  Nagel's first formal requirements was that the “laws” of the reduced theory must be derivable from the laws and associated coordinating definitions of the reducing theory. This deducibility requirement was intended to capture the idea that the explanatory principles (or laws) of the reducing theory ought to explain the explanatory principles (or laws) of the reduced theory. Nagel's second formal requirement, the connectability requirement, was that all essential terms of the reduced theory must either be contained within or be appropriately connected to the terms of the reducing theory by way of additional assumptions. The connectability requirement is presupposed by the derivability requirement, but making it explicit helps emphasize an important task and potential stumbling block for carrying out theoretical reduction.