Axiomatization and Models of Scientific Theories Décio Krause Email author Jonas R. B. Arenhart Fernando T. F. Moraes Article

First Online: 08 March 2011 DOI :
10.1007/s10699-011-9226-y

Cite this article as: Krause, D., Arenhart, J.R.B. & Moraes, F.T.F. Found Sci (2011) 16: 363. doi:10.1007/s10699-011-9226-y
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Abstract In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal , for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science.

Keywords Structures Models Set-theoretical predicates Formal languages

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Authors and Affiliations Décio Krause Email author Jonas R. B. Arenhart Fernando T. F. Moraes 1. Research Group in Logic and Foundations, Department of Philosophy Federal University of Santa Catarina Florianópolis Brazil