 Nagel’s major (and perhaps most controversial) contribution was the introduction of bridge principles. The notion of bridge principles, (also: ‘bridge laws’ and ‘coordinating definitions’) can be spelled out in several different ways. The most common way in accord with Nagel (1961: chap. 11, Sec. II.3) is to describe them syntactically as bi-conditionals linking terms in the vocabularies of the two theories. In the same context, however, Nagel describes them in terms of the ‘nature of the linkages postulated’ (Nagel 1961: 354). He distinguishes three such linkages: