This paper utilizes a logical correspondence theorem (which has been proved elsewhere) for the justification of weak conceptions of scientific realism and convergence to truth which do not presuppose Putnam’s no-miracles-argument (NMA). After presenting arguments against the reliability of the unrestricted NMA in Sect. 1, the correspondence theorem is explained in Sect. 2. In Sect. 3, historical illustrations of the correspondence theorem are given, and its ontological consequences are worked out. Based on the transitivity of the concept of correspondence, a correspondence-based notion of convergence to truth is developed in Sect. 4. In the final Sect. 5 it is argued that the correspondence theorem together with the assumption of ‘minimal realism’ yields a justification of a weak version of scientific realism, which is then compared to metaphysical realism and to instrumentalism.