Generalizing empirical adequacy II: partial structures
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Generalizing empirical adequacy II: partial structures Sebastian Lutz1 Received: 17 May 2018 / Accepted: 31 January 2019 © The Author(s) 2019
Abstract I show that extant attempts to capture and generalize empirical adequacy in terms of partial structures fail. Indeed, the motivations for the generalizations in the partial structures approach are better met by the generalizations via approximation sets developed in “Generalizing Empirical Adequacy I” (Lutz in Synthese 191:3195–3225, 2014b. https://doi.org/10.1007/s11229-014-0440-3). Approximation sets also generalize partial structures. Keywords Empirical adequacy · Constructive empiricism · Partial structures · Approximation sets · Approximation · Partial isomorphism · Partial homomorphism
1 Introduction Van Fraassen’s constructive empiricism, with its central notion of empirical adequacy, and the partial structures approach, with its central notions of partial truth and partial isomorphism, are two major lines of research in the semantic view, according to which scientific theories are best represented by model- or set-theoretic structures. Proponents of the partial structures approach have argued that these two approaches are a perfect fit for each other: Da Costa and French (1990) have discussed a means for describing empirical adequacy as partial truth, and Bueno (1997) has used the notions of partial structure, partial isomorphism, and partial truth for generalizing empirical adequacy. I will argue that da Costa and French’s attempt at describing empirical adequacy fails (Sect. 2), as does Bueno’s attempt at generalizing empirical adequacy (Sect. 4). As shown in the first part of this discussion (Lutz 2014b), empirical adequacy is under certain conditions equivalent to the technical notion of generalized approximate truth, and it can be generalized with the help of approximation sets so that it can deal with situations involving lack of knowledge and approximations. I argue in this part of the
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Sebastian Lutz [email protected] Department of Philosophy, Uppsala University, Box 627, 751 26 Uppsala, Sweden
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discussion that this generalization of empirical adequacy fits Bueno’s motivations better than his own generalizations (Sect. 4). I will further show that the central concepts of the partial structures approach, partial truth (Sect. 2), partial isomorphism, and partial homomorphism (“Appendix A”) can be captured in terms of approximation sets. Therefore everything that can be expressed with partial structures can be expressed with approximation sets. Indeed, approximation sets are more expressive than partial structures, which cannot express approximate functions nor approximate constants (Sect. 3). The initial motivation for Bueno’s generalizations was Suárez’s criticism of constructive empiricism. I briefly show that both the criticism (“Appendix B”) and the first of Bueno’s replies (“Appendix C”) fail, while Bueno’s second reply succeeds even against Suárez’s unjustified criticism. This success, however, is the result of an almos
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