Ivano Zanzarella

Abstract The Greek composer and architect Iannis Xenakis has shown in Formalized Music (1963) how it is possible to compose or describe music and sound by means of probabilistic laws from mathematics, information theory and statistical mechanics. In his theory, scientific concepts and properties such as entropy take on a musical meaning in that they become also properties structurally instantiable by music. Philosophically speaking, this raises many important questions about the relation between science and the arts. One of these questions concerns in particular the possibility for aesthetic symbols (like musical compositions) to convey scientific understanding, and understanding in general. In the present work, I claim that this question can be answered positively. In general, understanding does not necessarily depend on truth, explanation and propositionality (non-factualism, non-reductivism). Understanding can be conveyed also in non-propositional domains, in particular by means of exemplification. Since aesthetic and musical symbols are non-propositional, they can advance understanding possibly by exemplification, and in particular scientific understanding as long as they exemplify scientific concepts and properties. I moreover substantiate my claim by taking a case study: the concept of entropy in music. On the basis of Xenakis’ stochastic theory of music, I show how by exemplifying this concept, music can advance understanding of it.

Because of its non-representational nature, music has always had familiarity with computational and algorithmic methodologies for automatic composition and performance. Today, AI and computer technology are transforming systems of automatic music production from passive means within musical creative processes into ever more autonomous active collaborators of human musicians. This raises a large number of interrelated questions both about the theoretical problems of artificial musical creativity and about its ethical consequences. Considering two of the most urgent ethical problems of Musical AI (music job replacement and machine musical authorship), we show in this essay the strict dependence of every form of acknowledgment of a moral and legal status to systems of automatic music production from the theoretical account of musical creativity by turns implicitly or explicitly adopted, arguing, on the basis of pragmatic reasons, for the necessity and the desirability of this acknowledgment.

In the present paper the philosophical and mathematical continuity alleged by A. Robinson in Nonstandard Analysis (1966) between his theory and Leibniz’s calculus is investigated. In Section 1, after a brief overview of the history of analysis, we expose the historical, mathematical and philosophical aspects of Leibniz’s calculus. In Section 2 the main technical aspects of nonstandard analysis are presented, and Robinson’s philosophy is discussed. In Section 2.1 we claim the absence of a complete and direct continuity and the only possibility of a conceptual similarity between Leibniz’s and Robinson’s theories, both at the philosophical and at the mathematical level.

This essay aims to inquiry into the main factors responsible for the growth of modern acoustics, which basically have to be traced back to the empirical turn occurred in science of music around 1600. Helmholtz’s theory of sound will be regarded as most scientifically significant archetype of modern acoustics. In Section 1 a general historical overview of the science of music will be given and its importance for the development of modern science and mathematics considered. In Section 2 the internal historical roots of modern acoustics, thus of Helmholtz’s theory of sound will be analyzed. Finally, in Section 3 positive and negative elements of Helmholtz’s acoustic will be discussed and its external historical roots as well as its actual epistemological relevance examined.

Originally appeared in the field of thermodynamics, the concept of entropy, especially in its statistical acceptation, has found applications in many different disciplines, both inside and outside science. In this work we focus on the possibility of drawing an isomorphism between the entropy of Boltzmann’s statistical mechanics and that of Xenakis’s stochastic music theory. We expose the major technical aspects of the two entropies and then consider affinities and differences between them, both at syntactic and at semantic level, hereto particularly referring to the philosophical problem of the asymmetry of time.

The connection between science and mathematics is often considered necessary and insoluble. Therefore, a relationship between mathematics and humanities or arts is deemed exceptional or sometimes unnatural. Nevertheless, on the basis of historical, ontological and epistemological researches it can be noted that it’s impossible to warrant the immediate identification between mathematics and sciences on a deeper level than the practical one. Given the instrumentality and then the unnecessity of this connection, the relationship between mathematics and not-scientific disciplines is undeniable, even if the mathematics in the explicit formalisms which we know doesn’t appear in them. It’s possible to demonstrate this relationship not only with philosophical argumentations, but also whit empirical verifications, e.g. in the music and in particular in the music of J. S. Bach. Such an epistemological thought finally leads to the question on the possibility of knowledge in the art in comparison to the epistemological characteristics of the Galilean and Post-Galilean science.