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BEYOND LINGUISTIC INTERPRETATION IN THEORY COMPARISON

Part of: Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  21 December 2023

TOBY MEADOWS
TOBY MEADOWS*
Affiliation:
DEPARTMENT OF LOGIC AND PHILOSOPHY OF SCIENCE UNIVERSITY OF CALIFORNIA, IRVINE IRVINE, CA 92617 USA
*
E-mail: [email protected]
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Abstract

This paper assembles a unifying framework encompassing a wide variety of mathematical instruments used to compare different theories. The main theme will be the idea that theory comparison techniques are most easily grasped and organized through the lens of category theory. The paper develops a table of different equivalence relations between theories and then answers many of the questions about how those equivalence relations are themselves related to each other. We show that Morita equivalence fits into this framework and provide answers to questions left open in Barrett and Halvorson [4]. We conclude by setting up a diagram of known relationships and leave open some questions for future work.

Keywords

theoretical equivalencecategory theoryset theorymodel theory

MSC classification

Primary: 03A05: Philosophical and critical
Type
Research Article
Information
The Review of Symbolic Logic , Volume 17 , Issue 3 , September 2024 , pp. 819 - 859
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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