 These alternatives characterize bridge laws semantically in ways that seem more fundamental than their syntactic status and role in derivation. There is a gap between characterizing a sentence as a bi-conditional and as postulating the relevant sort of link. Bi-conditionals in themselves can express nothing other than truth functional relations, and real bridge laws cannot be defined in purely syntactic terms. Bi-conditionals are rendered true by a great variety of “links” (but ‘being rendered true by’ is not to be conflated with ‘postulating’): contingent co-instantiation or co-occurrence is not enough for reduction, even though it is enough for some bi-conditionals to hold (and, therefore, for some pairs of—possible—theories to instantiate the official Nagel model). Therefore, logical form (in first-order predicate logic) is not what we should focus on when we consider the syntactic nature of bridge laws. But what, then, is the relevant characterization? This is a matter of dispute among Nagel interpreters and those who refined the Nagel-model. Some tend to suggest weaker notions, such as (nomologically necessary) co-instantiation or co-relation (Dizadji Bahmani et al. 2010, also discussed in Klein 2009 and Kim 1998: 90, 2008), whereas others suggest stronger interpretations in terms of nomic conections or identities (Sklar 1967; Schaffner 1993; Esfeld &amp; Sachse 2007; van Riel 2011).