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DISTANCES BETWEEN FORMAL THEORIES

Published online by Cambridge University Press:  04 October 2019

MOHAMED KHALED ,
GERGELY SZÉKELY ,
KOEN LEFEVER  and
MICHÈLE FRIEND
MOHAMED KHALED*
Affiliation:
Faculty of Engineering and Natural Sciences, Bahçeşehir University
GERGELY SZÉKELY*
Affiliation:
Alfréd Rényi Institute of Mathematics, and Department of Natural Sciences, National University of Public Service
KOEN LEFEVER*
Affiliation:
Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel
MICHÈLE FRIEND*
Affiliation:
George Washington University
*
*FACULTY OF ENGINEERING AND NATURAL SCIENCES BAHÇEŞEHIR UNIVERSITY ISTANBUL, TURKEY E-mail: [email protected]
**SET THEORY, LOGIC AND TOPOLOGY ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS BUDAPEST, HUNGARY E-mail: [email protected]
†CENTRE FOR LOGIC AND PHILOSOPHY OF SCIENCE VRIJE UNIVERSITEIT BRUSSEL BRUSSELS, BELGIUM E-mail: [email protected]
‡DEPARTMENT OF PHILOSOPHY GEORGE WASHINGTON UNIVERSITY WASHINGTON, DC, USA and UNIVERSITÉ DE LILLE LILLE, FRANCE E-mail: [email protected]
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Abstract

In the literature, there have been several methods and definitions for working out whether two theories are “equivalent” (essentially the same) or not. In this article, we do something subtler. We provide a means to measure distances (and explore connections) between formal theories. We introduce two natural notions for such distances. The first one is that of axiomatic distance, but we argue that it might be of limited interest. The more interesting and widely applicable notion is that of conceptual distance which measures the minimum number of concepts that distinguish two theories. For instance, we use conceptual distance to show that relativistic and classical kinematics are distinguished by one concept only.

Keywords

Primary 03B9903C0703A10Secondary 03G9903B80network of theoriesdegrees of nonequivalenceconceptual distancerelativistic and classical kinematics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 3 , September 2020 , pp. 633 - 654
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Copyright
Copyright © Association for Symbolic Logic 2019 

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