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ON MORITA EQUIVALENCE AND INTERPRETABILITY

Published online by Cambridge University Press:  13 August 2019

PAUL ANH MCELDOWNEY
PAUL ANH MCELDOWNEY*
Affiliation:
Department of Philosophy, University of Notre Dame
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF NOTRE DAME 100 MALLOY HALL NOTRE DAME, INDIANA 46556, USA E-mail: [email protected] or [email protected]
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Abstract

In a recent article, Barrett & Halvorson (2016) define a notion of equivalence for first-order theories, which they call “Morita equivalence.” To argue that Morita equivalence is a reasonable measure of “theoretical equivalence,” they make use of the claim that Morita extensions “say no more” than the theories they are extending. The goal of this article is to challenge this central claim by raising objections to their argument for it and by showing why there is good reason to think that the claim itself is false. In light of these criticisms, this article develops a natural way for the advocate of Morita equivalence to respond. I prove that this response makes her criterion a special case of bi-interpretability, an already well-established barometer of theoretical equivalence. I conclude by providing reasons why the advocate of Morita equivalence should opt for a notion of theoretical equivalence that is defined in terms of interpretability rather than Morita extensions.

Keywords

03A1003F2500A3003A05Morita equivalenceinterpretabilitymany-sorted logictheoretical equivalence
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 2 , June 2020 , pp. 388 - 415
Copyright
Copyright © Association for Symbolic Logic 2019 

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