The Argument from One-Category Ontology to Atheism

According to L.A. Paul's one-category ontology, there is just one kind of thing: qualities (i.e., properties). Qualities are universals -- i.e., repeatable entities -- that (arguably) exist necessarily and a se, and have a nature closer to Aristotle's immanent (non-substantial) forms than Plato's transcendent forms (there are no uninstantiated qualities). All the rest of reality is ultimately explained in terms of mereological fusions of n-adic qualities.[1] The fusion relation is a composition relation, and so derivative entities are composed of basic qualities.[2], [3] The resultant picture is mereological bundle theory:

On my view, matter, concrete objects, abstract objects, and perhaps even spacetime are constructed from mereological fusions of qualities, so the world is simply a vast mixture of qualities, including polyadic properties (i.e., relations). This means that everything there is, including concrete objects like persons or stars, is a quality, a qualitative fusion, or a portion of the extended qualitative fusion that is the world-whole. I call my view mereological bundle theory. (Paul, "A One Category Ontology", p. 2) 
According to mereological bundle theory, the world (here, I need not confine myself to the physical world, so by ‘‘world’’ I mean the whole world, not just the cosmos) is a vast mixture of properties, some with a single location (whether in configuration space, or in spacetime, or in something else), some with many locations, some located everywhere, and perhaps even some without any location at all (Locations are defined by n-adic properties. For simplicity, take the fundamental space to be relational, and define up ‘‘points’’ in the space using these relations and properties). The world is constructed from arrangements of properties and relations that are fused together to make things of all sorts: concrete objects, abstract objects, events, states of affairs, facts, fields, regions, and anything else there is. So, according to the mereological bundle theorist, fields, particles, entangled systems of particles, spaces, molecules, cells, bodies, persons and societies are all constructed, most fundamentally, from fusions of properties and relations. (Paul, "Building the World From Its Fundamental Constituents", p. 242).

Paul's one category ontology provides a nice ontological framework for contemporary physics:

...consider the wave-function realist who takes the world-whole to be a wavefunction. On the GRW theory of the world, the world is a universal wave function that evolves in accordance with the dynamical laws. Understood in terms of mereological bundle theory, the wavefunction is the fusion of amplitude and phase properties (along with any other properties of the system) with structuring properties or relations, including the structuring relations described by Schrodinger’s equation and by the collapse postulate. A variant of this view can fit the Everettian approach, and one can also fit David Albert’s (1996) treatment of Bohmian mechanics by adding a world-particle that is simply a fusion of properties to the plurality of things. (Ibid., p. 254).

Paul's hypothesis of a one-category ontology is much more parsimonious than theism's, which posits irreducible substances -- and irreducibly different kinds of substances -- in addition to qualities. It also also has wider scope than theism, as it can explain God (if there is a god) in terms of a fusion of qualities. It can also explain the existence of God in terms of a derivative being that supervenes upon the modal space of qualities. Unfortunately, the latter two claims are incompatible with classical theism, as they violate the doctrine of divine simplicity and both conjuncts of the aseity-sovereignty doctrine (i.e., the doctrine that (i) God is an absolutely independent being, dependent upon/derivative of nothing and (ii) everything distinct from God depends upon her for their existence). All else being equal, then, a one-category ontology of qualities is a more plausible theory of ultimate reality than theism.

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[1] On Paul's account, the relation of mereological bundling here is not a fundamentally spatiotemporal one of spatiotemporal parts composing a spatiotemporal whole. This is because contemporary physics seems to have shown that spacetime isn't fundamental (think, for example, of wave function realism with respect to quantum mechanics, theories of quantum gravity that take spacetime to be emergent, etc.).

[2] Question: How does a quality become spatiotemporally localized on Paul's view? Answer: By bundling with spatiotemporal properties/relations: "Objects may have their locations in virtue of being fused with whatever location properties and relations there are that define the actual space of the world, and many objects will have a physical structure in virtue of having location properties and relations as parts of their fusions, or in virtue of being part of a larger fusion which has location properties and relations as parts. The character of the space might not be what we take the character of ordinary spacetime to be, but the structure of the space is generated by fusing qualitative properties with relevant properties and relations that define the space as determined by modern physics. Hence, the view is consistent with (and explicitly accommodating of) various approaches in modern physics: it is friendly to structuralism, and is perfectly consistent with realist interpretations of the ontology of quantum mechanics, for example, with realism about the wavefunction." (Paul, Building the World From Its Fundamental Constituents", p. 242).

[3] As Paul points out, her one-category ontology is compatible with a parts-to-whole mosaic, as well as a holistic whole-to-parts picture. She prefers the latter because it's a better fit with with quantum holism/entanglement phenomena.

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