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Axiomatization and Models of Scientific Theories

Krause, Décio and Arenhart, Jonas R. B. and Moraes, Fernando T. F. (2010) Axiomatization and Models of Scientific Theories. [Preprint]

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    Abstract

    In this paper we discuss two approaches to the axiomatization of scien- tific 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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    Item Type: Preprint
    Keywords: Structures, Models, Set-Theoretical Predicates, Formal Lan- guages.
    Subjects: General Issues > Models and Idealization
    Depositing User: Décio Krause
    Date Deposited: 30 Sep 2010
    Last Modified: 07 Oct 2010 11:20
    Item ID: 5563
    URI: http://philsci-archive.pitt.edu/id/eprint/5563

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