Making sense in music
An enquiry into the formal pragmatics of art (part 1)

by Jos Kunst (1978)


Summary and plan of the book
Samenvatting (summary in Dutch)
Curriculum vitae (in Dutch)
Stellingen (in Dutch)


This book has been motivated by (among other things) the author's need to do something about the utter helplessness of all those who, professionally or otherwise, want to comment on any given music, and say what it does to you. Obviously, this is no mean task, and, more specifically, no music critic shall be helped out just by working his way through these pages. But, on the other hand, any musicology envisioned along the lines laid down here is bound to be, in the long run, of great value, even to him. For I think that our obvious inability to deal, within our verbal system, with such definite musical phenomena has made us shrink away, so to speak, from music, at both its and our detriment: it has been "magicized", given over to glossy stardom romance or to the esoterism of in-breeding, or even to both.

The author is strongly in favour of a rationally oriented culture, and, moreover, of rational approaches gaining access even to such radically non-verbal activities as music. He expects from that both a debunking and a maturing of the role of music within our culture; at the same time, its workings, and also the uses people put it to, will, he hopes, become open to inspection. Music itself might then be taken seriously at last.

In order to make at all possible such a fundamental approach to music we have had to conduct our enquiry on three levels of generality: first, on that of musicology proper; second, on that of aesthetics, and third, on that of semiotics in a general sense. On all three levels we have had to either formulate crucial new concepts or adjust existing ones, notably by generalizing them; without that, the integration of music theory in a general philosophical framework would not have been possible, at least not in the simple way we will be arguing for.

Moreover, a certain amount of formal logical machinery has been deployed; we express the hope that the logically unitiated among our readers will not be too easily scared away by it. It is no mere clothing: not only is it (as often) a useful tool to obtain precision, in the sense that the exact relations between (parts of) a theory and counterexamples to it are more easily pinpointed, but it also specifically allows for abstractions and generalizations to be made on the basis of it. (After all, what logic is about is the "goodness" (validity) of any argument when abstraction is made from the truth or falsity of its premisses and conclusion.) Thus, we probably could not have ourselves formulated the most crucial concept of this book, the Bivalence Function, without the help of mathematical formalism, and we certainly could not have convincingly communicated it to any reader. After all, only a formalism will permit abstraction-cum-generalization on this scale to really smoothly go through. But, on the other hand, this confronts us with the problem of many of our prospective readers being unfamiliar with these methods. In presenting our mathematical apparatus we have therefore tried to steer a reasonable middle course. The book is meant to be relatively self-contained, in the sense that, certainly, it refers its reader to books and articles of a more purely mathematical nature. but that he may consult those as and when he sees fit: it can, I take it, be fairly well understood by any careful and motivated reader who wants to postpone,for the moment, his initiation to logical technicalities. Nevertheless, the very first elements of the propositional calculus would come in handy, and I doubt whether any reader could reap any long-term profit from our work if he refused to fill in the gaps in his mathematical knowledge.

Let us briefly review the most salient features of our proposal. Firstly, the well-known Morrisian trichotomy syntax-semantics-pragmatics is taken up and extended to percepts generally. (The traditional applications of these terms, precisely in as far as they give rise to competences embodied in humans and thus can be assessed by the methods of experimental psychology (cf. psycholinguistics!), then arise as special cases.)

Let a concept be a recognitional capacity of any sort. (Throughout the book, we will use the term in just this sense.) Let a percept 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 have then a wellformedness criterion: a percept is well-formed iff (logicians' shorthand for: "if and only if", or altematively, "just in case" ) such a match is attainable. Consider, then, the following threefold proposal:

SYNT – In the syntactical processing of a percept, the perceptor will decide the matter of its well-formedness: the question whether or not a match can be found for it.

SEM – In the semantical processing the perceptor, treating the percept as an object (as a type), will specify the conceptual structure that permits the matching to go through.

PRAG – In the pragmatical processing the perceptor, treating the percept as an event (as a token), will let the successful match feed back on existing conceptual structures.

We will now take these three in turn.

SYNT – Relative to some given person (persons) a syntactical theory of percepts is, given the above definition, at least conceivable. The traditional case of verbal language well-formedness can be accounted for if the person in question is the idealized "native speaker" of some language, operating in an equally idealized "general", or "neutral" context (which excludes, among many other things, poetry). His status is thus that of a theoretical construct.

SEM – Next: to specify which conceptual structure is activated by the successful match with a given percept is to specify what could be termed the percept's "informational content": given the conceptual structures an individual has evolved in his lifetime (his set of "possible worlds": this term is used here in its quite general sense of "possible states of affairs"), his semantical processing of a percept specifies those possible worlds which are compatible with it.[1] (After all, only God's perception could be such that it uniquely determines just one (the) world.)
In the case of verbal sentences, this notion of compatibility typically involves something like Lewis's "truthfulness-and-trust-in-L" convention being in force; the familiar "truth conditions" formulation is then easily seen to result.

PRAG – Finally, pragmatics. As this book's subtitle suggests, we mean to have something to say about that, at least where art is concemed. But here we face the problem that no generally accepted approach of pragmatics is available as yet. Montague's gives the truth conditions for sentences containing indexical expressions: it is a semantics incorporating special context-dependent ("pragmatical") variables. Proposals made by theorists of literature (see, e g., T.A. van Dijk's paper in M. de Mey et al. 1977) involve the formulation of what is called "adequacy conditions"; they seem to presuppose the existence of systematic relations between utterances and contexts to which they are "adequate". Now whereas there may exist some such systematic relations which are typically governed by (more or less general) conventions, we would not recommend the general use of such a concept of pragmatics, not even for the whole of written verbal language. On the other hand, everybody agrees that a pragmatical description of verbal sentences, and, generally, utterances, will have to take into account the context in which they occur, be it linguistic or non-linguistic; consequently, the most general approach would be, I take it, to require that a pragmatical theory describe, for each sentence/utterance, the change effected by its use, e g., through comparing "conceptual state" descriptions (before vs after). If, then, we consider a set of possible utterances in relation to (some theory about) the speaker's (utterer's) intentions, this yields "adequacy conditions"! And if some theoretical speaker's aim is to conform to some given convention, we are back with van Dijk, which is all to the good. If, lastly, this convention is anything like the Lewisian truthfulness-and-trust-in-L convention, the adequacy conditions turn out to be truth conditions and we are back with Montague. The Montague enterprise, simply because it does involve context descriptions, is thus seen to be a pragmatics after all, albeit a rather severely restricted one.

Let this show how we propose to analyze the current uses of these terms as special cases of a possible generalized use.

Now back to our percepts. Needless to say, pragmatics as we now have it easily covers their case. We will use a simple example. The sound of rain outside can be heard and recognized a as such by me: it is then found well-formed and interpreted semantically, as detailed above. It also admits of a pragmatical description: a description of the change effected by it. In such a description may then loom large such questions as whether I brought my umbrella with me or not: in one case I may still feel free to go as I please, in the other I may know myself to be marooned where I am – until the rain stops, that is. Thus all my conceptual structures-in-use may be affected: these notably include any propositional attitudes I may have: knowledge, beliefs, fears, hopes, etc... It is interesting to note that the verbal sentence: "it is raining outside", addressed to me by someone, corresponds more and more closely to the percept just mentioned as one moves from the syntactical, via the semantical, towards the pragmatical descriptions of them.

This quite general and unified treatment of the triad syntax-semantics-pragmatics constitutes our first important starting point. The second is in our taking up Hintikka's "logic of perception" (see his 1969 and 1975). This move, even if perhaps not our idea of using one of his key formulations to analyze, quite generally, the semantical processing of percepts (see footnote (1) above), is taken by us to be entirely in agreement with Hintikka's own views. It provides us with an analysis of (aspects of) perception which enables us to make somewhat more precise the difference between what could be called "natural" perception, i.e. perception based on our knowledge of natural law on the one hand, and "musical" ("pictural", etc.) perception on the other, which is based on our knowledge of musical (etc.) law-likeness. This is done in terms of logics already extant in the literature, but for which, up till now, no interesting pratical use had been found (the Lewis Logics S7, S8). Next, a structure is designed on this basis which is intended to uniquely charaterize our experience of art. It is meant to embody a pragmatical description: it specifies the conceptual change effected by a percept. This structure, together with some work devoted to making precise its interpretation, constitutes this book's chief contribution to the field of aesthetics.

This same structure has also interesting consequences in the field of musicology proper. It provides the basis for a (computer implementable) modeling of specific music listening processes. (A Minsky frame is, in our terms, just a large scale (global) and possibly ill-defined concept exhibiting certain logical relationships with a number of smaller scale (and possibly better defined) ones (cf 3.3). We owe a debt to Otto Laske for having brought this fact to our attention.) In this way, some progress is made towards a theoretically respectable experimental psychomusicology. Moreover, given the fact that in the last few years musicologists have been repeatedly trying to establish contact with what they took to be neighbouring disciplines (linguistics, semiotics), given, on the other hand, the (rather trivial) immunity to falsification achieved by the resulting theories and their lack of explanatory power, a new departure in the discussion would seem to be welcome. And that is what is offered here.

Lastly we might envision some sidelines we think could be of interest.

First, I think that our approach to the different fields of non-verbal conceptualization and non-verbal knowledge might be fruitful in psychology. A treatment that uses a 3x3 matrix of one-digit natural numbers, or a chess position, as paradigms of visual stimuli and uses them to test theories purported to cover also what is called visual memory (see H. Simon, The Sciences of the Artificial, Cambridge Mass. 1969) seems to us to be distressingly unaware of what could constitute central cases of specifically visual concepts.

Second, the relations between problem solving and emotions worked out here might prove of some interest to those psychologists who study the relation between intelligence and motivation. It is the present author's opinion that, at least in many versions used in debates on education, current theorizing on intelligence considers it too often as a set of problem solving capacities somehow "designed into" the human (by Nature, the Creator, the School System, or whatnot) instead of as a set of strategies produced by the subject himself in his transactions with an interesting environment. I, for one, think that interesting environments (the term does certainly not refer to just art and things like it) are far from equally distributed among the social classes.

– But these are rather wide horizons.

Still a speculation, but one we are willing to endorse as our own, is the possibility to analyze existing musical behaviour patterns, be they laid down in recordings, in scores, in social conventions surrounding music, or in music teaching, for the conceptual structures they promote and/or support, and thus to come to conclusions regarding the choices one has to make with respect to music. Musical activities, we will argue, are effectively meaningful activities, and therefore fitting objects for ethical "goodness" or "badness" qualifications. That is why all human agents engaged in a musical situation find themselves in an ethical situation as well: and we hope that the research initiated by the present book will help them to get a clearer view of it. Obviously, texts and personal credos are insufficient clues, and often, I think, even quite misleading ones.

In view of this our "cognitive musicology" must also be linked up with cognitive sociology; non-musical and musical conceptual structures characteristic for social groups must be the objects of theoretical and empirical study; in this way we may be able to overcome the primitive stage of mechanically assigning "tone-systems" to social classes and to find explanations instead of just facts-to-be-explained.

As to the so-called "psychophysics of music", I think it just cannot continue doing without any theory about how people recognize music as such. Up till now, the cultural prestige of music clearly has helped fund-raising – but most results are about it by innuendo only.

As a contribution to the debate on universals in music, we will, by shifting the level on which to look for them, actually argue for the existence of an important one: the one on which our definition of music will be based.

Ours will be, as we hinted above, a cognitive musicology. In its own way it will account for all three elements of John Blacking's beautiful formula (cf p. 101 of the Faber edition of his How Musical is Man?) which describes music as "exceptionally cooperative and exploratory behaviour" – and the account it will give will specifically show how all three of them, the music's exceptionality, its having to do in different ways with cooperativeness, and its exploratory nature, actually merge into one concept – our *music* concept.

And *music*, as we will define it in chapter 4, will there be claimed by us to be, in fact, just music and nothing else.


Thanks are due in the first place to Jan Vriend, the collaboration with whom provided me with much of this book's initial impetus. Next, students and colleagues associated with the Bijscholingsinstituut van het Amsterdams Konservatorium (BIVAK) have given me useful criticisms and substantial encouragement. Otto E. Laske has helped me putting into focus the place of what I was doing within the larger frame of advanced musicological endeavour, and has, by sitting up and taking notice, enabled me to overcome a period of, I hope, unreasonable despondency. Nevertheless, it was J.J.A. Mooij who finally brought me into contact with the learned circles to which he belongs, and thereby saved me from the status of the isolated crackpot. S.J. Doorman and Marius Flothuis have then taken on to systematically supervise my work, they have invested many hours in discussing it with me, and ought to be credited with many of its qualities. Nevertheless, needless to say, all responsibility for its remaining defects rests exclusively with me. Students and colleagues of the Utrecht Musicology Institute have repeatedly "talked back" to me, to my immeasurable profit. Finally, all those belonging to my more or less immediate environment have, sometimes rather ruthlessly, been subjected to tenacious questioning and/or lecturing on my part; I thank them for allowing this to go on for so long.


A first version of some of the material contained in this book has appeared before under the title: Making Sense in Music 1: the Use of Mathematical Logic, in: Interface 5 (1976) pp. 3-68. In being incorporated in the present final version, it has not so much been re-arranged, as, rather, been fundamentally rethought, and, in part, even re-written from scratch.

Summary and plan of the book

The book is divided in five chapters.

The introductory chapter 0, starting out (0.0) from a tentative approximation of the problem of musical meaning, first (0.1 and 0.2) takes stock of existing literature on the subject and shows in what sense it remains unsatisfactory; it then (0.30.7) goes on to look for what could be a fresh startingpoint for theoretical musicology. Two notions are discussed: in the first place (0.3, 0.4) Hintikka's "Iogic of perception", which a) embodies an analysis of perception basic enough to encompass non-verbal perception such as that of music, and which b) can also be rendered articulate enough to admit of definite and interesting statements with respect to it; in the second place (0.5, 0.6) an important idea recurring here and there in the literature which can be made to reflect, we take it, essential parts of our discriminating art from non-art (the idea of what we will call the unlearning-plus-learning process). Lastly (0.7) a first inventory is given of the requirements any mathematical formalism ought to fulfill if it is to be able to represent even elementary musical listening situations.

Chapter 1 provides a brief introduction to such (already existing) modal and tense logics as we are going to need for our purpose of applying to music Hintikka's perception logic. It is shown, in particular, how the (commonly neglected) Lewis systems S7 and S8 could be of crucial importance to semiotic theory.

Next, chapter 2 uses the apparatus thus developed in tackling the "unlearning-plus learning" process: it presents (2.1, 2.2) and applies in some simple examples (2.3, 2.4) the central concept of this book: the Bivalence Function.

Chapter 3 uses a short Chopin piano piece in showing how the structures developed so far can be made to form larger-scale "networks", and how these, in their turn, can be interpreted as "pragmatical maps", representing musics-as-heard.

Chapter 4, finally, returns to the broader issue of art in general. It endeavours to narrow down the interpretation of the Bivalence Function in such a way as to make it a suitable definiens of art-as-we-perceive-it (4.2, 4.3). It is shown that the primitive concepts of Hintikka's perception logic, combined with David Lewis' definition of the notion of convention and with our Bivalence Function notion, actually suffice to give an interesting definition of art in that sense. It is also shown (4.1) that any theory incorporating our Bivalence Function concept will be able to provide an explanation for the emotional aspects of art-perception, as well as for its cognitive values. Art is thus vindicated as an effective, or at least possibly effective, means of human communication. Exactly what might be the content of that communication in the case of music is assessed in 4.4. Lastly (4.5), we return again to existing musicological theories; this time in order to compare to them our own, in its now available explicit formulation. Also, the experimentalization problem for our theory is briefly looked into.


Het boek telt vijf hoofdstukken.

Hoofdstuk 0 combineert een critisch overzicht van de bestaande musicologische literatuur over het onderwerp 'muziek en betekenis' met een eerste onderzoek naar wat, voor dit probleemgebied, een nieuw uitgangspunt kan zijn. Voorlopige karakterisering van de zgn. afleer-leer-processen.

Hoofdstuk 1 presenteert enkele modale en tijd-logica's en geeft een mogelijke interpretatie van een tweetal systemen die van speciaal belang zijn voor de beschrijving van het muziek-horen (en wellicht ook voor theorie en praktijk van de semiotiek in meer algemene zin).

Hoofdstuk 2 gebruikt deze interpretatie bij de formalisering van de in hoofdstuk 0 geïntroduceerde afleer-leer-processen.

Hoofdstuk 3 demonstreert de mogelijkheden van deze formalisering naar aanleiding van een kort piano-stuk van Chopin.

Hoofdstuk 4 verbindt een aantal conclusies aan de ideeën uit de vorige hoofdstukken. De conventietheorie van David Lewis en onze formalisatie van afleer-leer-processen worden gecombineerd in een definitie van kunst-perceptie. De problemen van muzikale emoties en muzikale betekenissen worden opnieuw bezien.

Tenslotte moge ik de Nederlandstalige lezer verwijzen naar mijn artikel: Muziek en Communicatie, in: Wijsgerig perspektief, jaargang 18, nummer 5 (1978, juni).

Curriculum vitae

Geboren 3/1/36 te Roermond; gymnasium B 1947-1953; staatsexamen gymnasium A 1954, doctoraal examen Letteren (cum laude) 1960, militaire dienst (met talrijke examens) 1961-1963, 1e prijs componistenconcours Gaudeamus 1969; Prijs voor Compositie Amsterdamsch Conservatorium 1970. Composities te vinden bij Donemus Amsterdam, Peters Londen en het instituut voor Sonologie te Utrecht; artikelen in Het Franse Boek, Interface en Wijsgerig Pespectief. Werkadres: Instituut voor Muziekwetenschap, Drift 21, Utrecht.


behorende bij het proefschrift van Jos Kunst
Making sense in music: an enquiry into the formal pragmatics of art

Promotiedatum: 20 oktober 1978


Onze burgercultuur is gemaakt in de tijd en de ruimte van het XlXe-eeuwse industrieproletariaat, en is daarom redelijk wel te vergelijken met een helerstransactie.


In geval van een conflict tussen sociale groepen kunnen mensen niet voorkomen dat ze hun cultuur als wapen gaan hanteren.


Tegen de stelling dat de uitgebuiten het moeten hebben van hun eigen cultuur zijn belangrijke tegenvoorbeelden aan te voeren: met name de proletarische groepen die, in eigen land of als geïmporteerde gastarbeiders, uitgesloten zijn van hun eigen cultuur.


Op grond van zijn statuten kan van het Genootschap van Nederlandse Componisten worden geëist dat het onder zijn leden een discussie over cultuur als wapen entameert.


De mededeling van Louis Andriessen, in zijn toelichting op zijn compositie "De Staat", dat dit werk bedoeld is als een bijdrage tot de discussie over muziek en politiek, kan moeilijk anders dan als kunst worden opgevat.


Om de diepte van Rudy Koopmans' stelling: "Muziek is als zodanig niet rechts of links; teksten kunnen dat wel zijn" te doorpeilen is het voldoende haar te vergelijken met haar omkering: "Taal is als zodanig niet rechts of links; muziekstukken kunnen dat wel zijn".


Een onmisbare motor in de emancipatie der uitgebuiten wordt gevormd door de kwade trouw van de uitbuiters.


De enige weg naar spreiding van de cultuur begint bij zelfbeheer in de bedrijven.


Fatsoenlijke democratische besluitvorming vereist, dat in het (hypothetische) geval waarin

  1. honderd personen de beschikking hebben over één radiozender, en
  2. negenennegentig alleen maar Beethoven willen horen, en een alleen maar de Beatles,

Beethoven en Beatles ieder de helft toegewezen krijgen van de voor hen beiden beschikbare zendtijd.


Zgn. "authentieke uitvoeringen" van oude muziek zijn niets anders dan een vorm van conceptual art – een strikt modern gezelschapsspelletje.


Een promotieplechtigheid moet, zolang ze nog onvermijdelijk blijft, door alle betrokkenen met gepaste ernst worden verdragen (cf Part IV: Norms of Partiality, in: E. Ullmann-Margalit, The Emergence of Norms, Oxford 1977).