Models, Postulates, and Generalized Nomic Truth Approximation

Abstract

The qualitative theory of nomic truth approximation, presented in Kuipers (From instrumentalism to constructive realism. On some relations between confirmation, empirical progress, and truth approximation. Synthese library, vol. 287. Kluwer Academic Publishers, Dordrecht, 2000), in which ‘the truth’ concerns the distinction between nomic, e.g. physical, possibilities and impossibilities, rests on a very restrictive assumption viz. that theories always claim to characterize the boundary between nomic possibilities and impossibilities. In Chap. 2 we have already shown that truth approximation is possible by ascribing, in Popperian spirit, theories only an excluding function. By fully recognizing two different functions of theories, viz. excluding and representing (including), this chapter drops the restrictive assumption by conceiving theories in development as tuples of postulates and models, where the postulates claim to exclude nomic impossibilities and the (not-excluded) models claim to represent nomic possibilities. Revising such ‘two-sided’ theories becomes then a matter of adding or revising models and/or postulates in the light of increasing evidence, now captured by a special kind of theories, viz. ‘data-theories’. Under the assumption that the data-theory is true, achieving empirical progress on its basis provides good reasons for the abductive conclusion that truth approximation has been achieved as well. As in Chap. 2, the notions of truth approximation and empirical progress are formally direct generalizations of the earlier ones. However, truth approximation is now explicitly defined in two-sided terms of increasing truth-content and decreasing falsity-content of theories, whereas empirical progress is defined in terms of lasting increased accepted-content and decreased rejected-content in the light of increasing evidence. As already noted in Chap. 2, these definitions are strongly inspired by a paper of Gustavo Cevolani, Vincenzo Crupi and Roberto Festa, viz., “Verisimilitude and belief change for conjunctive theories” (Erkenntnis, 2011).