Properties, Persistence, Profusion

Rethinking the ‘One over Many’ Problem

Chris Tillman :: University of Manitoba

Marist :: 09.19.25

0. The ‘One over Many’ Problem

Apparently, there can be something identical in things which are not identical. Things are one at the same time as they are many. How is this possible? (D.M. Armstrong 1978: 11)

Explaining identity among diversity: Classical Approaches

·       Platonist Realism There are abstract Forms in which distinct concrete things participate

·       Aristotelian Realism There are abstract universal entities ‘present in’ distinct concrete things

·       Nominalism Distinct concreta can ‘share a name’ without literally sharing anything intrinsic

·       ‘Ostrich’ Nominalism It is a brute fact that distinct concrete things resemble each other

·       ‘Class’ Nominalism Distinct concreta form sets (‘classes’) that track resemblances

·       ‘Trope’ Nominalism Certain non-repeating ‘tropes’ resemble each other/form ‘classes’/‘fuse’

In general, Realist views endorse repeatability by saying there is an abstract entity that is repeatable and has such-and-such character (Platonism vs Aristotelianism)

In general, Nominalists reject repeatability since they reject abstract entities (or, at least, repeatable abstracta, if they accept abstract classes and tropes—cf. Cowling et al. 2025)

All parties share a common commitment to the Platonist ideology of abstract vs concrete (even if they think one of the ideological categories is unoccupied); a central metaphysical task is to situate the ‘furniture of the universe’ with respect to the abstract/concrete distinction.

1. Against Abstract/Concrete

·       No one knows what it is! Here are some proposals from Falguera et al. 2021, which are fodder for a fun afternoon developing counterexamples:

Concrete Abstract

Causal Acausal

Spatiotemporal Non-spatiotemporal

Contingent Necessary

Particular General

Urelement Set

·       ‘Metaphysical Misfits’ that seem neither abstract nor concrete

A very incomplete list: these words, this talk, the paper on which it is based, the institution we’re in, the clothes we’re wearing, the brands responsible for them, our body parts, our genes, our epigenotypes, the atoms we are made of, the species we belong to, the ideas we have and have learned, the songs and stories we engage with, the country we’re in, the laws that ‘govern’ it, and on and on and on and on.

(Many ‘creatures of metaphysics’ are metaphysical misfits, too—‘impure’ sets, states of affairs, events, singular propositions and properties, and so on—golems of supposed abstracta and concreta!)

·       Detriment to the debates: Many theorists of ‘metaphysical misfits’ (such as ontologists of art or linguistics, to pick just two) devote a lot of time and effort to arguing about whether this or that metaphysical misfit is ‘really’ abstract or concrete, against the backdrop of utter consensus that no one knows what these alleged distinctions even amount to. Fruitless degenerating research programme.

The abstract/concrete distinction . . . is a relic of a certain theory . . . But this is just a theory, nothing more. It’s not sacrosanct; nothing supports it other than tradition; and it should stand aside if it obstructs attractive simplification of ideology. (Sider 2013: 284.)

2. Revisiting the One over Many

The problem, at its core, is to explain identity among diversity; the phenomenon of repeatability. The ‘Classical Approaches’ countenance a single model of repeatability: abstract entities of a broadly Platonist or Aristotelian bent. But ‘abstract’ is a theoretical term of art. We can drop the deleterious ideology and look at the problem anew.

Identity among diversity shows up in a few distinct ways:

Properties Sometimes diverse entities have the same quality/feature/attribute/aspect/property, as when those jeans and her hair are both blue. Blueness repeats by being manifested by those jeans and her hair.

Persistence Sometimes an entity or individual itself ‘repeats’ when different material manifests it, as in the case of us (or our bodies). Mark Carney in the ‘60s and Mark Carney in his 60s ‘are’ ‘both’ Mark Carney, but the material making up Carney in the ‘60s is distinct from the material making up Carney now that he’s in his 60s. Carney is an object that repeats.

Profusion Sometimes instead there is a repeatable object. The letter ‘o’ doesn’t seem to ‘persist’ over the page by having different manifestations; at least, not in the way Carney seems to persist over time by being manifested by different material. Rather, there are many distinct ‘o’s that are all ‘o’s, in some sense. ‘o’s are profuse repeatable objects as opposed to repeatable qualities like blue or objects that repeat, like Carney.

(Perhaps, when stated this way, shorn of Platonist ideology, you struggle a bit to see the important differences between these ways of manifesting identity among diversity. Me, too.)

But Properties is usually addressed by adopting one of the ‘Classical Approaches’ above, while Profusion is usually approached through the lens of C.S. Peirce’s (1906) ‘type/token’ distinction (with an eye to the ‘Classical Approaches’), and Persistence receives a completely different treatment, usually in terms of versions of ‘three-dimensionalism’/endurantism or ‘four-dimensionalism’/perdurantism.

3. A Different Approach: Locationism

A central tenet of Locationism is that repeatable entities are in some sense manifestable or manifested. This is the sense in which qualities are ‘present in’ substances, people are found where their ‘nutrients’ are, and the word ‘of’ entered Old English and is found wherever Old English or its descendants are spoken. Locationism seeks to explain repeatability—identity among diversity—by scrutinizing the ‘manifestation structure’ of repeatable entities. Different constraints, presuppositions, or goals can yield different versions of Locationism.

A Guiding Thought

It's relatively uncontroversial that the 'metaphysical misfits' have at least a temporal location--the letter 'o' did not exist "since the Dawn of Time", nor did Marist. But our world is one in which the temporal and the spatial are intimately related. So if something has a temporal location, it ipso facto has a spatiotemporal location. So one way to start to get a grip on the nature of repeatable entities is by coming to terms with the ways in which they are spatiotemporally located. Hence, Locationism.

Two Toy Examples: Platonist Locationism and Eleatic Eternalist Endurantism

Platonist Locationism posits two ‘manifolds’, echoing Plato. One is the familiar spatiotemporal manifold; the other is ‘quality space’. There are also two locative relations on manifolds: spatiotemporal location and location in quality space. To share a spatiotemporal part is to jointly occupy a spatiotemporal location. To share a quality is to jointly occupy a location in quality space. Platonist Locationism yields an immediate account of Properties, though it’s underdeveloped with respect to Persistence and Profusion.

Eleatic Eternalist Endurantism posits a single spatiotemporal manifold where all regions are ‘equally real’ (Eternalism). Everything has a spatiotemporal location and is located where it is manifested (Eleatic) by being wholly located wherever it is manifested, and multiply wholly located iff it has more than one location (Endurantist). In pictures (due to Gilmore et al. 2024):