Axiomatization and Models of Scientific Theories |
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Authors: | Décio Krause Jonas R B Arenhart Fernando T F Moraes |
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Institution: | (1) Department of Philosophy, Princeton University, 08544 Princeton, NJ, USA |
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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. |
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