Contemporary musical ontology has become fixated on musical works, treating them as the primary—often exclusive—subject of metaphysical inquiry. This paper argues that such work-centrism is methodologically limiting. Musical work is a heterogeneous category that resists unified ontological treatment, while the very concept of a work proves historically contingent and practice-relative. Moreover, work-centrism leaves un(der)theorized vast ranges of musical phenomena that merit ontological consideration. These limitations are diagnosed from testing the work-centric methodology against four desiderata for an ontological theory of music, each motivated by reflecting on musical phenomena and practices. I then propose a compositional approach to musical ontology, focused on musical elements (pitches, rhythms, motifs) and their interrelations under compositional operations, as a promising alternative. This approach not only meets the desiderata but also systematically tracks musical content—what makes something musical—thereby offering a stable foundation for philosophical theorizing about music as such.

In this paper I develop a version of musical formalism inspired by Schopenhauer. First, I present a Schopenhauerian account of music with a background of his metaphysical framework. Then, I define meaningfulness as an analog to a Kantian notion of purposiveness and argue that, in light of Schopenhauer, music is meaningful as a direct manifestation of the universal will. Given the ineffable nature of what music points to, its form lacks any representation of meaning. Music is therefore the mere form of meaningfulness, and it is precisely this mere form that gives rise to the infinite possibilities to ascribe it with a variety of musical meaning.

Generativism holds that objects enter our ontology by being generated from others via certain operations. Much work addresses specific cases—sets, mereological fusions, neo-Fregean abstractions—yet a foundational question persists: what makes an operation generative? Existing approaches localize generativity to particular applications, appealing to grounding, real definition, or essence, but each fails to generalize across the full range of paradigmatic cases. I argue that generativity is a global, structural feature of an operation's systematic applicative behavior. Working within a higher-order framework with plurals and a Finean logic of essence, I propose that an operation is generative when it is saturable—its applicative profile admits coherent refinement in every context so that every admissible behavior is uniquely realized—and every realized behavior traces a generative path affording the output an essential identity-explanation. The framework provides a unified account of iterative, compositional, and abstraction-based generation, showing that what appear to be heterogeneous modes of ontological formation are instances of the same structural phenomenon.

Non-eliminative structuralism struggles to reconcile the idea that mathematical objects are "positions in structures" with rigorous accounts of their identity. Dominant bottom-up approaches—generating positions via abstraction and reading off structural identities—work for sets but encounter friction with rigid and non-rigid structures pulling in different directions. I propose a top-down alternative: treat morphisms as metaphysically prior to objects, generate the structure itself first, then derive the positions it warrants. The paper introduces structural saturability as a criterion for generativity and develops Yoneda Essence, an essentialist interpretation of the Yoneda Lemma: an object's identity is exhaustively constituted by the network of transformations it supports. Taking the natural numbers as paradigm, I show how a canonical number structure is generated as the unique initial object from homomorphisms between discrete dynamical systems. The approach treats rigid and non-rigid cases uniformly and offers a rapprochement: generativity tracks essences in a structural way.

The platonist position in musical ontology faces a familiar puzzle: music seems created, historically situated, and intention-dependent, yet platonism treats musical objects as abstract and mind-independent. Attempts to preserve both often either deny that works are created or revise the orthodox conception of abstracta. This paper argues that this tension is illusory and proposes a trifold ontological framework on which the illusion dissolves: (i) a musical space of structural objects; (ii) pathways through that space constructed by composers; and (iii) presentations (performances, scores) that manifest these pathways. This distinction relocates the intuition of creation to pathways and presentations, while reserving the structural resources they utilize as uncreated abstracta. By analyzing the formal features of musical objects—specifically their multiplicity, invariance, and inheritance—I demonstrate that platonism offers the most compelling account of musical structure. This ontology respects both the abstract identity of music and the contingent, creative practices of its history.

Hanslick’s declaration that music’s content is tönend bewegte Formen (“sonically moving forms”) harbors an underappreciated tension: Formen suggests rigidity, bewegte insists on dynamism, tönend demands experiential accessibility. Standard formalisms privilege one component at the expense of others. I propose a reconstruction in which movement is primary. A musical form is a category whose objects are musical elements and whose morphisms encode directed transitions—leading, departing, resolving—between them. Since a category is individuated by its morphisms, a form is determined by its transition-pattern rather than any particular inventory of named elements, making the framework culturally neutral. Three kinds of musical movement are distinguished, with two further modes—enrichment and expansion—introduced via functors. The resulting formalism explains how meaning and affect emerge from compositional structure: music is expressive because its transition-structure maps, via structure-preserving functors, onto the dynamic contours of experiential processes, without reducing music to propositional content.

Fine's antipositionalism elegantly handles relations by replacing primitive argument-places with substitution patterns, but its extension to higher-order types remains unexplored. How can neutrality be preserved when predicates apply to relations themselves? I reconstruct antipositionalism by treating completions as functions from occurrence indices to objects, with the symmetric group acting by re-indexing, and identify three strategies for higher-order predication: manner-blind (the predicate holds of every completion), maximally permissive (of some completion), and equivalence-sensitive (application depends on equivalence classes of completions). I argue the third best preserves antipositionalist virtues and propose that the relevant equivalence is induced by substitution isomorphisms—pairs of re-indexing bijections and object-assignments satisfying compositional laws. The resulting isomorphism classes serve as arguments for higher-order predicates, maintaining neutrality while representing distinct ordered completions. I close by examining whether the framework is really antipositionalist or some disguised form of positionalism.