README⤓ .txt 2026-07-17T121634.146 000000000000720 Logics in which necessarily equivalent formulas are not interchangeable. A possible-worlds semantics identifies a proposition with a set of worlds, and that identification is what makes 2+2=4 and every other necessary truth the same proposition. The entries here refuse it, and each refuses it by replacing the point of evaluation or the semantic value with something finer: a partial state that exactly verifies, an impossible world where classical laws fail, a content or subject-matter that a formula is about.
Aboutness⤓ .md 2026-07-17T121634.146 000000000000736 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".
Analytic Implication⤓ .md 2026-07-17T120407.600 000000000000824 Parry (1933), Fine (1986), Ferguson. Proscriptive principle. Containment of content. Anti-paradox of relevance. Strongest content connection.
Containment Logic⤓ .md 2026-07-15T233537.000 000000000016704 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.
Essence and Accident⤓ .md 2026-07-15T074449.000 000000000014184 Fine (1994), Correia. Essential vs accidental properties. Not reducible to necessity. Object-relative modality. Foundation for metaphysics.
Ground⤓ .md 2026-07-17T121634.146 000000000000712 Kit Fine, "Guide to ground" and "The pure logic of ground" (2012); Correia, "Grounding and truth-functions" (2010) and later work; Schnieder, deRosset. The formal side of the metaphysical grounding literature: a consequence relation for "because" in its explanatory rather than causal sense, where the disjunction is grounded in the disjunct and not the reverse.
Impossible Worlds⤓ .md 2026-07-15T233537.000 000000000017200 Routley's non-classical worlds (1980) and Rescher–Brandom (1979); Priest's development (1997, 2005); Nolan's defence of impossible worlds (1997); Berto and Jago's Impossible Worlds (2019) is the standard treatment. Extension of possible worlds. Worlds where contradictions hold. Non-trivial impossible reasoning. Hyperintensional semantics.
Situation Semantics⤓ .md 2026-07-17T120407.600 000000000000816 Barwise, Perry (1983). Situations vs possible worlds. Partial information. Constraints and infons. Foundation of situated cognition.
Truthmaker Semantics⤓ .md 2026-07-17T120407.600 000000000000824 Fine (2010s). Exact verification. States as truthmakers. Hyperintensional. Foundation of exact semantics.
CRITERIA⤓ .txt 2026-07-17T121634.146 000000000000736 Not sufficient: Being non-truth-functional, since every intensional operator is that (Modal). A modal operator over a Kripke frame, however fine the accessibility conditions—a frame still identifies a proposition with a set of worlds, and necessary equivalents stay interchangeable (Modal). A third truth value or a degree (Algebraic). Failing a classical law for any reason other than the fineness of the semantic value.