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The semantic view of theories and higher-order languages

Hudetz, Laurenz (2017) The semantic view of theories and higher-order languages. [Preprint]

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Several philosophers of science construe models of scientific theories as set-theoretic structures. Some of them moreover claim that models should not be construed as structures in the sense of model theory because the latter are language-dependent. I argue that if we are ready to construe models as set-theoretic structures (strict semantic view), we could equally well construe them as model-theoretic structures of higher-order logic (liberal semantic view). I show that every family of set-theoretic structures has an associated language of higher-order logic and an up to signature isomorphism unique model-theoretic counterpart, which is able to serve the same purposes. This allows to carry over every syntactic criterion of equivalence for theories in the sense of the liberal semantic view to theories in the sense of the strict semantic view. Taken together, these results suggest that the recent dispute about the semantic view and its relation to the syntactic view can be resolved.

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Item Type: Preprint
Keywords: Semantic view of theories; Syntactic view of theories; Syntax-semantics debate; Higher-order logic; Mathematical models; Language dependence; Set-theoretic structures; Bourbaki structures; Internal languages
Subjects: General Issues > Structure of Theories
Depositing User: Mr. Laurenz Hudetz
Date Deposited: 01 Nov 2017 16:03
Last Modified: 01 Nov 2017 16:03
Item ID: 14084
Subjects: General Issues > Structure of Theories
Date: 2017

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