© 2025. All rights reserved.
Site created with
Hakyll.
Modified theme
lanyon-hakyll
based on
Lanyon.
© 2025. All rights reserved.
Site created with
Hakyll.
Modified theme
lanyon-hakyll
based on
Lanyon.
A working bibliography on theoretical equivalence in logic and philosophy of science, with links to published versions and freely accessible preprints. Entries are grouped thematically.
@book{halvorson2019logic,
author = {Hans Halvorson},
title = {The Logic in Philosophy of Science},
publisher = {Cambridge University Press},
year = {2019},
annote = {A systematic and accessible treatment of formal criteria for theoretical equivalence---definitional, Morita, and categorical---situated within the broader philosophy of science. The most comprehensive single source on the subject.},
}
A systematic and accessible treatment of formal criteria for theoretical equivalence—definitional, Morita, and categorical—situated within the broader philosophy of science. The most comprehensive single source on the subject.
@article{weatherall2019compass1,
author = {James Owen Weatherall},
title = {Part 1: Theoretical Equivalence in Physics},
journal = {Philosophy Compass},
volume = {14},
number = {5},
year = {2019},
doi = {10.1111/phc3.12592},
annote = {First part of a two-part survey. Covers empirical equivalence and formal definitional criteria, with applications to classical mechanics and electromagnetism.},
}
First part of a two-part survey. Covers empirical equivalence and formal definitional criteria, with applications to classical mechanics and electromagnetism.
@article{weatherall2019compass2,
author = {James Owen Weatherall},
title = {Part 2: Theoretical Equivalence in Physics},
journal = {Philosophy Compass},
volume = {14},
number = {5},
year = {2019},
doi = {10.1111/phc3.12591},
annote = {Second part covers categorical equivalence and the relation between equivalence and duality in physics (gauge theory, general relativity).},
}
Second part covers categorical equivalence and the relation between equivalence and duality in physics (gauge theory, general relativity).
@book{dewar2022structure,
author = {Neil Dewar},
title = {Structure and Equivalence},
series = {Cambridge Elements in Philosophy of Physics},
publisher = {Cambridge University Press},
year = {2022},
doi = {10.1017/9781108914581},
annote = {A concise survey of theoretical equivalence, surplus structure, and gauge theory, aimed at philosophers of physics. Connects formal criteria to questions of ontology and representation. An accessible entry point that synthesizes the Barrett--Halvorson and Weatherall lines of work.},
}
A concise survey of theoretical equivalence, surplus structure, and gauge theory, aimed at philosophers of physics. Connects formal criteria to questions of ontology and representation. An accessible entry point that synthesizes the Barrett–Halvorson and Weatherall lines of work.
@mastersthesis{washington2018equivalence,
author = {Evan Elijah Washington},
title = {On the Equivalence of Logical Theories},
school = {Princeton University},
year = {2018},
type = {Bachelor's Thesis},
note = {Department of Mathematics. Advised by Hans P. Halvorson.},
annote = {An undergraduate thesis examining formal criteria for theoretical equivalence between logical theories, including definitional and categorical notions. Develops results in the Barrett--Halvorson tradition.},
}
An undergraduate thesis examining formal criteria for theoretical equivalence between logical theories, including definitional and categorical notions. Develops results in the Barrett–Halvorson tradition.
@incollection{butterfield2020dualities,
author = {Jeremy Butterfield},
title = {On Dualities and Equivalences Between Physical Theories},
booktitle = {Philosophy Beyond Spacetime},
editor = {Nick Huggett and Keizo Matsubara and Christian W{\"u}thrich},
publisher = {Oxford University Press},
year = {2020},
url = {https://arxiv.org/abs/1806.01505},
annote = {A wide-ranging survey bridging the formal logic and philosophy of physics literatures on equivalence and duality. Covers T-duality, AdS/CFT, and general formal criteria within a unified framework; particularly useful for seeing how physics dualities relate to philosophical notions of equivalence.},
}
A wide-ranging survey bridging the formal logic and philosophy of physics literatures on equivalence and duality. Covers T-duality, AdS/CFT, and general formal criteria within a unified framework; particularly useful for seeing how physics dualities relate to philosophical notions of equivalence.
@phdthesis{kemeny1949typetheory,
author = {John George Kemeny},
title = {Type-Theory vs. Set-Theory},
school = {Princeton University},
year = {1949},
annote = {An early systematic comparison of type theory and set theory as logical foundations, establishing conditions under which they can be regarded as equivalent. One of the first rigorous treatments of the question of logical synonymy.},
}
An early systematic comparison of type theory and set theory as logical foundations, establishing conditions under which they can be regarded as equivalent. One of the first rigorous treatments of the question of logical synonymy.
@article{shulman2019material,
author = {Michael Shulman},
title = {Comparing Material and Structural Set Theories},
journal = {Annals of Pure and Applied Logic},
volume = {170},
number = {4},
pages = {465--504},
year = {2019},
doi = {10.1016/j.apal.2018.11.002},
url = {https://arxiv.org/abs/1808.05204},
annote = {A systematic formal comparison of material set theories (e.g. ZF, where sets have members that are themselves sets) and structural set theories (e.g.\ ETCS, where structure is given by morphisms rather than membership). Establishes precise conditions under which the two approaches are equivalent.},
}
A systematic formal comparison of material set theories (e.g. ZF, where sets have members that are themselves sets) and structural set theories (e.g.ETCS, where structure is given by morphisms rather than membership). Establishes precise conditions under which the two approaches are equivalent.
@article{gajda1987syntactical,
author = {Adam Gajda and Micha{\l} Krynicki and Les{\l}aw Szczerba},
title = {A Note on Syntactical and Semantical Functions},
journal = {Studia Logica},
volume = {46},
pages = {177--185},
year = {1987},
doi = {10.1007/BF00370379},
annote = {Studies the correspondence between syntactical functions (operations on formulas) and semantical functions (operations on model classes / functors between models). Proves that a syntactical function has a correlated semantical function if and only if it preserves propositional connectives up to logical equivalence, and that a semantical function has a syntactical correlate if and only if it is continuous in the model-class topology. Connects functor-based and formula-based perspectives on theory translation.},
}
Studies the correspondence between syntactical functions (operations on formulas) and semantical functions (operations on model classes / functors between models). Proves that a syntactical function has a correlated semantical function if and only if it preserves propositional connectives up to logical equivalence, and that a semantical function has a syntactical correlate if and only if it is continuous in the model-class topology. Connects functor-based and formula-based perspectives on theory translation.
@incollection{visser2006categories,
author = {Albert Visser},
title = {Categories of Theories and Interpretations},
booktitle = {Logic in Tehran: Proceedings of the Workshop and Conference on Logic, Algebra, and Arithmetic},
editor = {Ali Enayat and Iraj Kalantari and Mojtaba Moniri},
series = {Lecture Notes in Logic},
volume = {26},
publisher = {A K Peters},
pages = {284--341},
year = {2006},
doi = {10.1201/9781439865873-16},
annote = {A thorough study of the category whose objects are first-order theories and whose morphisms are interpretations. Develops the compositional structure of interpretations, characterizes isomorphisms (bi-interpretability and synonymy), and examines how model-theoretic properties behave under interpretation. An indispensable technical reference for the formal study of inter-theory relationships.},
}
A thorough study of the category whose objects are first-order theories and whose morphisms are interpretations. Develops the compositional structure of interpretations, characterizes isomorphisms (bi-interpretability and synonymy), and examines how model-theoretic properties behave under interpretation. An indispensable technical reference for the formal study of inter-theory relationships.
@incollection{debouvere1965synonymous,
author = {K. L. de Bouv{\`e}re},
title = {Synonymous Theories},
booktitle = {The Theory of Models: Proceedings of the 1963 International Symposium at Berkeley},
editor = {J. W. Addison and Leon Henkin and Alfred Tarski},
publisher = {North Holland},
year = {1965},
pages = {402--406},
annote = {One of the earliest logical treatments of definitional equivalence between theories in different signatures. Introduces synonymous theories and proves a characterization theorem via Beth's theorem.},
}
One of the earliest logical treatments of definitional equivalence between theories in different signatures. Introduces synonymous theories and proves a characterization theorem via Beth's theorem.
@incollection{szczerba1977interpretability,
author = {L. W. Szczerba},
title = {Interpretability of Elementary Theories},
booktitle = {Logic, Foundations of Mathematics and Computability Theory},
editor = {Robert Butts and Jaakko Hintikka},
publisher = {Reidel},
address = {Dordrecht},
year = {1977},
pages = {129--145},
doi = {10.1007/978-94-010-1138-9_8},
annote = {Studies interpretability between elementary theories with applications to geometry. Includes results on theories formulated with points only versus points and lines, directly relevant to the scope of Morita equivalence.},
}
Studies interpretability between elementary theories with applications to geometry. Includes results on theories formulated with points only versus points and lines, directly relevant to the scope of Morita equivalence.
@article{andreka2005mutual,
author = {Hajnal Andr{\'e}ka and Judit X. Madar{\'a}sz and Istv{\'a}n N{\'e}meti},
title = {Mutual Definability Does Not Imply Definitional Equivalence: A Simple Example},
journal = {Mathematical Logic Quarterly},
volume = {51},
number = {6},
pages = {591--597},
year = {2005},
doi = {10.1002/malq.200410043},
annote = {Provides a concrete counterexample showing that mutual definability does not imply definitional equivalence. Essential for understanding the logical geography between competing criteria.},
}
Provides a concrete counterexample showing that mutual definability does not imply definitional equivalence. Essential for understanding the logical geography between competing criteria.
@article{tsementzis2017syntactic,
author = {Dimitris Tsementzis},
title = {A Syntactic Characterization of {Morita} Equivalence},
journal = {Journal of Symbolic Logic},
volume = {82},
number = {4},
pages = {1181--1217},
year = {2017},
doi = {10.1017/jsl.2016.30},
url = {https://arxiv.org/abs/1507.02302},
annote = {Gives a purely syntactic characterization of Morita equivalence via common Morita extensions, bridging the syntactic and categorical approaches.},
}
Gives a purely syntactic characterization of Morita equivalence via common Morita extensions, bridging the syntactic and categorical approaches.
@article{vanbenthem1984mathematical,
author = {Johan van Benthem and David Pearce},
title = {A Mathematical Characterization of Interpretation between Theories},
journal = {Studia Logica},
volume = {43},
number = {3},
pages = {295--303},
year = {1984},
doi = {10.1007/BF02429844},
annote = {Gives a clean model-theoretic characterization of interpretation in terms of reduction functions on model classes. Bridges the Tarski-school interpretability results and later philosophical work; clarifies the relationship between interpretability and definitional equivalence.},
}
Gives a clean model-theoretic characterization of interpretation in terms of reduction functions on model classes. Bridges the Tarski-school interpretability results and later philosophical work; clarifies the relationship between interpretability and definitional equivalence.
@article{pelletier2003synonymous,
author = {Francis Jeffry Pelletier and Alasdair Urquhart},
title = {Synonymous Logics},
journal = {Journal of Philosophical Logic},
volume = {32},
number = {3},
pages = {259--285},
year = {2003},
doi = {10.1023/A:1024122029337},
annote = {Studies when two logical systems are synonymous---when mutual translations compose to the identity on both sides. Connects de Bouv\`ere's synonymy to propositional and modal settings, and proves several characterization theorems.},
}
Studies when two logical systems are synonymous—when mutual translations compose to the identity on both sides. Connects de Bouvère's synonymy to propositional and modal settings, and proves several characterization theorems.
@article{pelletier2008correction,
author = {Francis Jeffry Pelletier and Alasdair Urquhart},
title = {Synonymous Logics: A Correction},
journal = {Journal of Philosophical Logic},
volume = {37},
number = {1},
pages = {95--100},
year = {2008},
doi = {10.1007/s10992-007-9053-y},
annote = {Corrects an error in a lemma from the 2003 paper. Should be read alongside it.},
}
Corrects an error in a lemma from the 2003 paper. Should be read alongside it.
@article{lefever2019nondisj,
author = {Koen Lefever and Gerg\Ho Sz{\'e}kely},
title = {On Generalization of Definitional Equivalence to Non-Disjoint Languages},
journal = {Journal of Philosophical Logic},
volume = {48},
number = {4},
pages = {709--729},
year = {2019},
doi = {10.1007/s10992-018-9491-0},
annote = {Extends definitional equivalence---classically defined only for theories with disjoint signatures---to theories sharing vocabulary. Directly relevant to the scope and limitations of Morita equivalence as a philosophical criterion.},
}
Extends definitional equivalence—classically defined only for theories with disjoint signatures—to theories sharing vocabulary. Directly relevant to the scope and limitations of Morita equivalence as a philosophical criterion.
@article{friend2019distances,
author = {Mich\`ele Friend and Mohammad Khaled and Koen Lefever and Gerg\Ho Sz{\'e}kely},
title = {Distances Between Formal Theories},
journal = {Review of Symbolic Logic},
volume = {12},
number = {4},
pages = {639--660},
year = {2019},
url = {https://arxiv.org/abs/1807.01501},
annote = {Introduces a metric on the space of theories measuring how many additional sorts are needed to reach definitional equivalence. Extends the Andr\'eka--M\'adar\'asz--N\'emeti framework into a quantitative measure of theoretical distance.},
}
Introduces a metric on the space of theories measuring how many additional sorts are needed to reach definitional equivalence. Extends the Andréka–Mádarász–Németi framework into a quantitative measure of theoretical distance.
@article{andreka2024testing,
author = {Hajnal Andr{\'e}ka and Judit X. Madar{\'a}sz and Istv{\'a}n N{\'e}meti and Gerg\Ho Sz{\'e}kely},
title = {Testing Definitional Equivalence of Theories via Automorphism Groups},
journal = {Review of Symbolic Logic},
volume = {17},
number = {4},
pages = {1097--1118},
year = {2024},
annote = {Shows that automorphism groups of models serve as a computable invariant for testing definitional equivalence. The most recent result from the Budapest school; directly extends the 2005 paper in this bibliography.},
}
Shows that automorphism groups of models serve as a computable invariant for testing definitional equivalence. The most recent result from the Budapest school; directly extends the 2005 paper in this bibliography.
@article{friedman2025biinterpretability,
author = {Harvey Friedman and Albert Visser},
title = {When Bi-Interpretability Implies Synonymy},
journal = {Review of Symbolic Logic},
year = {2025},
note = {Published online},
annote = {Identifies conditions under which bi-interpretability---the weaker notion common in proof theory and arithmetic---implies synonymy in the sense of de Bouv\`ere. Settles a long-standing question about the logical relationship between these two criteria.},
}
Identifies conditions under which bi-interpretability—the weaker notion common in proof theory and arithmetic—implies synonymy in the sense of de Bouvère. Settles a long-standing question about the logical relationship between these two criteria.
@unpublished{meadows2023risk,
author = {Toby Meadows},
title = {Risk and Theoretical Equivalence in Mathematical Foundations},
year = {2023},
note = {Preprint},
url = {https://escholarship.org/uc/item/8b76h619},
annote = {Brings together consistency, interpretability, and probability as instruments for foundational theory comparison, with emphasis on set theory. Addresses counterintuitive results about pointwise interpretability and proposes a novel framework for comparing the epistemic risk profiles of competing foundational theories.},
}
Brings together consistency, interpretability, and probability as instruments for foundational theory comparison, with emphasis on set theory. Addresses counterintuitive results about pointwise interpretability and proposes a novel framework for comparing the epistemic risk profiles of competing foundational theories.
@article{arana2025expansion,
author = {Diego Arana Segura},
title = {Equivalence and Theory Expansion},
journal = {Synthese},
volume = {206},
pages = {147},
year = {2025},
doi = {10.1007/s11229-025-05236-8},
annote = {Examines how theory expansion — adding new vocabulary or axioms — interacts with notions of theoretical equivalence. Explores when expansions preserve or break equivalence, with implications for how equivalence criteria should handle the growth of theories.},
}
Examines how theory expansion — adding new vocabulary or axioms — interacts with notions of theoretical equivalence. Explores when expansions preserve or break equivalence, with implications for how equivalence criteria should handle the growth of theories.
@incollection{sider2020equivalence,
author = {Theodore Sider},
title = {Equivalence},
booktitle = {The Tools of Metaphysics and the Metaphysics of Science},
publisher = {Oxford University Press},
year = {2020},
pages = {177--209},
chapter = {5},
url = {https://tedsider.org/books/tools.html},
annote = {A sustained treatment of theoretical equivalence from a metaphysical perspective, arguing that equivalence requires not merely formal or empirical equivalence but sameness of fundamental structure. Engages with and extends the debate between deflationary and inflationary accounts.},
}
A sustained treatment of theoretical equivalence from a metaphysical perspective, arguing that equivalence requires not merely formal or empirical equivalence but sameness of fundamental structure. Engages with and extends the debate between deflationary and inflationary accounts.
@article{north2025middleway,
author = {Jill North},
title = {Paving the Way for a Middle Way on Theoretical Equivalence},
journal = {Philosophy of Physics},
year = {2025},
note = {Forthcoming},
url = {https://jillnorth.org/North%20-%20Paving%20the%20Way%20for%20a%20Middle%20Way.pdf},
annote = {Argues for a middle way between deflationary and inflationary positions on theoretical equivalence, avoiding both the view that formal equivalence is sufficient and the view that only a rich notion of sameness of content suffices. Prepares the ground for a moderate account that takes seriously both structural and interpretive considerations.},
}
Argues for a middle way between deflationary and inflationary positions on theoretical equivalence, avoiding both the view that formal equivalence is sufficient and the view that only a rich notion of sameness of content suffices. Prepares the ground for a moderate account that takes seriously both structural and interpretive considerations.
@unpublished{march2024kinematics,
author = {Eleanor March},
title = {Categorical Equivalence and the Kinematics-Dynamics Distinction},
year = {2024},
note = {Preprint},
url = {https://philsci-archive.pitt.edu/24191/1/KPMs-pitt.pdf},
annote = {Extends the categorical equivalence programme to a theory's full space of kinematically possible models, not just its dynamically possible models. Motivates the extension via a first-order logic case where categorical equivalence of dynamical models is too weak, and develops a notion of kinematical categorical equivalence with wide implications for the equivalence literature.},
}
Extends the categorical equivalence programme to a theory's full space of kinematically possible models, not just its dynamically possible models. Motivates the extension via a first-order logic case where categorical equivalence of dynamical models is too weak, and develops a notion of kinematical categorical equivalence with wide implications for the equivalence literature.
@article{jacobs2025cosmic,
author = {Caspar Jacobs and Eleanor March},
title = {Kinematical Equivalence and Cosmic Conspiracies},
journal = {British Journal for the Philosophy of Science},
year = {2025},
doi = {10.1086/738831},
url = {https://philsci-archive.pitt.edu/24504/1/Kinematics_and_Cosmic_Conspiracies%20%281%29.pdf},
annote = {Applies March's notion of kinematical equivalence to the debate between reduced and sophisticated theories. Argues that Dewar's claim that these are equivalent fails because the two are kinematically inequivalent, and that this inequivalence underlies Jacobs's earlier finding that only sophisticated theories can explain otherwise mysterious 'cosmic conspiracies'.},
}
Applies March's notion of kinematical equivalence to the debate between reduced and sophisticated theories. Argues that Dewar's claim that these are equivalent fails because the two are kinematically inequivalent, and that this inequivalence underlies Jacobs's earlier finding that only sophisticated theories can explain otherwise mysterious 'cosmic conspiracies'.
@article{meadows2024linguistic,
author = {Toby Meadows},
title = {Beyond Linguistic Interpretation in Theory Comparison},
journal = {Review of Symbolic Logic},
volume = {17},
number = {3},
pages = {819--859},
year = {2024},
doi = {10.1017/S1755020323000321},
annote = {Assembles a unifying categorical framework for comparing theories, organising a table of equivalence relations and the containment relationships among them. Shows that Morita equivalence fits the framework and answers questions left open in Barrett and Halvorson. Includes a topological proof that certain superficially similar theories are not definitionally equivalent.},
}
Assembles a unifying categorical framework for comparing theories, organising a table of equivalence relations and the containment relationships among them. Shows that Morita equivalence fits the framework and answers questions left open in Barrett and Halvorson. Includes a topological proof that certain superficially similar theories are not definitionally equivalent.
@unpublished{meadows2024halvorson,
author = {Toby Meadows},
title = {The Halvorson Examples},
year = {2024},
note = {Preprint},
url = {https://philsci-archive.pitt.edu/26635/1/The_Halvorson_Example.pdf},
annote = {Gives a new topological proof that Halvorson's example of a pair of theories with equivalent categories but no definitional equivalence is genuine. The converse of the key theorem reveals a surprising class of superficially similar theories that are definitionally equivalent after all, shedding new light on what makes the original example work.},
}
Gives a new topological proof that Halvorson's example of a pair of theories with equivalent categories but no definitional equivalence is genuine. The converse of the key theorem reveals a surprising class of superficially similar theories that are definitionally equivalent after all, shedding new light on what makes the original example work.
@article{pinter1978properties,
author = {Charles C. Pinter},
title = {Properties Preserved under Definitional Equivalence and Interpretations},
journal = {Zeitschrift f{\"u}r mathematische Logik und Grundlagen der Mathematik},
volume = {24},
pages = {481--488},
year = {1978},
annote = {Characterizes which model-theoretic properties are preserved under definitional equivalence and under interpretations. An early systematic investigation of what is invariant when two theories are related by interpretation, directly relevant to debates about what theoretical equivalence requires.},
}
Characterizes which model-theoretic properties are preserved under definitional equivalence and under interpretations. An early systematic investigation of what is invariant when two theories are related by interpretation, directly relevant to debates about what theoretical equivalence requires.
@article{quine1975empirically,
author = {W. V. O. Quine},
title = {On Empirically Equivalent Systems of the World},
journal = {Erkenntnis},
volume = {9},
pages = {313--328},
year = {1975},
annote = {Proposes equivalence via reconstrual of predicates. One of the two canonical philosophical proposals (with Glymour) that motivated subsequent formal work.},
}
Proposes equivalence via reconstrual of predicates. One of the two canonical philosophical proposals (with Glymour) that motivated subsequent formal work.
@incollection{glymour1971theoretical,
author = {Clark Glymour},
title = {Theoretical Realism and Theoretical Equivalence},
booktitle = {{PSA} 1970: Proceedings of the Biennial Meeting of the Philosophy of Science Association},
editor = {Roger Buck and Robert S. Cohen},
series = {Boston Studies in the Philosophy of Science},
volume = {8},
publisher = {Reidel},
address = {Dordrecht},
year = {1971},
pages = {275--288},
annote = {Introduces definitional equivalence (common definitional extension) into philosophy of science as part of a defense of scientific realism. The founding text for the programme.},
}
Introduces definitional equivalence (common definitional extension) into philosophy of science as part of a defense of scientific realism. The founding text for the programme.
@book{glymour1980theory,
author = {Clark Glymour},
title = {Theory and Evidence},
publisher = {Princeton University Press},
year = {1980},
annote = {Contains the most developed version of the common-definitional- extension criterion for theoretical equivalence; Chapter III is the key reference.},
}
Contains the most developed version of the common-definitional- extension criterion for theoretical equivalence; Chapter III is the key reference.
@article{coffey2014theoretical,
author = {Kevin Coffey},
title = {Theoretical Equivalence as Interpretive Equivalence},
journal = {British Journal for the Philosophy of Science},
volume = {65},
number = {4},
pages = {821--844},
year = {2014},
doi = {10.1093/bjps/axt034},
annote = {Argues that formal criteria are insufficient: two theories are equivalent only if they share the same interpretation of the world. An important critical voice in the debate.},
}
Argues that formal criteria are insufficient: two theories are equivalent only if they share the same interpretation of the world. An important critical voice in the debate.
@article{barrett2016morita,
author = {Thomas William Barrett and Hans Halvorson},
title = {Morita Equivalence},
journal = {Review of Symbolic Logic},
volume = {9},
number = {3},
pages = {556--582},
year = {2016},
doi = {10.1017/S1755020316000174},
url = {https://arxiv.org/abs/1506.04675},
annote = {Introduces Morita equivalence to philosophy of science as a criterion intermediate between definitional and categorical equivalence. Shows that adding new sorts by explicit definition is theoretically inert.},
}
Introduces Morita equivalence to philosophy of science as a criterion intermediate between definitional and categorical equivalence. Shows that adding new sorts by explicit definition is theoretically inert.
@article{barrett2016glymour,
author = {Thomas William Barrett and Hans Halvorson},
title = {Glymour and {Quine} on Theoretical Equivalence},
journal = {Journal of Philosophical Logic},
volume = {45},
number = {5},
pages = {467--483},
year = {2016},
doi = {10.1007/s10992-015-9382-6},
annote = {Shows that Glymour's and Quine's criteria are not equivalent to each other, and maps the logical relations among four formal criteria for theoretical equivalence.},
}
Shows that Glymour's and Quine's criteria are not equivalent to each other, and maps the logical relations among four formal criteria for theoretical equivalence.
@incollection{halvorson2017categories,
author = {Hans Halvorson and Dimitris Tsementzis},
title = {Categories of Scientific Theories},
booktitle = {Categories for the Working Philosopher},
editor = {Elaine Landry},
publisher = {Oxford University Press},
year = {2018},
doi = {10.1093/oso/9780198748991.003.0017},
annote = {Argues that the category of models (with appropriate morphisms) is the correct invariant for theoretical content, and that categorical equivalence is the appropriate notion of theoretical equivalence.},
}
Argues that the category of models (with appropriate morphisms) is the correct invariant for theoretical content, and that categorical equivalence is the appropriate notion of theoretical equivalence.
@article{barrett2022mutual,
author = {Thomas William Barrett and Hans Halvorson},
title = {Mutual Translatability, Equivalence, and the Structure of Theories},
journal = {Synthese},
volume = {200},
number = {3},
year = {2022},
doi = {10.1007/s11229-022-03733-8},
annote = {Shows that mutual translatability without compatibility conditions does not imply definitional equivalence, and investigates the structural commitments that survive under weaker notions of intertranslatability.},
}
Shows that mutual translatability without compatibility conditions does not imply definitional equivalence, and investigates the structural commitments that survive under weaker notions of intertranslatability.
@article{hudetz2019definable,
author = {Laurenz Hudetz},
title = {Definable Categorical Equivalence},
journal = {Philosophy of Science},
volume = {86},
number = {1},
pages = {47--75},
year = {2019},
doi = {10.1086/700966},
annote = {Proposes definable categorical equivalence, requiring that the equivalence functors themselves be definable. Bridges the Morita and categorical approaches while avoiding over-identification of inequivalent theories.},
}
Proposes definable categorical equivalence, requiring that the equivalence functors themselves be definable. Bridges the Morita and categorical approaches while avoiding over-identification of inequivalent theories.
@unpublished{weatherall2019categorical,
author = {James Owen Weatherall},
title = {Why Not Categorical Equivalence?},
year = {2019},
url = {https://arxiv.org/abs/1812.00943},
note = {Preprint},
annote = {Argues against categorical equivalence as the default standard: two theories can be categorically equivalent yet intuitively inequivalent, because the criterion is insensitive to the choice of morphisms.},
}
Argues against categorical equivalence as the default standard: two theories can be categorically equivalent yet intuitively inequivalent, because the criterion is insensitive to the choice of morphisms.
@article{mceldowney2022morita,
author = {Paul Anh McEldowney},
title = {On {Morita} Equivalence and Interpretability},
journal = {Review of Symbolic Logic},
volume = {15},
number = {4},
pages = {1057--1100},
year = {2022},
doi = {10.1017/S1755020321000022},
annote = {Shows Morita equivalence implies mutual faithful interpretability but not vice versa, sharpening the map of logical relations between equivalence criteria.},
}
Shows Morita equivalence implies mutual faithful interpretability but not vice versa, sharpening the map of logical relations between equivalence criteria.
@article{barrett2020structure,
author = {Thomas William Barrett},
title = {Structure and Equivalence},
journal = {Philosophy of Science},
volume = {87},
number = {5},
pages = {1184--1196},
year = {2020},
doi = {10.1086/710401},
annote = {Argues that theoretical equivalence cannot be settled independently of prior commitments about how to individuate theoretical content: any such commitment entails a corresponding standard of equivalence.},
}
Argues that theoretical equivalence cannot be settled independently of prior commitments about how to individuate theoretical content: any such commitment entails a corresponding standard of equivalence.
@article{barrett2022count,
author = {Thomas William Barrett},
title = {How to Count Structure},
journal = {No{\^u}s},
volume = {56},
number = {2},
pages = {295--322},
year = {2022},
doi = {10.1111/nous.12392},
annote = {Develops a framework for comparing the amounts of structure that theories posit, using Beth's and Svenonius' definability theorems. Connects equivalence criteria to questions of ontological parsimony.},
}
Develops a framework for comparing the amounts of structure that theories posit, using Beth's and Svenonius' definability theorems. Connects equivalence criteria to questions of ontological parsimony.
@article{halvorson2012scientific,
author = {Hans Halvorson},
title = {What Scientific Theories Could Not Be},
journal = {Philosophy of Science},
volume = {79},
number = {2},
pages = {183--206},
year = {2012},
doi = {10.1086/664745},
annote = {Argues that the semantic (model-theoretic) view of theories cannot individuate scientific theories correctly: it conflates distinct theories and is insensitive to differences that matter for equivalence. The paper that initiated the main contemporary exchange on formal criteria.},
}
Argues that the semantic (model-theoretic) view of theories cannot individuate scientific theories correctly: it conflates distinct theories and is insensitive to differences that matter for equivalence. The paper that initiated the main contemporary exchange on formal criteria.
@article{glymour2013theoretical,
author = {Clark Glymour},
title = {Theoretical Equivalence and the Semantic View of Theories},
journal = {Philosophy of Science},
volume = {80},
number = {2},
pages = {286--297},
year = {2013},
doi = {10.1086/670261},
annote = {Response to Halvorson 2012. Defends a weaker criterion based on isomorphism of model categories and argues it captures the cases that philosophically matter.},
}
Response to Halvorson 2012. Defends a weaker criterion based on isomorphism of model categories and argues it captures the cases that philosophically matter.
@article{halvorson2013semantic,
author = {Hans Halvorson},
title = {The Semantic View, If Plausible, Is Syntactic},
journal = {Philosophy of Science},
volume = {80},
number = {3},
pages = {475--478},
year = {2013},
doi = {10.1086/671077},
annote = {Brief reply to Glymour 2013. Argues that any workable version of the semantic view implicitly relies on syntactic structure, collapsing the distinction between syntactic and semantic approaches.},
}
Brief reply to Glymour 2013. Argues that any workable version of the semantic view implicitly relies on syntactic structure, collapsing the distinction between syntactic and semantic approaches.
@article{barrett2017quine,
author = {Thomas William Barrett and Hans Halvorson},
title = {Quine's Conjecture on Many-Sorted Logic},
journal = {Synthese},
volume = {194},
number = {9},
pages = {3563--3582},
year = {2017},
doi = {10.1007/s11229-016-1107-z},
annote = {Proves Quine's conjecture that any many-sorted first-order theory is definitionally equivalent to a one-sorted theory. Shows the number of sorts is not a genuine feature of theoretical content under definitional equivalence.},
}
Proves Quine's conjecture that any many-sorted first-order theory is definitionally equivalent to a one-sorted theory. Shows the number of sorts is not a genuine feature of theoretical content under definitional equivalence.
@article{barrett2017geometry,
author = {Thomas William Barrett and Hans Halvorson},
title = {From Geometry to Conceptual Relativity},
journal = {Erkenntnis},
volume = {82},
number = {5},
pages = {1043--1063},
year = {2017},
doi = {10.1007/s10670-016-9858-y},
annote = {Uses definitional equivalence to sharpen the Poincar\'e conventionalism debate: Euclidean and non-Euclidean geometries supplemented with appropriate universal forces are definitionally equivalent, giving a precise sense in which the choice of geometry is conventional.},
}
Uses definitional equivalence to sharpen the Poincaré conventionalism debate: Euclidean and non-Euclidean geometries supplemented with appropriate universal forces are definitionally equivalent, giving a precise sense in which the choice of geometry is conventional.
@article{nguyen2017scientific,
author = {James Nguyen},
title = {Scientific Representation and Theoretical Equivalence},
journal = {Philosophy of Science},
volume = {84},
number = {5},
pages = {982--995},
year = {2017},
doi = {10.1086/693988},
annote = {Connects formal criteria for theoretical equivalence to debates about scientific representation. Argues that representational considerations can force inequivalence judgments even when formal criteria are satisfied.},
}
Connects formal criteria for theoretical equivalence to debates about scientific representation. Argues that representational considerations can force inequivalence judgments even when formal criteria are satisfied.
@article{hudetz2017semantic,
author = {Laurenz Hudetz},
title = {The Semantic View of Theories and Higher-Order Languages},
journal = {Synthese},
volume = {196},
number = {3},
pages = {1131--1149},
year = {2019},
doi = {10.1007/s11229-017-1502-0},
annote = {Shows that formulating the semantic view in higher-order logic dissolves apparent differences between syntactic and semantic approaches. Bears on whether categorical equivalence captures the same notion as definitional equivalence.},
}
Shows that formulating the semantic view in higher-order logic dissolves apparent differences between syntactic and semantic approaches. Bears on whether categorical equivalence captures the same notion as definitional equivalence.
@article{dewar2018translating,
author = {Neil Dewar},
title = {On Translating between Logics},
journal = {Analysis},
volume = {78},
number = {4},
pages = {622--630},
year = {2018},
doi = {10.1093/analys/any001},
annote = {Proposes a criterion for when two logics are theoretically equivalent, based on the existence of faithful translations between them. Shows that syntactic translatability and semantic equivalence come apart in general, and argues that the right criterion must be sensitive to the inferential role of the logical constants.},
}
Proposes a criterion for when two logics are theoretically equivalent, based on the existence of faithful translations between them. Shows that syntactic translatability and semantic equivalence come apart in general, and argues that the right criterion must be sensitive to the inferential role of the logical constants.
@article{dewar2019ramsey,
author = {Neil Dewar},
title = {Ramsey Equivalence},
journal = {Erkenntnis},
volume = {84},
number = {1},
pages = {77--99},
year = {2019},
doi = {10.1007/s10670-017-9948-5},
annote = {Proposes a criterion for theoretical equivalence based on Ramsey sentences: two theories are Ramsey-equivalent when their Ramsey sentences are logically equivalent. Situates this criterion relative to definitional equivalence and explores its connections to structural realism.},
}
Proposes a criterion for theoretical equivalence based on Ramsey sentences: two theories are Ramsey-equivalent when their Ramsey sentences are logically equivalent. Situates this criterion relative to definitional equivalence and explores its connections to structural realism.
@article{dewar2019supervenience,
author = {Neil Dewar},
title = {Supervenience, Reduction, and Translation},
journal = {Philosophy of Science},
volume = {86},
number = {5},
pages = {942--954},
year = {2019},
doi = {10.1086/705445},
annote = {Clarifies the formal relationships between supervenience, reduction, and translation between theories. Shows that several notions of reduction and supervenience can be explicated in terms of definability, unifying them within a common logical framework.},
}
Clarifies the formal relationships between supervenience, reduction, and translation between theories. Shows that several notions of reduction and supervenience can be explicated in terms of definability, unifying them within a common logical framework.
@article{dewar2023interpretation,
author = {Neil Dewar},
title = {Interpretation and Equivalence; or, Equivalence and Interpretation},
journal = {Synthese},
volume = {201},
number = {4},
year = {2023},
doi = {10.1007/s11229-023-04102-9},
annote = {Examines the relationship between interpretation and equivalence between theories, arguing the two are more tightly connected than is often supposed. Analyzes several formal accounts and considers their philosophical implications.},
}
Examines the relationship between interpretation and equivalence between theories, arguing the two are more tightly connected than is often supposed. Analyzes several formal accounts and considers their philosophical implications.
@article{dewar2023internal,
author = {Neil Dewar},
title = {On Internal Structure, Categorical Structure, and Representation},
journal = {Philosophy of Science},
volume = {90},
number = {1},
pages = {188--195},
year = {2023},
doi = {10.1017/psa.2022.10},
annote = {Distinguishes internal structural equivalence from categorical equivalence and argues they come apart in important cases. Bears on whether categorical equivalence can serve as a sufficient criterion for theoretical equivalence.},
}
Distinguishes internal structural equivalence from categorical equivalence and argues they come apart in important cases. Bears on whether categorical equivalence can serve as a sufficient criterion for theoretical equivalence.
@article{dewar2023convention,
author = {Neil Dewar},
title = {Equivalence and Convention},
journal = {Philosophy of Science},
volume = {91},
number = {5},
pages = {1242--1250},
year = {2023},
doi = {10.1017/psa.2023.148},
annote = {Argues that conventional choices---such as which predicates to take as primitive---affect whether two theories count as equivalent. Connects theoretical equivalence to the broader role of convention in scientific language.},
}
Argues that conventional choices—such as which predicates to take as primitive—affect whether two theories count as equivalent. Connects theoretical equivalence to the broader role of convention in scientific language.
@article{teitel2021theoretical,
author = {Trevor Teitel},
title = {What Theoretical Equivalence Could Not Be},
journal = {Philosophical Studies},
volume = {178},
number = {12},
pages = {4119--4149},
year = {2021},
doi = {10.1007/s11098-021-01639-8},
annote = {Argues that no purely formal criterion can fully capture theoretical equivalence, because equivalence judgments require substantive input about which features of a theory carry representational significance.},
}
Argues that no purely formal criterion can fully capture theoretical equivalence, because equivalence judgments require substantive input about which features of a theory carry representational significance.
@article{wilhelm2021structure,
author = {Isaac Wilhelm},
title = {Comparing the Structures of Mathematical Objects},
journal = {Synthese},
volume = {199},
pages = {6357--6369},
year = {2021},
doi = {10.1007/s11229-021-03072-0},
url = {https://philsci-archive.pitt.edu/27486/1/Comparing%20the%20Structures%20of%20Mathematical%20Objects.pdf},
annote = {Defends a criterion for comparing the amounts of structure of mathematical objects using automorphism groups: object X has at least as much structure as Y just in case X's automorphism group is a subgroup of Y's. Argues this 'Subgroup' criterion is superior to the rival SYM* approach. Directly engaged by Barrett, Manchak, and Weatherall (2023).},
}
Defends a criterion for comparing the amounts of structure of mathematical objects using automorphism groups: object X has at least as much structure as Y just in case X's automorphism group is a subgroup of Y's. Argues this 'Subgroup' criterion is superior to the rival SYM* approach. Directly engaged by Barrett, Manchak, and Weatherall (2023).
@article{rosenstock2016holonomy,
author = {Sarita Rosenstock and James Owen Weatherall},
title = {A Categorical Equivalence between Generalized Holonomy Maps on a Connected Manifold and Principal Connections on Bundles over that Manifold},
journal = {Journal of Mathematical Physics},
volume = {57},
number = {10},
pages = {102902},
year = {2016},
doi = {10.1063/1.4965445},
url = {https://arxiv.org/abs/1504.02401},
annote = {Establishes a categorical equivalence between generalized holonomy maps on a connected manifold and principal connections on bundles over that manifold. Clarifies the sense in which the holonomy and fiber bundle formulations of gauge theories are equivalent, and bears on debates about how much structure gauge theories genuinely posit.},
}
Establishes a categorical equivalence between generalized holonomy maps on a connected manifold and principal connections on bundles over that manifold. Clarifies the sense in which the holonomy and fiber bundle formulations of gauge theories are equivalent, and bears on debates about how much structure gauge theories genuinely posit.
@article{north2009structure,
author = {Jill North},
title = {The Structure of Physics: A Case Study},
journal = {Journal of Philosophy},
volume = {106},
number = {2},
pages = {57--88},
year = {2009},
annote = {Uses Lagrangian versus Hamiltonian mechanics to argue that formally equivalent theories can differ in mathematical structure and thereby in what they reveal about the world. An influential challenge to purely formal criteria.},
}
Uses Lagrangian versus Hamiltonian mechanics to argue that formally equivalent theories can differ in mathematical structure and thereby in what they reveal about the world. An influential challenge to purely formal criteria.
@article{rosenstock2015einstein,
author = {Sarita Rosenstock and Thomas William Barrett and James Owen Weatherall},
title = {On {Einstein} Algebras and Relativistic Spacetimes},
journal = {Studies in History and Philosophy of Modern Physics},
volume = {52},
pages = {309--316},
year = {2015},
doi = {10.1016/j.shpsb.2015.09.004},
url = {https://arxiv.org/abs/1506.00124},
annote = {Shows that general relativity and Geroch's Einstein-algebra formulation are categorically dual (and hence equivalent in a strong formal sense). A worked application of categorical methods to philosophy of physics.},
}
Shows that general relativity and Geroch's Einstein-algebra formulation are categorically dual (and hence equivalent in a strong formal sense). A worked application of categorical methods to philosophy of physics.
@article{weatherall2016newtonian,
author = {James Owen Weatherall},
title = {Are {Newtonian} Gravitation and Geometrized {Newtonian} Gravitation Theoretically Equivalent?},
journal = {Erkenntnis},
volume = {81},
pages = {1073--1091},
year = {2016},
doi = {10.1007/s10670-015-9783-5},
url = {https://arxiv.org/abs/1411.5757},
annote = {Argues that standard and geometrized Newtonian gravitation are theoretically equivalent via a categorical equivalence of their model categories, answering a question left open by earlier work using Glymour's criterion.},
}
Argues that standard and geometrized Newtonian gravitation are theoretically equivalent via a categorical equivalence of their model categories, answering a question left open by earlier work using Glymour's criterion.
@article{curiel2014classical,
author = {Erik Curiel},
title = {Classical Mechanics Is {Lagrangian}; It Is Not {Hamiltonian}},
journal = {British Journal for the Philosophy of Science},
volume = {65},
number = {2},
pages = {269--321},
year = {2014},
doi = {10.1093/bjps/axs034},
annote = {Argues at length that Lagrangian and Hamiltonian mechanics are not theoretically equivalent despite their mathematical relationship, because they have different solution spaces. A careful counterpoint to North 2009 and to naive appeals to formal equivalence in mechanics.},
}
Argues at length that Lagrangian and Hamiltonian mechanics are not theoretically equivalent despite their mathematical relationship, because they have different solution spaces. A careful counterpoint to North 2009 and to naive appeals to formal equivalence in mechanics.
@article{lebihan2018duality,
author = {Baptiste Le Bihan and James Read},
title = {Duality and Ontology},
journal = {Philosophy Compass},
volume = {13},
number = {12},
year = {2018},
doi = {10.1111/phc3.12555},
annote = {A survey of philosophical issues raised by string-theoretic dualities (T-duality, AdS/CFT). Asks whether dual theories are equivalent descriptions of one world, and how to reason about ontology when we lack a duality-invariant formulation.},
}
A survey of philosophical issues raised by string-theoretic dualities (T-duality, AdS/CFT). Asks whether dual theories are equivalent descriptions of one world, and how to reason about ontology when we lack a duality-invariant formulation.
@article{weatherall2020equivalence,
author = {James Owen Weatherall},
title = {Equivalence and Duality in Electromagnetism},
journal = {Philosophy of Science},
volume = {87},
number = {5},
pages = {1172--1183},
year = {2020},
doi = {10.1086/710630},
annote = {Applies the recent philosophical literature on theoretical equivalence to bear on dualities in physics. Focusing on electromagnetic duality, which is a simple example of S-duality in string theory, argues that the duality fits naturally into at least one framework for assessing equivalence---that of categorical equivalence---but that it fails to meet a necessary condition for equivalence on that account. The duality does not preserve "empirical content" in the required sense; instead, it takes models to models with "dual" empirical content.},
}
Applies the recent philosophical literature on theoretical equivalence to bear on dualities in physics. Focusing on electromagnetic duality, which is a simple example of S-duality in string theory, argues that the duality fits naturally into at least one framework for assessing equivalence—that of categorical equivalence—but that it fails to meet a necessary condition for equivalence on that account. The duality does not preserve "empirical content" in the required sense; instead, it takes models to models with "dual" empirical content.
@article{nguyen2020surplus,
author = {James Nguyen and Nicholas J. Teh and Laura Wells},
title = {Why Surplus Structure Is Not Superfluous},
journal = {British Journal for the Philosophy of Science},
volume = {71},
number = {2},
pages = {665--695},
year = {2020},
doi = {10.1093/bjps/axy026},
annote = {Argues against eliminating gauge structure via theoretical equivalence moves. Surplus mathematical structure can carry genuine explanatory and predictive work even when not directly represented in the physical ontology.},
}
Argues against eliminating gauge structure via theoretical equivalence moves. Surplus mathematical structure can carry genuine explanatory and predictive work even when not directly represented in the physical ontology.
@article{barrett2023automorphism,
author = {Thomas William Barrett and John Byron Manchak and James Owen Weatherall},
title = {On Automorphism Criteria for Comparing Amounts of Mathematical Structure},
journal = {Synthese},
volume = {201},
number = {6},
pages = {191},
year = {2023},
url = {https://arxiv.org/abs/2204.11973},
annote = {Examines whether the size of an automorphism group is a reliable guide to the amount of structure a theory posits. Finds the criterion fails in general, with implications for Weatherall-style arguments in philosophy of physics.},
}
Examines whether the size of an automorphism group is a reliable guide to the amount of structure a theory posits. Finds the criterion fails in general, with implications for Weatherall-style arguments in philosophy of physics.
@article{dewar2019sophistication,
author = {Neil Dewar},
title = {Sophistication about Symmetries},
journal = {The British Journal for the Philosophy of Science},
volume = {70},
number = {2},
pages = {485--521},
year = {2019},
doi = {10.1093/bjps/axx021},
annote = {Defends a ``sophisticated'' attitude toward theories related by a symmetry (such as a gauge symmetry): rather than treating them as two distinct theories with the same empirical content, we should regard them as equivalent formulations of the same theory. Argues this avoids the problems of both naive realism about gauge structure and eliminativist reduction, drawing on the holonomy formulation of electromagnetism.},
}
Defends a ``sophisticated'' attitude toward theories related by a symmetry (such as a gauge symmetry): rather than treating them as two distinct theories with the same empirical content, we should regard them as equivalent formulations of the same theory. Argues this avoids the problems of both naive realism about gauge structure and eliminativist reduction, drawing on the holonomy formulation of electromagnetism.
@article{weatherall2024teleparallel,
author = {James Owen Weatherall and Insa Meskhidze},
title = {Are General Relativity and Teleparallel Gravity Theoretically Equivalent?},
journal = {Philosophy of Physics},
volume = {2},
number = {1},
year = {2024},
doi = {10.31389/pop.152},
url = {https://arxiv.org/abs/2406.15932},
annote = {A careful philosophical analysis of whether general relativity and teleparallel gravity---a reformulation using torsion rather than curvature---are theoretically equivalent. Applies standard formal criteria and finds the question is more subtle than it appears.},
}
A careful philosophical analysis of whether general relativity and teleparallel gravity—a reformulation using torsion rather than curvature—are theoretically equivalent. Applies standard formal criteria and finds the question is more subtle than it appears.