Late Night Thoughts Listening to Luigi Nono

2 June 2009


Luigi Nono

For the six months or so that I have been posting to this forum I have been quite preoccupied with intensely practical questions in history, economics, politics, diplomacy and how these spheres of activity are related in a substantive way to human nature.

When Heilbronner wrote his famous book about economists he called them the “the worldly philosophers,” which invites an implicit comparison to unworldly or otherworldly philosophers who do not concern themselves with the ordinary business of life. Be that as it may, it is possible, I think, to be both — thinking both the worldly and the unworldly by turns. Thus is the thinker likely to experience a dialectic not only within the realms of thought, but also as part of the ordinary business of his life.

I find myself today thrown back onto the most abstruse and obscure points of technical philosophy in my attempt to clarify my understanding of very worldly concepts that attempt to elucidate what Marshall called “the ordinary business of life.” I find that I am once again taking down my reference works on ontology, epistemology, and philosophy of logic from my bookshelves, and this, I think, is a good thing. The cross-fertilization of thought, whether inter-disciplinary or intra-disciplinary, is usually a source of fruitful meditation. In particular, I find myself working on the idea of constructivism.

Constructivism means many different things to many different persons. It would almost seem that a sense of “constructivism” has been defined for every conceivable special field of inquiry or endeavor. There is constructivism in the visual arts, and a constructivism in music, and a constructivism in sociology, and, what most concerns me, a constructivism in the philosophy of logic and mathematics.

Dr. David C. F. Wright quoted his friend British composer Reginald Smith Brindle regarding a visit to Luigi Nono:

I went there mostly while he was composing Il Canto Sospeso, a politically orientated work of choral-orchestral character which involved the most abstruse constructivism I have ever come across. Mathematics governed every detail of the composition … the pitch of the notes, their duration, volume and sound character. In his study, there was a wall entirely covered with successions of numbers, notes and performance details and from this he extracted all the details of the composition. It seemed to me that all his intense constructivism was a certain formula for the creation of non-music, yet from recordings of his music, I got the impression of a highly sensitive artistry.

What Brindle describes is more commonly known as integral serialism or total serialism. The relation between constructivism and serialism is an interesting question in itself, but one that I will not address here. And while I don’t have a CD of Il Canto Sospeso, I did have a recording by the Arditti Quartet of Nono’s fragmente – stille, an idiotma, so I put this on as my theme music for constructivism.

I regard the philosophy of mathematics as the ultimate proving ground for all philosophical theories. One finds philosophical theories applied to the philosophy of mathematics in their purest form, and it is in their purest form that theories are seen in their nakedness, revealed to all the world for what they are. This is especially true for constructivism, but while constructivism is best tested by the austere ontology of logic and mathematics, it has universal implications.

Constructivism is a methodological concept, and the distinction between constructive methods and non-constructive methods recapitulates the ancient division between idealism and realism in ontology. One could say that constructivism is idealism put into practice as a method. What, then, is the method of idealism?

At present I am only trying to get clear about the concept of constructivism, its proper scope as a concept. I sent off an e-mail to the phil-logic discussion listserv and got some replies both on-list and off-list that provided some initial stimulation. It is, however, extraordinarily difficult to develop a sympathetic discussion on an e-mail listserv. Even when others are the list are interested in the idea, the tone of discussion can be brutal at times. There is a value in brutal honesty and openness of discussion, but there is also a value in having someone with whole one can share inchoate ideas and help to bring out what is valuable in them without destroying a fragile thought. However, I have no one to act as my intellectual second (i.e., kaishakunin, 介錯人) and thus I pour it out here instead.

It takes a true friend to perform the office of kaishakunin.

It takes a true friend to perform the office of kaishakunin.

I found an interesting discussion of constructivism in Detlefsen’s contribution to the Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, in which Detlefsen does try to formulate the theoretical unity of constructivism, although he never touches on predicativism. Should predicativism be considered something utterly different? There is also a great discussion of constructivism by Michael Hallett in the Handbook of Metaphysics and Ontology edited by Hans Burkhardt and Barry Smith, published by Philosophia Verlag (Hallett’s article is “mathematical objects”). While these two discussions are a great starting point, they don’t get to the essence of the question that is troubling me at the moment.


The many varieties of constructivism are different not only in detail but also importantly different in conceptual scope. Intuitionism, finitism, predicativism, and other conceptions that might generally be called constructivistic in tendency all restrict classical formal reasoning, but there does not seem to be any prima facie unity in virtue of which all deserve to be called constructivist. One of my off-list responses from the phil-logic listserv suggested that there would be “push back” at any attempt to classify intuitionism as a form of constructivism.

handbook of metaphysics and ontology

James Robert Brown’s The Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures has a section on “Constructivist Approaches” that quotes from Errett Bishop’s Foundations of Constructive Analysis. I don’t have a copy of Bishop’s book, so this is helpful. Bishop, at least, explicitly identifies his approach as constructivist, unlike Brouwer or Heyting, Poincare or Weyl, Yesnin-Volpin and Gauthier, Kielkopf and Wittgenstein. This self-ascribed constructivist identity carries more weight than all the other uses of “constructivist” combined.

James Robert Brown

Perhaps constructivism in its pure form should be defined more narrowly, strictly in terms of the avoidance of pure existence proofs, for example. But if we define constructivism more narrowly, then it would seem that there is still a need for a concept under which would fall all those theories of formal reason that restrict what Torkel Franzen called “classical eclectism,” and which would include a narrowly defined constructivism as well as other doctrines previously called constructivist. What concept could we use to cover all instances of principled restrictions upon formal reasoning, and is there any unity of motive in formulating and propounding principled limitations on formal reasoning?

The obvious course of action would be to elucidate the principles embodied in all such doctrines, loosely called “constructivist” up until now, and seek to systematically interrelate them. In every police drama one sees on television, the detectives on a difficult case assemble a large bulletin board upon which they display symbols for clues, and then map the interrelations between clues in an attempt to find a pattern that will solve the case. We need the conceptual equivalent of this in order to understand constructivism.

Two other obvious courses of action present themselves: simultaneously driving down into the foundations of constructivist doctrines while also extrapolating their consequences to the utmost limit. A convergence or divergence of either development would point to fundamental commonality or fundamental incommensurability.

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4 Responses to “Late Night Thoughts Listening to Luigi Nono”

  1. Alexander said

    Strange. It seems like all people on the internet (including myself) all over the world that listen to this constructivist music are interested in philosophy of mathematics, general semantics, logic, politics, scientific method and economics. It’s a very special social phenomenon.

    • geopolicraticus said

      Thanks for your interesting comment. As I am unaware of this social phenomenon, I would be happy to hear more. So if you’d like to elaborate, please do.



  2. Alexander said

    Throughout my life I’ve been questioning everything trying to find explanation to everything. For instance, I was never satisfied by mathematics that I was taught at school. This subject was presented without depth or substance as a mere number of algorithms aimed solely at some practical matters. That made me want to study Peano’s arithmetic as well as works of the luminaries such as Bertrund Russell, Ludwig Wittgenstein, Gödel and Frege. The abovestated example represents my attitude to life. I am never satisfied with any explanation. I observe life as a big mystery that let us into infinite possibilities of discovery. And it seems like music such as Luigi Nono’s Il Canto Sospeso or any other constructivist piece of art do correspond with my vision of life. Moreover, this art greatly corresponds with the aesthetics of the modern world because it allows me to observe my life and life in general as a dramatic and poetic experience the same way as some people of the 19th century observed life when listening to Wagner.
    I discussed constructisvist music with some people on the internet and I came to the conclusion that most of them share my attitude towards life. They question life the same way I do. In most cases they are interested in the same subjects that I am interested in. So, from my point of view such strict relation between interests in life and interests in art may be referred to as a social phenomenon. Though, I can not but mention that this phenomenon is not very widespread.
    I hope that my explanation wasn’t too long. Thank you for your interest.

    • geopolicraticus said

      Dear Alexander,

      No, not at all too long. I appreciate it that you made the effort to describe your relationship to twentieth century music and its relationship in turn to the wider cultural milieu.

      Bertrand Russell also questioned his earliest lessons in mathematics, and he went on to write Principia Mathematica with Alfred North Whitehead, so the questioning of not merely received habits of thought but presumed certainties has a history worthy of emulation.

      Your description of your early experience of mathematics education puts your finger right on the same thing that bothered me. Mathematics taught as a grab bag of algorithms is meaningless. Attempts were made to show that mathematics was relevant by showing that it was practical, but no effort was made (at , least, none in my experience) to show the theoretical unity and therefore the intellectual meaningfulness of mathematics.

      Best wishes,


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