A quasi-set theory without atoms and its application to a quantum ontology of properties

DÉCIO KRAUSE; JUAN PABLO JORGE; OLIMPIA LOMBARDI

SYNTHESE (DORDRECHT)

SPRINGER

Lugar: Berlin; Año: 2025

0039-7857

One of the mainontological challenges posed by quantum mechanics is the problem of theindistinguishability of so-called “identical” particles, that is, particlesthat share the same state-independent properties. In the framework of thisphilosophical problem, a quasi-set theory was formulated to provide a propermetalanguage to deal with quantum indistinguishability; this theory includedcertain Urelemente called m-atoms,representing essentially indistinguishable objects. In turn, over the last twodecades, the Modal Hamiltonian Interpretation proposed an ontology ofproperties, totally devoid of objects, where quantum systems are bundles ofinstances of universal properties. Therefore, the original quasi-set theory, with its m-atoms, does not adequately reflect the structure ofan ontology devoid of objects. The purpose to the present article is tointroduce a new quasi-set theory that does not include atoms at all: elementaryitems correspond to properties and are also represented by quasi-sets, whichcan be only numerically different. The final aim is to apply this new quasi-settheory to the MHI ontology.