The analysis begins with Leibniz’s principle of the identity of the indiscernibles: if two objects share every property, they are identical. Its contrapositive holds that any two distinct objects must differ in at least one property. Although this formulation is logically stringent, the paper argues that it relies on a naïve separation of an object from the state and environment in which it exists. Properties are also difficult to compare without specifying the resolution, boundary conditions, initial conditions and time at which they are measured. Information about every possible property is necessarily incomplete, making the apparent universality of Leibniz’s original criterion problematic.

Quantum mechanics makes the difficulty particularly clear. Electrons and photons of the same type cannot, in principle, be distinguished as individuals solely by assigning them different properties or histories. As physicist Hermann Weyl put it, “Even in principle one cannot demand an alibi of an electron.” Quantum entanglement further weakens the idea that an object can be evaluated independently of its surroundings. Measuring one member of an entangled pair immediately changes the state associated with the other, even when the members are widely separated. Under these conditions, the connected entity and its state may have to be considered together rather than as an autonomous object opposed to an external environment.

The paper distinguishes bosons from fermions as a starting point for a physical account of individuality. Bosons, including photons, can occupy the same quantum state, and a boson combined with a particular delocalized state may itself be indistinguishable from another equivalent combination. Fermions, including electrons, cannot occupy the same quantum state because of the exclusion principle. This prevents two electrons from being in precisely the same state, but it does not make “electron” a personal name. Electrons can move between states and roles during chemical reactions, allowing the particle to be identified independently of a particular state. The term “electron” is therefore treated as a generic designation rather than a name reserved for an individual.

To accommodate this feature, the proposed identity criterion embeds each object in an environment that defines its state. The environment can be local, such as the elastic and electric effects surrounding an impurity atom in a crystal, or it can extend beyond a local region in the limiting case of quantum entanglement. Two objects are considered identical only when exchanging them leaves all relevant properties of the sufficiently large zone unchanged across relevant embeddings and, for time-dependent properties, throughout the relevant time. The formal exchange test also requires transferability: an object must remain identifiable when placed in different roles or states. This modified approach evaluates an object together with its state-defining surroundings rather than assuming that the two can be separated cleanly.

The distinction between constituents and compound objects becomes important at larger scales. Two impurity atoms can be identical if they produce the same properties in the bulk of a crystal and at its surface. By contrast, a crystal containing an immobile impurity in its bulk may remain distinct from one containing the same impurity at the surface, even though a thought experiment could imagine transferring the atom between the two positions. The paper calls this virtual transferability: the constituent can be considered transferable for purposes of identifying the particle, but the two constituted crystals are not genuinely interchangeable. A dislocation or other defect can also be decisive at low temperatures, yet disappear at sufficiently high temperatures and long waiting times. Irreversibility and individuality are therefore not absolute yes-or-no properties; they depend on physical parameters, including temperature and the relevant time scale.

Macroscopic comparisons introduce averaged properties and what the author calls statistical identity. Two crystals may appear identical in average composition, shape or defect concentration while differing in their microscopic arrangement. Enlarging the zone under examination incorporates more particles and interactions, making additional microscopic differences relevant. The transition between microscopic and macroscopic identity is thus controlled in part by the size of the region considered. Some properties, such as percolative properties or properties highly sensitive to tiny deviations from a perfect state, reveal microscopic differences that broader averages conceal. A measurement that establishes statistical identity therefore does not necessarily establish strict identity in every microscopic respect.

Following increasing complexity, the framework traces a progression from elementary particles to atoms, molecules, condensed matter, crystals, cells, organisms and people. Small, defect-free ice crystals may remain reproducible and interchangeable, whereas larger crystals can develop cracks, boundaries, dislocations, inclusions and other frozen structural features that make them singular. Snowflakes illustrate how unique surface morphology can arise, although the author notes that individuals are not ordinarily given personal names because snowflakes are still treated as reproducible. The Cullinan diamond is presented differently: its exceptional size and unique frozen features were understood to be unreproducible, making an individual name appropriate. Even here, however, the boundary between a feature that is negligible and one that justifies individual naming is not completely sharp.

Irreversibility by itself is therefore insufficient in the analysis; irreproducibility is also required. A stable dislocation can distinguish a defective crystal from a perfect one, but a comparable feature might be recreated under suitable conditions, weakening the case for a personal name. A person, by contrast, accumulates an extensive sequence of structural changes through a particular history. Ageing is relevant under the paper’s physical meaning of irreversibility as a frozen, non-equilibrium condition, although the author distinguishes this usage from other biological meanings of irreversibility. Twins and clones do not erase the effects of their separate histories: accumulated differences cannot be reversed or reproduced in full. The same reasoning can apply to transient but uniquely structured events, which helps explain why individual hurricanes are commonly given personal names.

The analysis also clarifies the difference between generic designations and personal names. A designation such as methane identifies molecules treated as identical under specified conditions, while a taxonomic term such as “bear” identifies a group of similar individuals without singling out one. A personal name marks an entity whose individuality is practically or culturally relevant. Uniqueness alone does not guarantee that naming is reasonable: people do not usually name individual mosquitoes or plants, although they commonly name pets. The paper’s illustrative sequence moves from mammals to bears, then to a particular bear family, and finally to one family member, showing how narrowing the properties retained in a description produces increasing individuation. Overall, the framework remains a philosophical proposal rather than a quantitative model or an experimentally tested law. Its central claim is that philosophical principles become useful for physical reality only when their terms are reconciled with physics: strict indistinguishability calls for generic designations, irreversible structure enables individuation, and irreproducibility makes personal naming appropriate.

Subject of Research: A theoretical framework for physical identity, individuality and personal naming

Article Title: Identity, individuality and naming

Article References: Maier, J. (2026). Identity, individuality and naming. Humanities and Social Sciences Communications, 13(1), Article 1844. https://doi.org/10.1057/s41599-026-09507-8

Image Credits: AI Generated

DOI: 10.1057/s41599-026-09507-8

Keywords: identity of indiscernibles, quantum indistinguishability, personal naming, irreversibility, irreproducibility, many-body systems, philosophy of physics, statistical identity, quantum entanglement, ageing, Identity, individuality