Containment Logic

Origin. Angell's analytic containment (1977, 1989) and Parry's earlier proscriptive principle are the ancestors. The modern systems: Fine's truthmaker semantics for exact entailment and containment (2016, 2017); Correia's account of factual equivalence and containment (2004, 2010); Yablo's Aboutness (2014), where containment is subject-matter inclusion. Ferguson (2023) surveys the family.

Models. A contains B when B's content is part of A's. Not just truth preservation. Intensional structure matters. Relates to grounding and essence.

Formalism.

Containment relation: A ≤ B: A's content contained in B's. Partial order on propositions. Not same as entailment. Structural, not just modal.

Truthmaker containment: What makes A true contains what makes B true. Truthmaker of disjunction ≤ truthmaker of disjuncts. Compositional structure.

Yablo's aboutness: Proposition about certain subject matters. A ⊃ B only if A, B share subject matter. Irrelevance blocked. Content-based implication.

Exact truthmaking: State s exactly makes A true. Not too much, not too little. Precise fit between truthmaker and truth. No extraneous content.

Fine's state space: States (situations) as truthmakers. States can fuse, factor. Bilateral semantics. Part-whole structure.

Subject matter: m(A) = what A is about. A → B requires m(B) ⊆ m(A ∧ B). Connection requirement. Aboutness preservation.

Comparison with relevance: Both require connection. Containment: mereological. Relevance: variable sharing. Different metaphors.

Symbols.

Symbol	Unicode	Meaning
≤	U+2264	containment
⊏	U+228F	proper containment
m(A)	—	subject matter of A
⊩ᵉ	—	exact truthmaking

Metatheory. Content mereology. Truthmaking. Grounding. Subject matter.

Applies to. Philosophy of logic. Metaphysics. Truthmaker theory. Aboutness.

Limitations. Metaphysically loaded. Technical complexity. Limited formalization. Interpretation debates.