Supersubstantivalism

Where the relationist denies that spacetime is a substance at all, the supersubstantivalist takes the opposite extreme: not only is spacetime a substance, it is the only substance. Material objects are not things in spacetime, occupying its regions from outside; they simply are regions of spacetime, or states or properties of it. A particle is a knot, a lump, or a local intensity of the one underlying entity — the spacetime field itself. On this monistic picture the traditional dualism of container and contents, spacetime plus the matter that fills it, collapses into a single geometrical stuff. It is the boldest form of substantivalism, and although a minority view, it has recurred whenever physics has seemed to reduce matter to geometry.

This page states the position, its history, and its costs and benefits; it is the counterpart, at the substantival extreme, of the relationism developed in Mach's principle.

The core thesis

Ordinary substantivalism is dualistic: it says spacetime exists in its own right, but so do material bodies, and the bodies stand in an occupation relation to spacetime regions — the region is here, the body is here, and the body "fills" it. Supersubstantivalism eliminates one side of this. There is spacetime, and material objects are identical to (or wholly constituted by, or reducible to) spacetime regions and their geometrical or field-theoretic properties. Instead of matter at a region, there is just a region in a certain state.

Two grades are worth distinguishing:

Identity supersubstantivalism — a material object is the spacetime region it occupies. To be a table is to be a certain four-dimensional tube of spacetime with the right properties.
Constitution/property supersubstantivalism — material objects are not identical to regions but are constituted by them, or are states of the spacetime field, much as a wave is a state of the ocean rather than a thing added to it.

Either way, the ontological inventory contains one basic kind of thing.

The historical thread: matter as geometry

Supersubstantivalism has surfaced repeatedly whenever it looked as though matter might be nothing but structured space:

Descartes held that extension is the essence of body and that there is no vacuum — the physical world just is extended substance, so that "body" and "space" are not really distinct. This is an early monism of extension, though Cartesian in idiom.
Clifford, in the nineteenth century, conjectured that matter and its motion are just variations in the curvature of space — "the theory of space-curvature which I hold" — an astonishing anticipation of general relativity.
Einstein's general relativity gave the idea real physics: the metric field is a dynamical entity in its own right, and matter curves it. This invited the thought that matter itself might be a feature of the metric.
Wheeler's geometrodynamics (mid-twentieth century) pursued exactly this: the programme of building particles, charge, and fields out of pure geometry — "mass without mass, charge without charge" — with wormholes and curvature knots standing in for matter. Wheeler's slogan was that physics is "geometry all the way down." Although geometrodynamics did not succeed as a complete theory, it is the clearest modern expression of the supersubstantivalist impulse.

The case for

Supersubstantivalism is motivated by parsimony and by the trajectory of physics:

Ontological economy. One kind of substance is simpler than two. The awkward primitive relation of occupation — how exactly does a body "fill" a region? — disappears, because the body is the region.
Fit with field theory. Modern physics already describes matter as excitations of fields defined at every point of spacetime — see particles as excitations of quantum fields. If a particle is a mode of a field, and the field is a state of spacetime, the supersubstantivalist reading is a small further step: everything is local structure of the one spacetime entity.
Dissolving the hole worry differently. With matter identified with spacetime states, some of the awkward questions about the relation between the manifold and the fields take on a different shape (though the hole argument's core about point-identities still bites).

The case against

The problem of subregions. If a table is identical to a region of spacetime, what distinguishes the table-region from the countless arbitrary neighbouring regions that are not tables? The view must supply a principled account of which regions are objects and which are mere geometrical parcels — otherwise it either over-populates the world with junk objects or must smuggle back a matter/space distinction to mark the difference.
Change and modality. A body seems able to move — to occupy different regions at different times. But a region cannot change which region it is. Identity supersubstantivalism must therefore reconstrue motion and persistence, typically in a four-dimensionalist key (the object is the whole tube, "motion" is the tube's shape), which ties it to contested views about persistence.
Empirical underdetermination. Nothing in the physics forces the identification: one can always read the same theory dualistically (spacetime plus fields on it). Supersubstantivalism is an interpretive choice, and its rivals accuse it of buying economy at the price of intuitive violence — tables and people turning out to be, quite literally, shaped bits of space.

Where this sits

Supersubstantivalism marks the far substantival pole of the ontological question and of the substantivalism–relationism spectrum: the relationist says there is no spacetime over and above bodies, the dualist says there is both, and the supersubstantivalist says there is only spacetime. It draws its plausibility from the way general relativity and quantum field theory already geometrise and "field-ify" matter, and its persistence problems push it toward the four-dimensional ontology of the block universe. With this the ontology subfolder is complete; the time pages take up the second master question — whether the passage of time is real.