Axiomatization and Models of Scientific Theories
 Décio Krause,
 Jonas R. B. Arenhart,
 Fernando T. F. Moraes
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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 firstorder 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.
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 Title
 Axiomatization and Models of Scientific Theories
 Journal

Foundations of Science
Volume 16, Issue 4 , pp 363382
 Cover Date
 20111101
 DOI
 10.1007/s106990119226y
 Print ISSN
 12331821
 Online ISSN
 15728471
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Structures
 Models
 Settheoretical predicates
 Formal languages
 Authors

 Décio Krause ^{(1)}
 Jonas R. B. Arenhart ^{(1)}
 Fernando T. F. Moraes ^{(1)}
 Author Affiliations

 1. Research Group in Logic and Foundations, Department of Philosophy, Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil