The Epsilon-Reconstruction of Theories and Scientific Structuralism

Erkenntnis 81 (2):407-432 (2016)
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Abstract

Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of theoretical terms and a suitable choice semantics for it. Second, to analyze whether Carnap’s approach is compatible with a structuralist conception of mathematics.

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References found in this work

Introduction to mathematical philosophy.Bertrand Russell - 1919 - New York: Dover Publications.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
What is structural realism?James Ladyman - 1998 - Studies in History and Philosophy of Science Part A 29 (3):409-424.
Philosophy of mathematics: structure and ontology.Stewart Shapiro - 1997 - New York: Oxford University Press.

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