We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann algebras as a base category (Section 2); and the relation of our generalized valuations to (i) the assignment to quantities of intervals of real numbers, and (ii) the idea of a subobject of the coarse-graining presheaf (Section 3).

Les œuvres musicales et les sons semblent devoir résister aux tentatives faites pour leur attribuer un sens stable et clairement défini. Historiquement, le flou sémantique qui les caractérise a toujours compliqué la tâche de ceux qui se sont efforcés de leur attribuer une « valeur » esthétique, par exemple au sein d’une hiérarchie des genres. Il s’agit toujours d’endiguer leur dangereux excès asymbolique en les déchiffrant, en leur imposant symboles et prédicats. Le présent essai propose une analyse d’ Un re (...) in ascolto [ Un roi à l’écoute ] d’Italo Calvino (1976), redéfinissant à nouveaux frais la notion de souveraineté afin de mieux comprendre la nature d’une telle stratégie herméneutique, et les raisons de son échec. Le souverain tel que nous le décrit Calvino est-il en mesure de conférer un sens à la musique et au chant en les intégrant au sein d’un système sémantique clos? Ou l’expérience musicale doit-elle au contraire être décrite comme fondamentalement incompatible avec une telle herméneutique totalisante, appelant une analyse fondée sur une vision pluraliste, horizontale, et non-hiérarchique des relations entre les différents modes d’expression artistique? (shrink)

In the romantic tradition, music is consistently associated with madness, either as cause or cure. Writers as diverse as Kleist, Hoffmann, and Nietzsche articulated this theme, which in fact reaches back to classical antiquity and continues to resonate in the modern imagination. What John Hamilton investigates in this study is the way literary, philosophical, and psychological treatments of music and madness challenge the limits of representation and thereby create a crisis of language. Special focus is given to the decidedly autobiographical (...) impulse of the late eighteenth and early nineteenth centuries, where musical experience and mental disturbance disrupt the expression of referential thought, illuminating the irreducible aspects of the self before language can work them back into a discursive system. The study begins in the 1750s with Diderot's _Neveu de Rameau_, and situates that text in relation to Rousseau's reflections on the voice and the burgeoning discipline of musical aesthetics. Upon tracing the linkage of music and madness that courses through the work of Herder, Hegel, Wackenroder, and Kleist, Hamilton turns his attention to E. T. A. Hoffmann, whose writings of the first decades of the nineteenth century accumulate and qualify the preceding tradition. Throughout, Hamilton considers the particular representations that link music and madness, investigating the underlying motives, preconceptions, and ideological premises that facilitate the association of these two experiences. The gap between sensation and its verbal representation proved especially problematic for romantic writers concerned with the ineffability of selfhood. The author who chose to represent himself necessarily faced problems of language, which invariably compromised the uniqueness that the author wished to express. Music and madness, therefore, unworked the generalizing functions of language and marked a critical limit to linguistic capabilities. While the various conflicts among music, madness, and language questioned the viability of signification, they also raised the possibility of producing meaning beyond significance. (shrink)

In the romantic tradition, music is consistently associated with madness, either as cause or cure. Writers as diverse as Kleist, Hoffmann, and Nietzsche articulated this theme, which in fact reaches back to classical antiquity and continues to resonate in the modern imagination. What John Hamilton investigates in this study is the way literary, philosophical, and psychological treatments of music and madness challenge the limits of representation and thereby create a crisis of language. Special focus is given to the decidedly autobiographical (...) impulse of the late eighteenth and early nineteenth centuries, where musical experience and mental disturbance disrupt the expression of referential thought, illuminating the irreducible aspects of the self before language can work them back into a discursive system. The study begins in the 1750s with Diderot's _Neveu de Rameau_, and situates that text in relation to Rousseau's reflections on the voice and the burgeoning discipline of musical aesthetics. Upon tracing the linkage of music and madness that courses through the work of Herder, Hegel, Wackenroder, and Kleist, Hamilton turns his attention to E. T. A. Hoffmann, whose writings of the first decades of the nineteenth century accumulate and qualify the preceding tradition. Throughout, Hamilton considers the particular representations that link music and madness, investigating the underlying motives, preconceptions, and ideological premises that facilitate the association of these two experiences. The gap between sensation and its verbal representation proved especially problematic for romantic writers concerned with the ineffability of selfhood. The author who chose to represent himself necessarily faced problems of language, which invariably compromised the uniqueness that the author wished to express. Music and madness, therefore, unworked the generalizing functions of language and marked a critical limit to linguistic capabilities. While the various conflicts among music, madness, and language questioned the viability of signification, they also raised the possibility of producing meaning beyond significance. (shrink)