T-schema¶
The disquotational schema stating that the named sentence S is true if and only if S.
Core Idea¶
Object language and metalanguage must be separated, quotation or naming must be explicit and the schema is a family of instances rather than one unrestricted self-applicable sentence. For each suitable object-language sentence, the metalanguage pairs its name with the very condition it asserts, allowing an inductive truth definition to recover the correct extension for compound sentences. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
T-schema belongs to philosophical logic and is useful where the analyst can specify the typed philosophical logic carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the object and metalanguages, admissible sentence S and its name, truth predicate, biconditional instance, compositional recursion, use versus mention distinction, adequacy or Convention-T relation and restrictions preventing semantic paradox are explicit. The scope is broad within that domain but bounded by the need for the object and metalanguages, admissible sentence S and its name, truth predicate, biconditional instance, compositional recursion, use versus mention distinction, adequacy or Convention-T relation and restrictions preventing semantic paradox are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the object and metalanguages, admissible sentence S and its name, truth predicate, biconditional instance, compositional recursion, use versus mention distinction, adequacy or Convention-T relation and restrictions preventing semantic paradox are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to T-schema. T-schema compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed philosophical logic carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the object and metalanguages, admissible sentence S and its name, truth predicate, biconditional instance, compositional recursion, use versus mention distinction, adequacy or Convention-T relation and restrictions preventing semantic paradox are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of philosophical logic because they reuse the typed philosophical logic carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, For each suitable object-language sentence, the metalanguage pairs its name with the very condition it asserts, allowing an inductive truth definition to recover the correct extension for compound sentences., and type the carrier, state every parameter and convention in the definition, test that the object and metalanguages, admissible sentence S and its name, truth predicate, biconditional instance, compositional recursion, use versus mention distinction, adequacy or Convention-T relation and restrictions preventing semantic paradox are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction T-schema Domain-specific
Parents (1) — more general patterns this builds on
-
T-schema is a kind of Formalization Prime
The proposed strict upward parent is
prime:formalization.
Hierarchy paths (2) — routes to 2 parentless roots
- T-schema → Formalization → Representation → Abstraction
Neighborhood in Abstraction Space¶
T-schema sits in a crowded region of the domain-specific corpus (4th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Truth, Semantics & Logical Systems (18 abstractions)
Nearest neighbors
- Semantic theory of truth — 0.97
- Relevance logic — 0.93
- Metalogic — 0.93
- Doxastic logic — 0.93
- Metalanguage — 0.93
Computed from structural-signature embeddings · 2026-09-08