Aboutness and Subject Matter

Origin. Stephen Yablo, Aboutness (2014), building on Lewis's "Statements partly about an observation" (1988) and Perry's earlier work on subject matter. The thesis: a sentence has a subject matter distinct from its truth condition, and the difference does explanatory work — in confirmation, in what a partial truth gets right, in why "the King of France is bald" fails differently from "2+2=5".

Models. Two sentences can be true in exactly the same worlds and be about different things. Truth conditions divide the space of worlds; subject matter divides it differently — into cells of worlds that agree on the topic. A sentence's content is then a pair: which cells, and which partition. Necessary equivalents share the first and can differ in the second, which is where hyperintensionality enters without any appeal to impossible objects.

Formalism.

Subject matter as a partition: A subject matter m is an equivalence relation ≈_m on worlds. w ≈_m w′ : the worlds agree on m. "The number of planets" partitions by that number; "arithmetic" partitions trivially (all worlds agree).

Divisions and parts: m ≤ n : n is at least as fine as m — n settles everything m settles. Subject matters form a lattice under this order.

Partial content (Yablo): A part of φ's content: a proposition ψ with φ ⊨ ψ, holding where φ holds and for φ's reasons. Not every consequence is a part: φ ⊨ φ ∨ ψ, but φ ∨ ψ is not part of what φ says. The filter on consequences is subject matter, not entailment.

Truthmaker connection: Fine's exact verification gives the same filter from below: a state exactly verifies φ if it is wholly relevant to φ's truth. Yablo's subject matter is the fusion of φ's verifiers' subject matters.

Recursive subject matter: sm(p) = the partition p induces sm(¬φ) = sm(φ) — negation is about what it negates sm(φ ∧ ψ) = sm(φ) ∨ sm(ψ) — join in the lattice Necessary equivalents: sm(φ) need not equal sm(ψ).

The application Yablo wants: Partial truth: a false sentence can get its subject matter right. "The King of France is bald" is about French royalty; "2+2=5" is about arithmetic. Both false, differently.

Symbols.

Metatheory. The partition account and Fine's truthmaker account converge: both filter the consequences of φ down to the ones φ is about, one from above by dividing worlds, one from below by exact verifiers. Whether they agree in general is not settled, and the cases where they part company are the ones the literature argues about. Subject matter is not compositional in the way truth conditions are — sm(φ ∧ ψ) is fixed by the parts, but sm of a quantified sentence depends on the domain, which is why the recursive clauses stop where they do.

Applies to. Partial truth and approximate truth. Confirmation, where evidence bears on a hypothesis's subject matter rather than on its truth condition. Verisimilitude. The semantics of "about", "on the topic of", and change-of-subject objections in argument. Enthymeme and relevance in informal reasoning.

Limitations. Subject matter is stipulated as a partition rather than derived, so the theory answers what a subject matter does and not what fixes it — two accounts of the same sentence's topic will disagree and nothing adjudicates. The lattice structure makes fine subject matters cheap and coarse ones rare, which inverts the intuitive order. And the machinery is a semantics without a proof theory: there is no calculus of aboutness, and the entailments it licenses are read off models one at a time.

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