Armstrong (1989, 1997) defends a combinatorial theory of modality. Possibility, on this view, is the combinatorial space generated by recombining the actual world's fundamental constituents, particulars and universals (the concrete individuals and the repeatable properties they instantiate, in Armstrong's technical sense), in all possible ways consistent with their adicity (the number of argument-places a universal takes) and type. Possible worlds are not concrete (Lewis) or abstract (ersatzism); they are constructions out of actual elements. The space of possibility is wholly determined by what actually exists.

The combinatorialist's modality is grounded in the actual. The argument here is consonant with this in its commitment to the actuality of T, S, and Φ. Where the two part ways is on the source of the recombinatorial range. Armstrong takes the actual particulars and universals as primitive and lets recombination do the rest. The present argument identifies T, S, and Φ as necessary features of the actual, which means that recombination cannot generate worlds in which T, S, or Φ fail to obtain, since their failure is not a configuration of the elements but the absence of the conditions for any configuration.

This is a constraint on combinatorialism, not a refutation of it. Combinatorialism is consistent with the argument provided it acknowledges that the recombinations operate within the structural conditions, and that acknowledgement can be extracted from the combinatorial operation itself, without first granting the structural argument's conclusions. Combinatorial generation requires distinguishable constituents and admissible arrangements, so it directly presupposes a thin difference-role. But the modal construction is not itself a temporal process: possible combinations need not be produced one after another, and the constituents need not persist through an act of recombining. Temporal succession and causal bearing must be established within any concrete change-world represented by a combination, not inferred from the theorist's operation on the base. The structural conditions are therefore not items in the actualist base awaiting recombination: the difference-role is presupposed by any combinatorial generation, and the richer roles fall due wherever a combination is offered as a concrete change-world rather than a description.

A second observation. Combinatorialism faces a familiar pressure: it cannot easily generate alien properties, properties that no actual entity instantiates. If recombination is restricted to the actual, the modal range is narrower than most modal intuitions allow. Various extensions have been proposed (Armstrong himself, then Sider 2003): typically by admitting alien properties as primitive possibilities not generated by recombination, or by allowing modal primitives beyond the actualist base. The combinatorialist will call these workable refinements, but they are not free, and naming the cost precisely is what the objection requires. The appeal of combinatorialism was exactly its strict actualism (the thesis that only actually existing things exist, with no real merely-possible entities): the promise that the entire space of possibility is fixed by what actually exists, with nothing modal taken as primitive. An alien property admitted as a primitive possibility is, by definition, a possibility not fixed by the actual base, so the extension purchases modal adequacy by conceding the very reduction that made the position attractive. And the resulting view is no longer the actualist economy it advertised but a base of actual elements supplemented by free-floating modal primitives. The dilemma is stable: stay strictly actualist and the modal range is too narrow to capture ordinary modal intuition; widen it and the actualist motivation lapses.

Either horn is consistent with the present point, because T, S, and Φ are not candidate alien properties at all: not properties an entity might or might not instantiate, but conditions on there being entities, properties, or recombinations in the first place. The present argument does not turn on the resolution of this debate. What it offers is a fixed point: whatever combinatorialism includes or excludes, T, S, and Φ are not in the recombinable set. They are what the actual base must already instantiate for there to be anything to recombine.

*What converges.* Combinatorialism is, like ersatzism, a theory of how modal vocabulary is grounded. The present argument is a theory of what modal vocabulary describes. The two are compatible if the former locates its grounds within the structural conditions the latter identifies.


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← [4.4.2 Linguistic Ersatzism](<4.4.2 Linguistic Ersatzism.md>) | [4.4.4 Modal Fictionalism](<4.4.4 Modal Fictionalism.md>) →
