, or of signs which could be explained as essentially encoding words. Nevertheless reference is made to things not present. For that to be at all possible three fundamental requirements must be met.
It may be interesting to note in passing that the use of verbal language can be construed as a special case within the framework outlined here. Words are then taken to be "artificial" objects arbitrarily assignable to (aspects of) situations, and becoming in that way themselves elements of those situations. They are easily produced; they are possible (parts of) utterances (e.g. verbal sentences) which carry meaning; taken separately (and not forming on their own a complete utterance) they remain (pragmatically) meaningless. The special use of words is thus seen to lie in the fact that they so readily function as elements common to past and present situations.
Now for musical communication. Two cases are distinguished, corresponding to episodes (A) and (B) respectively. To (A) corresponds the communication between musician and listener(s); to (B) that between listeners. We will take these cases in turn.
Discharging the onus of proof, as mentioned above, will be beyond the scope of the present book. But certainly it can begin to work its way toward that goal, by providing conceptual clarity, and even establishing some sort of prima facie plausibility. In order to accomplish that, we will begin by taking stock of that part of the musicological literature that has been concerned with the theoretical problem of musical meaning.
Easily the most influential older writer on the subject is L.B. Meyer,whose Emotion and Meaning in Music (1956) even if it has not secured the whole-hearted approval of all musicologists and musicians, has, up till now, not been provided with equally authoritative and successful rival theories. (The semiological enterprise (cf. Musique en Jeu), however authoritatively presented, seems, by rather disturbing lack of success, to have ground to a sort of halt. We will get back to it later, 0.2.2.)
One of Meyer's chief qualities, according to the present writer, is the way in which he refuses to separate, in his theorizing, emotion from understanding. On our part, we will want to incorporate into our theory, however different from his it may turn out to be, the equivalents of those aspects of his work which have proved to be fruitful. Nevertheless, we conjecture that readers will be more sensible to the differences between the two approaches; and they are notable indeed.
Thus, to tackle first the two key words making up the title of his book, we think that the word emotion is used by him in a sense that, if compared with the current ordinary language use of the term with respect to music, is severely restricted in at least two important ways. Firstly, it is too easily equated by him to what he calls affect. By that term he designates the only linearly (only its strength varies) differentiated feeling-tone which is "aroused when a tendency to respond is arrested or inhibited" (see, e.g., p.12, p.14). Having thus reduced emotion to a linear thing, he readmits qualitative differentiation in two ways: in the musical material arousing the feeling-tone, and in the aspects relegated by him to a separate chapter at the end of the book: image processes, connotations and moods. (Relatively undifferentiated again with him are "motor responses", as he has them, also treated separately (end of chapter II).) Now in discussing the numerous musical excerpts throughout his book he constantly refers to possible emotions in terms of tension and release, produces in that way the impression that he is everywhere concerned with emotional content, and manages at the same time to be absolutely unspecific about it. Compared to the ordinary use of the term "emotion" this certainly constitutes an impoverishment. Precision is obtained at too high a price, and, worse, trivialized: "affect" never was a very imprecise notion. One is sometimes tempted to think of someone judging all literature by thriller standards. To be sure, these standards do apply, but they have their limitations.
Secondly, he limits himself to intra-musical relationships, and fails to cope in any reasonably integrated (i.e. other than purely ad hoc) way with the more elementary links that music has with non-music. That is why there is that odd mixed bag at the end of his book (Chapter VIII: Note on Image Processes, Connotations and Moods), just as there are at the end of the purely theoretical part some three or four pages (79-82) under a separate subtitle "Motor Attitudes and Motor Responses". On our part, we think that any theory about how music works and what it does ought to offer at least the theoretical possibility of integrating into one semantic field all those variegated, or perhaps not so variegated, vital and elementary aspects, in such a way that some account may be offered of what any listener so easily does in listening, viz., linking them up with so-called intra-musical relations.
Over to the other key word contained in the title of Meyer's book: meaning. He offers (p. 35) the following description of musical meaning: "(...) what a musical stimulus or a series of stimuli indicate and point to are not extramusical concepts and objects but other musical events which are about to happen. That is, one musical event (be it a tone, a phrase, or a whole section) has meaning because it points to and makes us expect another musical event". To restate in other words one aspect of this description: musical objects, in as far as they are meaningful, refer to other musical objects not yet realized. This clearly is a sense of "meaning" heavily fraught with pragmatical aspects: in order to know what a given musical object means I have to know the past of the given music (its "background", as Meyer has it), the musical laws that obtain in it, and I must take on to extrapolate that past into the future. No wonder that I will be often wrong, as Meyer's examples abundantly show, and precisely my being wrong constitutes for him something like the essence of musical effectiveness: from it come affect and release, and, as we saw, they are at the core of his theory. Thus, if I listen to a piece of music for the second time, the meanings of the musical objects contained in it may have changed rather drastically.
Now there may be nothing very fundamentally wrong with that view, except that it leaves just too many things unaccounted for. Here as in the preceding case, most of those aspects we, on our part, are going to subsume under the general term: sound comprehension, and furthermore all possible understanding of musical objects that we might achieve without referring to the music's future, are left untreated. In fact, Meyer seems to think they are fundamentally uninteresting, and here we disagree.
Also from the second half of the fifties dates an attempt to achieve an experimental grasp of semantical aspects of music: Robert Francès's La Perception de la Musique. Because of the fact that this book has really nothing to offer in the way of a musical theory, it need not retain us here for long. Suffice it to say that his way of testing listeners by analyzing their (free or guided) verbalizations precludes any of the music's specific precision from ever coming through. The only thing he really does is test through control groups the possible general validity of someone's (e.g. the composer's) verbal utterances. As a way of studying the music's semantical aspects, this strikes one as quite a roundabout route. Nevertheless, some results are there, and his line of attack is still being pursued (cf., e.g., Imberty 1975A and 1975B. In his case (cf. 1975A) lots of either highly speculative or extremely trivial theory follow his experimental results. He thus presents, in our opinion, a clear case of a vicious reversal of the order of theorizing/experimenting. After all, theories should lead to experiments, not the other way around.)
It is also on the basis of their (mostly implicit) epistemological preconceptions that Nicolas Ruwet, in his 1975 article, is rejecting the approach of a number of musicologists who, largely inspired by his own earlier publications, apply to music certain paradigms derived from natural language studies, notably those of distributional linguistics (Ruwet 1975 p.12). Here also the fact that a pre-theoretical fact-finding stage is postulated forms the central issue [2].
In this criticism we have no trouble following him. But when we examine the alternatives proposed by him, we still see disquieting symptoms of his relapsing into several old habits: he clearly has not freed himself from certain presuppositions that it would be well-advised to bring to light.
Thus, his admission in musical theory of a natural language theory like the Chomskyan generative grammar proves that such rather naive paradigm borrowing still goes unchallenged. Criticisms addressed to it, as it is applied to music, are rejected because of (supposed) misunderstandings of the theory.
Now theory-building, or theoryborrowing, for that matter, is all right, but one ought to see to it that it can be tested, or else anything goes. And Chomsky uses, as he has a right to do, freely the "native speaker's competence", viz. his own and his readers', as a means of testing his rules. (Simplification on our part is only relevant if it proves vicious.) So testing set-ups, for him, are easy to come by.
Nothing really like it is possible in music. And yet there are musicologists who "generate" exceedingly simple and symmetrical two-phase melodies as akin as they can manage to those of a second-rate composer named Tegnér who specialized in them, hire a "professional musician and arranger of music" to write harmonies for them, and blithely report: "The general reaction of Swedes listening informally to these melodies is that they are similar in style to those by Tegner." (Sundberg & Lindblom 1975 p.120; these authors are explicitly named by Ruwet as "serious" ones (Ruwet 1975 p.17)).
I absolutely fail to see why such statements are not a little more disturbing to those who write them down, and who immediately go on to stress the rigorous parallelism with linguistics. Let us at least try to spell out some of the things we feel to be wrong with them. Two aspects come to mind.
First: exactly what is one testing for? In the case of natural languages, it could be termed correctness, well-formedness: a yes-or-no matter (or limited number of such; cf. also note 6)). Syntactical theory, in order to become testable, sets itself the task of formulating the relevant questions. Any "syntax of music" should then take on an analogous task. It is there that crops up our first difficulty. Any question on well-formedness must be related to some specific music, as linguistic well-formedness is related to some specific language. I think that here just are no specific musics in that strong sense; there are at most vague, and often interconnected, areas with no clear borderlines defining them. And this fuzziness certainly destroys any easy analogy with natural language.
Second: what is one testing by? In the natural language case it is by the "native speaker's competence". In the case of music, a certain "competence" is also involved, but who is, with respect to which musics, the "native" musician ? ...In principle, the expression "native speaker" serves to rule out those who may have learned a language as their second (or third... etc.) one, and who therefore might not be reliable witnesses. Now it seems obvious, at least to the present author, that our music learning is not restricted to, and for things like the Bach choral style almost certainly takes place outside the blissful virgin years of our first language learning. One will perhaps be tempted to say that such (partial) musical competences are more like second (third... etc.) languages. But we, on our part, will prefer to reject these analogies altogether, and to replace them by an essentially different one, which will leave us with much greater methodological initiative (cf. 0.6).
Back to Ruwet's alternatives. In fact, on p.18 of his 1975 article he mentions a restriction on what one might ask of a "generative" theory, viz. the prediction just of some "kinds of phenomena, defined (only) by very general characteristics". But here also there is no trace of any specification of a viable and non-trivial testing method. And, for that matter, he has other proposals to make. We will not go into them in any detailed way, for they seem, for the moment at least, not extremely interesting. Lidov's proposal for defining phrase-level units, which he makes the most of, is found, at least in the way he finally weakens it (p. 32, towards the bottom of the page), to be rather trivial after all: his schemes of complementation (xyxy), disjunction (xxyy), and framing (xyyx) seems now easily reducible to (xx), (xy), and (xyx) respectively, leaving us with the conditions that a phrase be redundant (in the sense of unchanging) in some way, informative (in the sense of changing) in some other way, and finally owe its particular phrase-character, by the utter triviality of the two first conditions, only to the, also rather trivial, ABA like structure postulated in the last of the three schemes. Unhappily, we have not personally had access to Lidov's texts, and thus only know them through Ruwet.
Moreover, the fact that we do not share Ruwet's old preoccupation with the problem of defining musical units is bound up with a more fundamental difference between the two approaches. I think it is best described by saying that whereas he is chiefly interested in studying musical objects, e.g. pieces, we will be more interested in musical activities. Now, with regard to these, it would be fair to say that composing, playing and listening are musical activities which are not always separated in practice, and not separated in all cultures, but which in the western tradition have grown somewhat apart, in the specific sense that listening is an activity that all composers and players practice, but that playing, and still more so composing, have become activities that most users of music would not regard as their own. In fact, they seem interdefinable. Then it is the listening process that seems somehow to be the basic one, and thus the one that would serve best as a primitive. Composing would be defined as designing the listening situation, and playing as providing some specifiable physical necessary conditions of the listening situation. If all this holds water, it is perception that we must choose as our starting-point.
It is a nowadays generally accepted insight that perception itself is an activity that can be plausibly represented as computational. As Fodor 1975 has it (cf. p.44) it "typically involves hypothesis formation and confirmation" . To see something is to find a use for the concept I have of it, and, if (as we do) we take a concept to be any recognitional capacity, to recognize it.
Now all this need not, and in the vast majority of cases does not, become in any way a conscious process. Worse even: there are cases in which false inferences by my unconscious perception cannot be corrected by conscious intervention, viz. many cases of sensory illusions: one can consciously compensate for them, but "to be able to correct a sensory illusion in thought just is not the same thing as to be able to correct it in perception" (Hintikka 1975, p.199).
One assumption we will be making on behalf of our theory certainly makes for simplicity, viz. that auditory perception is, in the aforementioned fundamental respects, not different from perception through other channels. One (unessential) qualification might be considered: in general, one does not hear, as one sees, objects, but rather events or actions: processes. Still, these are conceptualized just as objects are.
If all this is true, can one not try and build up something like a "logic of perception"? Jaakko Hintikka (cf. his 1969 and 1975), who has indeed endeavoured to do so, views such specialized "branches of logic" as explanatory models (1969, p. 5) bringing out the "depth logic" which underlies the complex realities of our ordinary use of, e.g., perceptual words, and in terms of which these complexities can be accounted for. If we assume (as I, for one, am quite willing to do) that our handling of overt perceptual language is, in some sense, based on our handling of non-verbal perceptual concepts, such an explanatory model might actually help us in constructing a model of how humans handle those – it might even amount to just that, or at least to an interesting part of it.
However this may eventually turn out to be, an important link between this conception of "branches of logic" on the one hand and psychological theorizing on the other has been emphasized by Hintikka himself in his later 1975 (p. 59 ssqq); and we, in our turn, will find that notably the model-theoretical aspects of his proposal will contribute to a viable and interesting theoretical model of music listening.
What is the gist of Hintikka's proposal?
Perception (just like knowledge, belief, hope, fear, remembering, ..) is a so-called propositional attitude: the verb associated with it, typically constructed with a that-clause, ascribes to the person designated by its grammatical subject a certain relation to, a certain attitude vis-a-vis the proposition expressed by the that-clause, in this case the relation (attitude) of "perceiving". All these attitudes have an important feature in common: they involve modal notions: the taking into consideration of more than one possibility concerning the world. Compare the following three pairs of sentences (freely adapted from Hintikka 1969 p.155), in which a stands for a person, and p for a proposition:
(1a) necessarily p = in all possible states of affairs it is the case that p;
(1b) not necessarily p = there is a possible state of affairs in which not-p is true.
(2a) a perceives that p = in all possible states of affairs compatible with what a perceives it is the case
that p;
(2b) a does not perceive that p (understood in the sense "it is not the case that a perceives that p") =
there is a possible state of affairs compatible with what a perceives in which not-p is true.
(3a) a believes that p = in all possible states of affairs compatible with what a believes it is the case
that p;
(3b) a does not believe that p (understood in the sense "it is not the case that a believes that p") = there
is a possible state of affairs compatible with what a believes in which not-p is true.
What is interesting about these sentences is the fact that statements on propositional attitudes (and the reader may verify that this is true of the others as well) are shown to be analyzable as special cases of statements on modalities. The expression: "compatible with what a perceives (believes, knows, hopes, fears, remembers, ...)" can be used in each case to qualify what otherwise would amount to a necessity/possibility statement.
The idea that perception involves the handling of more than one possible state of affairs ("possible world") may seem counterintuitive to some. Let them consider the case, mentioned by Hintikka 1969 p. 156, of disclaiming a perception. Indeed I can say, with perfect good sense, that I do not see that p, and that I do not see either that not-p. It is readily seen that this amounts to a possibility statement of a special, perceptionrelated kind. One could translate it as follows: With respect to what I see, not-p is perfectly possible, and so is p. In this way, I am handling at least two different possible worlds. In the same way, we can translate the sentence: "I see that p" as "In as far as my seeing is reliable, it is not possible that not-p", or "In all possible worlds admitted by my visual perception, p" [3].
What makes such an account of perception particularly interesting is the fact that it does justice to the senses considered as information-gathering systems – a conception essential, I take it, to any cognitive theory of their functioning. As Hintikka has it on p. 62 of his 1975, "the notion of (semantical) information is closely tied to that of a possible world: to specify an information-content is to specify a set of possible worlds" . And just when does a perceive more than b ? "The only reasonable answer seems to be that a perceives more than b if and only if the class of possible worlds compatible with what he perceives is smaller than the class of possible worlds compatible with what b perceives" (1969 p. 157).
All this may well be convincing for as far as it goes – but it is, as yet, not sufficiently detailed to become specifically useful, e.g., to permit an account of art perception, or music hearing. Later on, we will have to provide characterizations of a) different classes of possible worlds, and b) specific relations obtaining between them, in order to display the real strength and fruitfulness of Hintikka's basic proposal.
There is one passage in Hintikka 1975 (cf. p. 62 top) in which he explicitly recognizes the epistemological birthright of non-verbal cognition. This is an area that is of essential interest to a theory of music. We will now briefly turn to it.
One of the areas in which philosophers, however reluctantly, have accepted the existence of some sort of non-verbal conceptualization, is the pre-verbal stage of infants. Cf. Quine: "In effect therefore we must credit the child with a sort of prelinguistic quality space" (Word and Object, p. 83). Kutschera (Sprachphilosophie, 1975, p. 128) also declares it obvious that a language could not possibly be learned without previous conceptualization of the infant's environment.
Such treatments of pre-verbal conceptualization commonly carry with them the overwhelming suggestion that once verbal language is there, there are virtually no non-verbal concepts left operative. However, and not only on intuitive grounds, we will argue strongly against that. At the same time, we will have occasion to criticize the ways in which some philosophers have been caricaturing them.
Thus Kutschera's book is a quite reliable one for purposes of acquainting oneself with the present (1971/74) state of the philosophy of language, but in areas as yet unexplored it blunders happily about, to the point even of becoming incoherent, and possibly even inconsistent within the space of half a page. Thus at p. 128 he begins by ascribing to infants a conceptual world akin to the one animals are credited with in the works of the biologist Üxküll. Ten lines lower, however, he tells us that preverbal concepts have still a very wide margin of vagueness ("haben sicherlich noch einen sehr breiten Vagheitsspielraum") and that verbal language, together with growing experience, will make them precise. Now it seems to me that vagueness, fuzziness of borderlines, is here mixed up with lack of objectivity, of intersubjective demonstrability. After all, Kutschera himself is, in the matter of learning processes, in favour of the hypothesis formation and confirmation model, and it is difficult to see how a child could learn to use a word correctly if not by using (possibly two or more) precise concepts. It would seem rather that out of a number of precise preverbal concepts one is selected by the language learned. Vague concepts just are not testable. Furthermore, it is difficult to see in what sense animals' concepts could be vague. They surely don't explain, let alone explicate, them to us, but they are very efficient in using them in practice. And that demands specific kinds of extremely high-level precision [4].
Now for some more intuitive talk. I think that most people, if faced with the problem of finding the shortest route from where they are to the nearest railway station, would, in their actual computing procedure, use words only in a very minor role or not at all. I even think that they proceed very much like my cats, when they hear their food being served at the other end of the house, and prove brilliantly prepared for all comers and double bends they have to manage. I think that there are many computational problems, e.g. those of a spatial nature, where conceptualizations other than verbal ones are by far the more efficient ones [5].
Whatever may be the truth about that, there is some strong empirical evidence for the claim that children in the pre-verbal stage compute in a medium which is a conceptually structured sensori-motor space (cf. Piaget 1961: "permanent object" schema, p. 290, p. 397). Now, in order to avoid undue simplification, it is very important to stress, as does Piaget on page 438, that perceptual activity functions only within the frame provided by "overall" activity and is thus both directed and informed by it. And, intuitively speaking, it would seem that for adults' thinking in spatial concepts the same thing goes. Thus, if asked for the shortest route to the nearest railway station, I may think of either going by car, or on foot, or taking the bus, etc., all these options actually affecting the final form of the route decided upon.
We are not always confronted with this kind of problem on such a high level of consciousness, but it would surely be ill-advised to say that they seldom arise. In fact, we are incessantly solving them, most of the time without consciously knowing it, in maintaining contact with our environment. In all our actions (or inactions) we take into account the behaviour of the world surrounding us, (at least) in as far as it is relevant to them. In a clear sense, we are all the time "reading" our environment. (Words, if they play any role at all in this, are not of essential importance; nor have they, in any necessary way, anything to do with generating the concepts involved.)
Now I want to set out a line of argument which, taken together with ideas to be developed below, will eventually enable us to give a relatively simple account of the way the different 'arts', including poetry and music, present, as many people will be intuitively inclined to admit, a family-likeness of some sort which sets them apart from non-art.
"Reading" the environment, in the sense just mentioned, is to be thought of, I think, as a continuous activity of matching incoming data with the internalized model of the external surroundings: as is proper, a computational activity. (Data may be, and often will be, sought out for just this purpose.) Now if we take a percept to be a set of incoming data which is sufficiently structured to admit of the discrimination: it can, or it cannot, be matched with some conceptual structure, we can define a notion of well-formedness of percepts, as the attainability of such a match. (Verbal language well-formedness then arises in a natural way within the purview of this definition, as a special case [6].)
One consequence of such a definition is obvious and, at the same time, of the utmost importance: it may happen that an organism, confronted with an ill-formed percept, reacts by adapting its intemal model, and, by doing so, makes the percept into a well-formed one. If the percept is at all likely to reoccur, it may be the case that the organism has adapted itself better to its environment, and many people will be inclined to say that it has learned something useful.
At least [7] part of this learning will be what is called concept learning in the literature. Fodor 1975 characterizes it as follows (p. 34/5): " (...) what concept leaming situations have in common is fundamentally this: the experiences which occasion the learning in such situations (under their theoretically relevant descriptions) stand in a confirmation relation to what is learned (under its theoretically relevant description). A short way of saying this is that concept learning is essentially a process of hypothesis formation and confirmation". And later (p. 87 note): " (...) it involves the projection and testing of hypotheses".
An edifying example of concept learning is provided by humans' learning to "read" stills: photographs, pictures and the like. It seems indeed at least overwhelmingly plausible that for higher animals (to say nothing about very young children) a "picture", an unmoving percept of "a man walking up a hill" just is not well-fommed. Sometimes even respectable philosophers seem to be led astray because they do not make these distinctions. In building up his case against the feasibility of images as making up the language of thought, Fodor, quoting Wittgenstein, seems to imply that stills are somehow simpler and therefore more plausible than moving images, whereas it would seem rather that they acquire even well-formedness only as artifacts, by specifically cultural concept leaming [8]. It is worthwile to take a closer look at his example. Wittgenstein (1953, p. 139, as quoted by Fodor 1975, p. 181) states that "a picture which corresponds to a man walking up a hill forward corresponds equally, and in the same way, to a man sliding down the hill backward". At least three levels of conceptualization are possible in this case.
The learning process described in 3) certainly is a case of concept learning in Fodor's sense. It is entirely convincing (although hardly an argument against an 'iconic' language of thought) and it does produce new concepts (cf. b) above ). But it certainly is a special case of concept learning, in that it involves also something like the breaking of a conceptual habit (cf a) above). This last feature is not essential to all concept learning.
It seems indeed reasonably safe to assume that our conceptual system involves, among other things, the use of open sets of concepts: sets which may, in principle, be added to without sacrificing anything. As plausible examples may count the set of my words in use; the set of my languages in use; the set of people I am acquainted with; the set of objects of which I know what they look like; the set of sounds of which I know what produces them, etc., etc. ... Not all concept learning means something like the above-mentioned unlearning-plus-learning process. On the other hand any unlearning-plus-learning (UNLL, for short) process is, by definition, a concept learning process. Why are we singling out these special learning processes?
Earlier (cf. 0.2.2), in talking about testing procedures in natural language studies, we have mentioned the crucial difference in this respect with music studies: it hinged on the notion of well-formedness. Later we have introduced a more general notion of well-formedness, of which natural language well-formedness was found to be a proper subcase (cf. 0.5.1). We will now see how this is going to help us in our search for a more plausible theory of music.
The defender of some theories we found reason to criticize above, Nicolas Ruwet, has not only published important papers on musical theory, but also on poetry (cf. his 1972, p. 151, p. 210). Common denominator of all essays contained in his 1972, and explicitly stated in several of them (see, e.g., his introduction), is the idea that the parallel music/poetry, rather than the parallel music/natural language should be explored. We, on our part, are going to take up again this idea, but in a rather more radical way, and with results very different from his; and we will start out from the specific difficulties he encountered when, trying to tackle poetry by linguistic means, he looked for a possible grammar of poetry (1972,ch.6). On p. 153 he mentions two problems to be solved. One of them we can discard: it merely indicates a problem area proper to natural language in its own right, but hitherto neglected: the study of linguistic relations through units larger than sentences. The other is more interesting, because it has to do with poetics proper: the existence of deviations from ordinary language. (Both his "liberties" and his "extra restrictions" are within this category.) In a later chapter (p. 217) he again points out the violation of natural language laws as creating major difficulties for any simple linguistic labeling of poetical facts.
Let us take a closer look at these "deviations" of poetry with respect to ordinary language. In the first place, and trivially, they must exist if I am at all able to recognize poetry as such -they then define the opposition poetry – ordinary language. In the second place, natural language well-formedness, specified as ordinary grammatical correctness of speech or writing, can be defined by rules rejecting certain sentences as ill-formed. Such boundaries are abolished in poetry: certain sentences occurring there would be considered well-formed by ordinary grammar standards and certain others not, but they do not necessarily belong to poetically different classes of sentences, and they certainly are not rejected for such reasons. Indeed, within our extended sense of well-formedness (0.5.1), we could even describe as in a certain way linguistically ill-formed many poetical utterances, or aspects thereof, that ordinary grammar would not frown upon.
For instance, it surely would not frown upon rhyme and metre. But these two, for a long historical period the traditional "warning signals" of poetry, do involve, in practice, an undeniable bending of the rules of language. (Bending of the rules: there are ostensible, public rules: these are obeyed; there are also hidden, implicit rules: these are broken.)
Thus, for metre. The (rare) case in which it conforms entirely to the rhythm laid down by ordinary language syntax, and which certain XVIIIth century poets, in their quest for naturalness, have cultivated, has, in historical practice, given rise to so-called "minor" poetry only. 'Strong' poetical effects achieved by metre are to be found where the two rhythms interfere most strongly: in the cases where they just fail to coincide; hence the importance of enjambment and related prosodic techniques. Words which would, in some sense, have passed unnoticed, stand out, sentences are "broken up" in more or less subtle ways. New meanings arise.
And what about rhyme? Apart from the marking of the metre (which is an important function of rhyme if it occurs at the end of the verses), it has the peculiarity of forming couples (or triples, etc.) of words on the basis of their "end sounds" (let us not try to be precise here). Now it is a well-established result in the study of poetics that this linking of the sound-form of words is bound up with a linking of the semantic fields they are assigned to: otherwise unrelated concepts come into close, and in some texts even quasi-permanent, contact. In this way new conceptual relationships are formed and exploited.
Lastly, and perhaps most generally (if not trivially), poetical language has a distinct tendency of combining words in unusual ways, or in ways specific to poetry, and thus of a special, restricted, usualness (cf, e.g., metaphorical and metonymical discourse, mixing of styles, etc.). This points in two important directions Firstly, words appear out of their habitual contexts, or, if you prefer,contexts are mixed.This implies the breaking of conceptual habits, and thus instantiates "unlearning" processes as treated above (cf 0.5.2). Secondly, and the emergence of fixed "poetical" styles proves that this may even be a stable long-term process, new concepts are produced: this corresponds to the "learning" processes of 0.5.2. Moreover, the two are linked: after all, I would not even bother to unlearn anything, that is, I would simply reject as ill-formed the deviating utterance, if there were nothing to be learned, that is, if I were not confronted with something like higher order well-formedness. Consequently, what is at issue here are precisely the UNLL processes meant above, nothing more and nothing less.
Now back to our competence problems. Just when is anybody a competent reader of poetry? An interesting difference with natural language competence is that whereas the latter is, in an important sense, completed at a relatively early stage in childhood, it would seem hazardous to assert anything even remotely like it of poetry or music. Indeed, there does not seem to be any precise point of closure of poetical or musical competence. Let us look into the case of poetry. It seems entirely reasonable to require, for the adequate understanding of any poetical text, at least the following two conditions.
PC 1. Knowledge of the natural language used.
PC 2. Knowledge of the literary background produced by the culture the text at issue belongs to, in as far as it draws upon it.
Now this second condition is the really delicate one. It will go through only for any particular poem, the one it calls "the text at issue", and it just does not specify any general requirements. This suggests that each individual poetical text would require a specially tailored competence of its own. On the other hand, there is the enigmatic restriction: "in as far as it draws upon it" . Surely the piece itself does not draw. And if we really are serious about the listener's/reader's situation being taken as a primitive (cf 0.3.0), what the author has meant to happen is irrelevant if no reader can make it happen. Consequently, it is the reader who draws upon what he assumes to be the text's literary background. And this makes for a very real and entirely pragmatic weakening of PC 2: it will have to be interpreted with respect to some given (competence-claiming) reader. Nevertheless, there may exist, for given texts, a certain consensus of qualified readers, which one may be inclined to give decisive weight.
All this will not be easy to settle in any non-trivial way. However, there is nothing very new about it. When we set out to explore the possible parallel with music, we may very well be treading rather more controversial ground. Let us begin by spelling out the corresponding competence conditions.
MC 1. Knowledge of the (non-musical) soundscape [9].
MC 2. Knowledge of the musical background produced by the culture the music at issue belongs to, in as far as it draws upon it.
Now what is meant by MC 1, and in what sense does it parallel PC 1? As a first approximation, it means the ability to use one's ears, where music remains unconsidered as yet. As we have seen above, this implies a highly structured conceptual organization on the part of the listener. The term "soundscape" is used to refer to the structured whole made up by all auditory concepts the listener has at this disposal, together with their conceptual relationships.
Problematic sounds may be responded to in two radically different ways, corresponding to the sorts of problem they confront us with. Firstly they may correspond to some possible state of my internal model of the world, but not with the state I actually believe the world to be in. My reaction is then something like "to go out and investigate". I may believe my house to be empty; then, footsteps on the stairs may be "problematic" in this sense. Verbal language analogues are easy to come by. Secondly, it may happen that an auditory percept cannot be brought into correspondence with any of the possible states of my model of the world. This makes it an ill-formed percept, as we defined these above (0.5.1). Just "going out and investigating" will not be enough, for concept learning is clearly called for. In the simplest possible case, new things bring new sounds, and I learn to "read" them as they come. This corresponds rather unproblematically to the learning of new words for new things in a verbal language. Less simple cases may call for revising, reorganizing my auditory concepts, e.g. in the event of an auditory "homonymy" . (The verbal language analogues are obvious.) Here UNLL processes of some sort are highly probable. Moreover, something like "going out and investigating", or otherwise receiving additional information, will also be involved in most cases.
Nobody will expect the analogy between soundscape knowledge and verbal language knowledge to hold indefinitely. Thus, it does not extend in any interesting way to sound analogues of grammarians' examples of ill-formed ("incorrect") speech. But these, if they occur outside grammarians' textbooks, are simply rejected out of hand, precisely in as far as they are ill-formed, and something analogous to medical help is indicated. The same thing goes for malfunctions of the ear.
PC 1 for poetry is a very obvious condition, and its continuous importance can be felt throughout any poetical text. MC 1 for music needs perhaps more introducing, if only of an exegetical nature. We begin by defining the corresponding level of music comprehension, which we will call sound comprehension. We have sound comprehension in as far as musical sounds, in being understood, mobilize in the listener concepts of a not purely intra-musical nature, concepts, roughly, we could have at our disposal even without knowing any music. Table I, below, shows that this definition guarantees a perfect correspondence with the poetry case.
A: Classes of concepts related to music
B: The parallel case for poetry
Now, pace some mistakenly purist aesthetes, this way of understanding makes itself felt throughout all and any music. Sound comprehension, as we defined it, is part and parcel of all music comprehension.
Firstly, and trivially, no music can even be heard without it. Music, as a member of the set of audible processes, is not an intra-musical concept. Secondly, and already less trivially, by way of a Gedankenexperiment, those of us who still remember not understanding at all purely electronic music may verify that this was, at least in part, due to the fact that the sounds simply refused to translate themselves as actions or events: they were unrecognizable (cf 0.3.1). Later, a specialized stock of actions/events may have come to be associated with these "electrical" sounds. (They were often called "abstract" at the time: they could not easily be associated to visual, spatial and motor concepts.) It is obvious that the use of reverberation, thanks to the suggestion of a (large) enclosed space in which the sounds are actually being produced by activity in it, provided, and still provides, an easy way out of this problem. Through reverberation, "electrical" sounds are easily transformed into what the naive listener would call "real" ones.
In the same perspective, it becomes possible to predict the way in which professional musicians, and to a certain extent connoisseurs in general, simply through their knowledge of how musical sounds actually are produced, move away from the more naive, and, if not dictated by the authority of a "program", often less controlled associations produced by beginners and/or amateurs. Indeed, for better or for worse, "programs" can be important, in that they may lead us to make important choices. For on the sound comprehension level, not only the totality of a sound, all of its aspects taken together, but also some aspect(s) of it taken separately, "abstracted" from it, may give rise to a partial understanding of it through the use of a (possibly) non-musical concept. This is probably the musically most interesting aspect of sound comprehension.
Some examples to illustrate the point. If I hear a music "coming back" ,this idea is borrowed from non-musical contexts. The same thing goes for the "suddenness" (or not) of changes, for things like interpreting a diminuendo-cum-concomitant timbre transformations as a music's sounding "farther and farther away"; for the whole association of musical tempo with speed; and generally for all successful metaphors. Now metaphors never are one hundred percent right, but a certain rightness they must have in order to function at all. Their use probably reflects our ability to handle abstractions, as we overtly do in the case of curve-like schemata, e.g. "beginning with almost nothing – then growing to a highest point – then gradually rediminishing and dying away". These schemata, of which there are many, and very different ones, are prepared in us through non-musical auditory (and other) experiences.
To summarize.
Knowing that one is listening to music, recognizing an instrument and a way of playing it, enjoying the (imaginary) muscular exertion and pleasure involved, all these things do not necessarily involve intra-musical concepts, and are thus to be classed under the heading of sound comprehension. Generally, all the innumerable ways in which musical sounds behave like possible non-musical ones, or mobilize concepts of a (possibly) non-auditory nature, belong in this category. Just as in poetry one uses all the time the concepts making up natural language competence, but in an unusual and in a specific way "problematic" manner, in listening to music the same thing goes for general auditory competence.
It is clear that what we call "sound comprehension" includes really rather much. (L.B. Meyer's motor responses, image processes, connotations and moods, as well as Ruwet's concrete, "biological" aspects (cf his 1975, p. 33), have their natural place in it, and if we succeed in modelling "musical semantics" in such a way that sound comprehension gets accomodated in it as naturally as it always accomodates itself in our musical experience, we may have made an important step forward.) In fact, sound comprehension has been defined negatively with respect to intra-musical understanding, and it may be convenient to have a (tentative) definition of this last category. Let us therefore lay down the following relation between perception and understanding: let "I hear something" mean "I understand the sound produced by it" and "I understand a sound" mean "I hear the process which produces it", and then, starting out from Hintikka's analysis of perception statements as qualified modality statements (cf 0.3), we have, by way of an example of "natural" (non-conventional) perception, "I hear someone mounting the stairs" meaning "I understand a sound of such-and-such description in such a way that the set of possible worlds compatible with what I perceive (or, obviously, otherwise know to be the case) all exhibit the causally necessary and sufficient conditions for producing that sound". In this way, a law-likeness for the sound is construed by me on the basis of my knowledge of the world around me, and natural law comes in as the essential ingredient. On the other hand, if I hear a certain musical behaviour, I understand it by "placing" it: by relating it to the precedent(s) that make it law-like. In other words, I then hear the musician conforming to some precedent(s) (cf also 4.2). The notion of "compatibility with what I hear", already a qualified modality statement, is thus again qualified, and a special "musical compatibility" is construed by the hearer (however much it may be felt to be "immediately evoked" by the music). The laws that obtain are conventional laws.
All this will be made more precise later. For the moment, it may readily be foreseen that the "natural law" understanding of sounds might very well exhibit differences with the "musical" understanding of them that are reflected in correspondingly different logics. Notably a) the classes of possible worlds, and b) the relations obtaining between them (cf 0.3.3 end) will be shown to determine these.
The main object of this book will be to investigate what we have called the UNLL process, the unlearning-plus-learning process. Let us first try to localize it, and thus to approach it, as it were, from the outside.
We represent the beginning of a (= some) music (as always in this book, a music-as-perceived) by the following diagram.
![[Fig. 1]](../plaatjes/proefschrift_fig_01.gif)
Fig. 1
When a piece of music starts, rather sooner than later, in fact as soon as we possibly can, we try to "place" it, i.e. to assign it a specific background, a specific past. This may be a matter of seconds or less. This stage is represented in Fig 1 by the letter A, the corresponding past by (A).
Later on, as the diagram suggest, it may be necessary to change over a different past (B), in order to keep being able to "place" the music; we then are at stage B. Remark that stage B encompasses the whole stretch formerly labeled A, but that it abandons past (A) in favour if past (B). Nevertheless my knowing-that-B must have begun somewhere after point A. Here are the really interexting moments to be found, the moments characterized by the coming in of disturbing evidence, the moments where my concept A "gets me into trouble", in a way.
Clearly two levels of "understanding" are to be distinguished here. The first is the "understanding" of musical material: it is explicated here as the assigning to it of a specific past, as recognizing it. The second-level "understanding" concerns the relations between, the interaction of, two (or more) musical materials. (We use the term "material" here on a purely heuristical basis, for clearly, any theoretical distinction hetween material and non-material seems hardly defendable.) It is obvious that any "material" that presents itself later than the first will probably need both levels of understanding and will thus be more than just material. (Similarly, the first material itself will (probably) have to reconsidered in the light of subsequent ones.)
To go back to Fig 1, it is clear that B implies not-A and that A implies not-B: Their pasts (A) and (B) do not intersect. (That is, in the (arbitrarily) chosen example.) So, when we have B, and also "B implies not-A", we have: not-A. Now it is important to stress here that that is not enough. At least we ought to have something like "We have now not-A but a moment ago we (thought we) had A", and also we need something that describes how the change involved in this has come about. Given that we have also "We have B but a moment ago we ((implicitly) thought we) had not-B" the problem at hand is that of the relations between A and B. We have somehow to construct a "musical space" that has got room to accomodate (at least) both A and B and the transition from A to B.
This may mean defining A and B in terms of each other or their components. Thus new concepts may arise. After all, knowing that B, we must explain to ourselves (in most cases not verbally, cf 0.7.5) how a moment ago we knew that A. Insights may be gained and new possibilities opened up. But it is important to stress that surely nothing in the way of a complete description is going to present itself. (Cf the partly parallel problem of ill-defined concepts (3.3).)
The next stage in the example represented in Fig 1 is one in which much less clearcut results seem possible. (Intuitively, one feels that negatively formulated concepts have a much wider and less determinate content than "positive" ones.) Nevertheless it seems reasonable to require that any eventual formalizing machinery be capable of handling also cases expressed by negation and disjunction. Now if we admit these connectives (not-. . .and. . .-or-. . .) we might be faced with serious problems. For if they are taken by us to mean anything like classical truth-functional negation and disjunction, we have the full classical propositional calculus (PC) on our hands. Now this would be too strong a system for many. Thus Otto Laske (in a paper delivered in 1973 at a semiotics symposum in Belgrade, and again in his 1975A) proposes to adopt a term coined by J. Piaget (in ch. VI of his 1961), viz. the term "infralogics". Infralogical operations can be described by opposition to the logical ones as follows: they (we quote the 1973 paper)
Now it seems to us that right about the time of the publication of Piaget's book some important developments in the area of logic have been made, notably the working-out of adequate model theories for modal logics (Kripke, Hintikka, Kanger and others) that enable us today to assess Piaget's "infralogics" and describe their logical status. On our part, we will have to make sure that Laske's anathema does not strike the logic we are going to choose.
I take it that Laske's rejection of logical methods is related to the Artificial Intelligence people's despondency about them as exemplified in Minsky 1975. Their case against logic is, in Minsky's case at least, seriously impaired by at least two factors. The first is their exclusive concentration on proof theory – no independent semantical methods are envisioned by them. In this book we will be presenting the logical systems we advocate, be they axiomatized or not, through semantical (model-theoretical) methods only. The second is their preoccupation with consistency as something "logic absolutely demands" . This may be so; but we will try to show that the conclusion they draw from it, viz., that logic can never be of any substantial help in the modeling of human cognitive behaviour (it often is quite accomodating with respect to certain "inconsistencies"!) need not be final as it stands. That is what we are now going to address ourselves to.
That PC, in its unenriched form, is indeed too strong for our use is perhaps most clearly illustrated by its inability to admit mutually conflicting hypotheses. In music (as in life at large) these are, we think, extremely frequent. The whole idea of "suspending one's judgment", but remaining alert all the same, means nothing else than continuing to match all incoming data with (at least) two mutually exclusive hypotheses, which are thus both maintained for a certain time. (Ours is not essentially a one-track mind.) Now a PC statement like "A∨¬A" (normally read as A or not A) would be totally uninformative, because it is equivalent to all tautological statements, and therefore cannot express any specific alternative at all. A statement like "A∧¬A" (both A and not-A), on the other hand, is even worse, because it is a contradiction, and thus entitles me, if I accept it, to assert anything [10]. What we need is a logic that admits of the existence of different, even mutually exclusive, paths within one framework. Now each of these paths is meant to "test a hypothesis", as it were, (but cf 0.7.5!), in order to hear, to interpret the music in such a way that it is self-consistent, that it preserves some character of what might be termed "law-likeness" . And this suggests the possibility of bringing in the venerable but traditionally vague concept of a "musical law", because it offers us the possibility of explicating it, and in that way, making it useful again. As an explication of "law-likeness" we have to offer the following, deceptively simple, definition. A music's behaviour is law-like iff it behaves as it always did in the past.
The real problem here is not in the question of admitting describable (but cf 0.7.5!) partial law-likenesses. It is, we believe, in the interpretation of the second "it". It is this that, in each concrete listening-process, determines a potentially variable, "subjective" [11] if you like, assessment of the law-likeness of a music's behaviour. Thus, if I am listening to a piece in sonata-form, and if I recognize it as such, the coming in of the second theme after the first is law-like: its past is defined by (among other things) pieces in sonata-form. But if I do not recognize it as such, the second theme may surprise me, and will either not be law-like or compel me to re-assess the music's past. (The parallel with the case graphically represented in 0.7.0. is evident, and to the point.)
An important epistemological problem concerns the fact that most of the concepts involved in understanding music remain non-verbal, and that, if we try to verbalize them (as we will in some cases be obliged to do below), they take on an awkwardly complicated verbal form. It is important to stress that this awkwardness, or this complexity, do not at all imply corresponding complexity or awkwardness in the musical concept translated. Musically very simple and efficient things, things simple to the ear, may be difficult to describe in a precise verbal language. Thus, if I "place" a music, as I did in 0.7.0, l need not at all do that in any verbal form.
This brings us to the concept of musical "emotions" . Let us disregard without further ado the only historically important "interpretations" of musical emotions as laid down in Italian terms for tempi etc. Let us furthermore make it clear that if the number of words indicating emotions in verbal language is any measure for the number of distinctions that can be made in describing musical "emotion" , direct verbalizing is hardly a fruitful strategy [12]. I think that a radically different approach is needed. Why not take an "emotion" to be: the (non-verbal) apprehending of non-verhal concepts interacting? Why not take it to be a "map of the situation", an internalized field of operations, possibly concomitant hopes and fears (...) not excluded?
In the final chapter of the present book (cf 4.1) we will show how such a conception can be integrated in a theory of emotions which also accounts for their more "visceral" aspects.
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