A relation between scientific or theoretical frameworks in which the laws, terms, or phenomena of one theory are systematically derived from, approximated by, or explained in terms of another theory, typically via formal derivation, limiting procedures, and explicit linking principles that translate vocabulary between frameworks.

Principle

Intertheoretic reduction requires (1) a mapping or bridge between central terms of the theories and (2) a derivation or limiting relation by which target laws or regularities follow from the reducing theory, possibly only approximately or under domain‑specific idealizations.

Demonstration

Illustrative scenario → Recognition → Action → Consequence: A philosopher models how a macroscopic theory's regularities can be recovered from a microtheory under idealization. Recognition: a candidate bridge identifies correspondences between observables. Action: the analyst derives the target regularity as an approximation or limit of microtheoretic laws. Consequence: explanations unify apparent anomalies and inform when and why the higher‑level theory applies.

Misapplication

Error: equating every successful connection between theories with complete elimination of the higher‑level theory. Plausibility: derivability suggests the higher theory is dispensable. Semantic error: conflating explanatory derivation with ontological elimination and overlooking approximation, domain restrictions, and pragmatic value of higher‑level descriptions.

Consequence

When successful, reduction increases explanatory unification and can identify mechanisms; when inapplicable, it highlights emergent autonomy, domain limits, and the need for distinct theoretical vocabularies and methods.

Reversal

Reductions can fail or be non‑extensional when vocabularies resist precise bridging (due to multiple realizability, conceptual incommensurability, or emergent phenomena), or when derivations hold only under idealizations that strip relevant higher‑level features.

Boundary

Clearly within: pairs of theories where target regularities are derivable or recoverable as limits of the reducing theory. Boundary case: theories with strong systematic correspondences but no full derivation. Clearly outside: paradigms with incompatible vocabularies and no reliable mapping between central predicates.

Semantic Tension

Tension with pluralism and emergentism: reduction favors unification and explanatory economy, while pluralism emphasizes autonomy of domain‑specific methods and concepts; both can be true in different cases and scales.

Synthesis

Intertheoretic reduction is a methodological and conceptual program that clarifies mechanisms and scope by making cross‑theory mappings explicit; its success depends on empirics, appropriate idealizations, and the semantics of theoretical terms.