Why the model-theoretic view of theories does not adequately depict the methodology of theory application
Philosophers of science have long debated issues pertaining to the nature of scientific theories, to their reference, and to how they are applied to phenomena. The logical positivist tradition claimed that scientific theories are formal axiomatic calculi, which when supplemented with the proper sets of correspondence rules entail observational sentences, the latter referring to the observable world. The process by which the deductive consequences of the calculus are stretched all the way to observational sentences is the process by which the theory gets applied to phenomena. The logical positivist conception of scientific theories has long been abandoned based on arguments that rebut several of its consequences which are by-products of its focus on syntax (see Suppe 1974). Namely, that it requires a theoretical/observational distinction and an analytic/synthetic distinction in the terms and sentences of a theory's language both of which seem to be untenable. Furthermore, that it relies on the obscure notion of correspondence rules for giving a partial physical interpretation to the formal calculus. Finally, this view was criticized because it withholds from models their representational role by attributing to them only the meta-mathematical role of interpreting the syntax.The conception that prevailed and managed to establish its own tradition after the demise of the logical positivist view is the Model-theoretic or Semantic view. In this tradition theories are considered to be classes of structures defined by a set-theoretical predicate. They are applied to phenomena by formal mappings (e.g. isomorphism) between one of their models (i.e. structures) and a data-model constructed from empirical information about the target physical system. The question of what theories refer to, in this view, is replaced with the surrogate question of what models represent. Since a theory understood in this manner is not a linguistic entity "representation" seems to be a more appropriate relation than reference. On the nature of theoretical representation there is no consensus among the advocates of the model-theoretic view, as they differ as to how they interpret the mapping relation. Some interpret the relation as an isomorphism (van Frassen 1980) or a partial-isomorphism (da Costa and French 2003) and understand models of theories to be mapped onto appropriate data structures that represent –at least the observable aspects of – target systems. Others hold that the models of a theory represent "idealized and abstract systems", that is, that the models represent only some of the aspects of the target physical systems and they do so counterfactually, i.e. they would represent the physical system if the idealized conditions that underlie the model construction were to obtain in the system (Suppe 1989).
Portides, D. (2010)., Why the model-theoretic view of theories does not adequately depict the methodology of theory application, in M. Surez, M. Dorato & M. Rédei (eds.), Epsa epistemology and methodology of science, Dordrecht, Springer, pp. 211-220.
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