Bundle theory, developed in different forms by Hume, Russell, and more recently by Paul (2017), holds that objects are bundles of properties without underlying substrates. Trope theory, developed by Williams (1953), Campbell (1990), and Maurin (2002), holds that properties are particularized (this redness here, that hardness there) rather than universals shared across instances. Both positions challenge the substance role of Φ (causal persistence across temporal change, the third structural Condition alongside T and S, borne by Substance just as T and S are borne by Time and Space): if there are no underlying substrates, what does causal persistence inhere in? If properties are particularized tropes, what bundles them into the persisting configuration the structural account requires?

The reply distinguishes the metaphysics of property-bearing from the structural role of Φ. The substance role is the role of causal persistence across temporal change: whatever obtains in such a way that the same configuration is causally connected from one moment to the next. Bundle theory and trope theory are accounts of how property-bearing works at a fine grain; they are not denials that something persists. A bundle that persists across time is, for the present argument, an instance of Φ. A collection of compresent tropes (tropes co-occurring at the same location) that maintains its compresence across temporal succession is, for the present argument, an instance of Φ. The present argument is not committed to the substrate metaphysics that bundle and trope theories deny; it is committed to the structural role those metaphysics still have to fill, however they fill it.

Two finer questions the bundle and trope theorist press do not change this. The first is Bradley's old regress: if the tropes are bound into one bundle by a relation, and that relation is itself a trope, it requires its own binder, and the bundle never closes. The regress is a real pressure on bundle theory's internal economy. Renaming compresence as S holding across Φ does not by itself solve it; the bundle theorist still owes an account of what unifies the tropes, whether primitive compresence, a non-relational tie, or another device. The structural account can remain neutral on that account while requiring any successful proposal to realize differentiation and continuity. Whatever the bundle theorist settles on (a primitive compresence relation, a non-relational tie, a brute fact of togetherness) the structural roles are what that settlement must instantiate, not a rival to it. The second is whether the bundle endures, wholly present at each moment, or perdures through distinct temporal parts. Φ is neutral between them: it asks only that the configuration be causally connected from one moment to the next, a demand the endurantist meets through identity and the perdurantist through genidentity among temporal parts. The persistence-metaphysics dispute (pressed in its perdurantist form at [§4.2.8](<4.2.8 Stage Theory.md>)) settles how Φ is realized, not whether it is.

*What is established.* The reply matches the reply to ontic structural realism ([§4.3.9](<4.3.9 Structural Realism.md>)) in shape. The present argument identifies the roles any configuration must instantiate; metaphysical accounts of how the roles are filled are downstream of the necessity claim. Bundle theory, trope theory, substance theory, and process theory are competing answers to a question that arises only after [§2.6.8](<2.6.8 Ontological Identity.md>) has specified the Φ / Physicality role and [§2.7](<2.7 Nothing to Consider.md>) has shown how that role belongs to the Conditions-as-Nature structure.


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← [4.3.9 Structural Realism](<4.3.9 Structural Realism.md>) | [4.3.11 Mereological Nihilism](<4.3.11 Mereological Nihilism.md>) →
