The aim of this paper is to make a plea for a new philosophical approach, or a new meta-theoretic account altemative to the ones represented by realism and instrumentalism, in the Philosophy of Science, and that will enable us to be more successful both in dealing with a rational explanation of the process of scientific development as well as with the notion of truth that is implied by the former. This new approach is consistent with the epistemology of Logik der Forschung, goes along with T. Kuhn's contribution, and gets its most explicit formulation in the "internal realism" of the last Putnam. The argument takes the following steps: 1) 1 begin with a very brief mention of the neopositivist approach to scientific development, concluding at his point that if anything has survived in that account of scientific development it can only be the idea of "convergence", linked to the notion of "reduction". 2) The notion of convergence in K. Popper's work is then analysed, showing that this notion can be understood in two quite different senses, depending on whether what we mean is Popper in its Logik der Forschung or the tarskian Popper, i.e., the Popper of verisimilitude. 3) 1 show then that the only notion of convergence that necessarily follows from the Logik der Forschung is consistent with T. Kuhn's approach and will only be slightly qualified by him, in such a way that Kuhn's qualified notion of convergence fits perfectly well within the framework of a falsationist epistemology. The strong controversy historically held between Popper' s and Kuhn' s followers that originated from The Structure of Scientific Revolutions by Kuhn, can only be understood when we mean by Popper the tarskian Popper, and hold a misleading interpretation of Kuhn's work. 4) A new meta-theoric approach is reached both in connection with the analysis and explanation of scientific progress and with the not less troublesome concept of truth. This new approach is very akin to the "internal realism" held by Putnam from 1976 onwards. Within the framework of this new approach an epistemic notion of truth is contended for, while the goal of scientific development is now not the search for an "absolute", "objetive" truth, but the concrete achievement of the ideal coherence of the whole of our beliefs between themselves, the coherence of the whole of our beliefs with the whole of our experiences, taking our experiencesin the way they are represented in our system of beliefs.