Abstract
Suppes proposes an analysis of the structure and identity of empirical theories with his model-theoretical approach and undertakes effective reconstructions of theories in diverse disciplinary fields. Here the authors analyse the results of these examinations under the optics of questions concerning the assumed ontological commitments, and for how they satisfy economic and other criteria.
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According to the structuralist position, theoricity must always be relativized, but not to a language (theoretical in contrast to an observational), but to a scientific theory. The exact denotation is, therefore, not “theoretical” but “T-theoretical” (Stegmüller 1979, p. 10). A concept t is called theoretical relative to theory T (or just T-theoretical) iff every determination of t in any application of T, presupposes the existence of a least one actual model of T. The distinction between T-theoretical and T-non-theoretical concepts form the basis of differentiation between potential models and partial potential models of a theory T. Potential models are those structures which exemplify all the concepts of the theory T. If we omit all theoretical terms from a potential model we are left with a partial potential model, i.e., a structure consisting of all and only the non-theoretical concepts of the theory
According to the semantic view: (1) Scientific theories are to be conceived primarily not as linguistic entities (sets of statements) but as certain nonlinguistic conceptual structures called partial or potential models, state spaces or configuration spaces. (2) The appropriate tool for the formal description of scientific theories is not logic but mathematics. An empirical theory T can be identified with its class of models M(T), the models being structured sets. Then, the class of models M(T) of an empirical theory T is used to express “the empirical claim” or the “theoretical hypothesis” of T, to wit the assertion that a certain class I(T) of real (or empirical) systems is a subclass of M(T) or, in more refined versions of the semantic view, that the elements of I(T) can be extended in a certain way to elements of M(T). This is only a rough outline of the semantic view of empirical theories (Mormann 1991).
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Usó-Doménech, J.L., Nescolarde-Selva, J.A. & Gash, H. Theorizing About Theories and Mathematical Existence. Found Sci 25, 587–595 (2020). https://doi.org/10.1007/s10699-020-09648-2
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DOI: https://doi.org/10.1007/s10699-020-09648-2