I introduce the constructivist notion of models of a physical theory in such a way as to be applicable to a scientific theory in general, that a theory in the exact sciences as well as in the social sciences. The distinction between an analytical apparatus and an experimental apparatus through the mediation of models allows for the generalization of a notion inspired by the work of David Hilbert and John von Neumann in the foundations of physics. If one inverts the direction of arrows or homomorphisms from the analytical apparatus, i.e. the set of logico-mathematical structures, to the experimental apparatus, i.e. the set of empirical data and experimental procedures, one can climb back from the experimental apparatus to the analytical apparatus via the model-building of data. Such a process insures the consistency of a scientific theory, either in the exact sciences or in the social sciences. This architecture of scientific enterprises may appear to have a formal character, but it has the advantage of setting the different fields of science into a unified scheme and under the light of a major philosophical debate in contemporary philosophy of science, the confrontation of realism and antirealism which extends to philosophy of physics, philosophy of logic, philosophy of language and philosophy of the social sciences, if one follows Jürgen Habermas or the defenders of constructionism, formerly called social constructivism or socio-constructivism. I conclude on the distinction between logico-mathematical constructivism and constructionism, as it has been named by Ian Hacking, in order to clearly differentiate between the foundational stances or philosophical options in what can be properly called “the logic of science” after the expression of the great American pragmatist Charles Sanders Peirce, followed in this by the logical empiricist Rudolf Carnap.