 Many models of theory reduction derive from the account of reduction due to Ernest Nagel (1949, 1961). Working within the philosophical framework of logical empiricism, Nagel construed reduction as a logical relation between theories, where a theory is understood as a system of statements, containing laws, formulated in a first-order formal language. The reducing theory TA reduces the reduced theory TB if the laws of TB can be logically derived from TA, which Nagel called the “condition of derivability”. However, if TB contains scientific terms that do not occur in the language of the reducing theory TA (“organismal reproduction” is not an expression of biochemistry), then derivability presupposes that the primitive expressions of TB (in particular, its predicates) can be logically related to the language of TA. Nagel made this explicit by a “condition of connectability”: reduction presupposes that there are statements (e.g., conditionals) that contain expressions both from TA and TB, such that TA together with these statements entails the laws of TB. These connectability statements are often called bridge principles (or correspondence rules, or reduction functions), and have been interpreted diversely. Nagel rejected the idea that bridge principles are analytic statements, but did not take a stand as to whether they are factual or conventional. Some philosophers have required that bridge principles are laws (rather than accidental generalizations), whereas others have maintained that they should express metaphysical identities between entities, properties, and processes (e.g., identifying cells with collections of molecules, in line with ontological reduction). Nagel himself construed reduction as an epistemic notion without ontological commitment; he did not require that bridge statements be biconditionals—mere conditionals when conjoined with TA sometimes logically entail TB. (The Kemeny-Oppenheim notion of reduction / theory replacement is weaker than Nagelian reduction as it does not require such bridge principles connecting TA and TB.)