David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Foundations of Science 16 (4):363-382 (2011)
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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References found in this work BETA
Stewart Shapiro (1991). Foundations Without Foundationalism: A Case for Second-Order Logic. Oxford University Press.
F. A. Muller (2011). Reflections on the Revolution at Stanford. Synthese 183 (1):87-114.
Patrick Suppes (1957). Introduction to Logic. Dover Publications.
Steven French & Décio Krause (2010). Remarks on the Theory of Quasi-Sets. Studia Logica 95 (1/2):101 - 124.
Gregory H. Moore (1980). Beyond First-Order Logic: The Historical Interplay Between Mathematical Logic and Axiomatic Set Theory. History and Philosophy of Logic 1 (1-2):95-137.
Citations of this work BETA
Jonas R. B. Arenhart (2012). Ontological Frameworks for Scientific Theories. Foundations of Science 17 (4):339-356.
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