18 found
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  1. How to count structure.Thomas William Barrett - 2022 - Noûs 56 (2):295-322.
    There is sometimes a sense in which one theory posits ‘less structure’ than another. Philosophers of science have recently appealed to this idea both in the debate about equivalence of theories and in discussions about structural parsimony. But there are a number of different proposals currently on the table for how to compare the ‘amount of structure’ that different theories posit. The aim of this paper is to compare these proposals against one another and evaluate them on their own merits.
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  2. Equivalent and Inequivalent Formulations of Classical Mechanics.Thomas William Barrett - 2019 - British Journal for the Philosophy of Science 70 (4):1167-1199.
    In this article, I examine whether or not the Hamiltonian and Lagrangian formulations of classical mechanics are equivalent theories. I do so by applying a standard for equivalence that was recently introduced into philosophy of science by Halvorson and Weatherall. This case study yields three general philosophical payoffs. The first concerns what a theory is, while the second and third concern how we should interpret what our physical theories say about the world. 1Introduction 2When Are Two Theories Equivalent? 3Preliminaries on (...)
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  3. Glymour and Quine on Theoretical Equivalence.Thomas William Barrett & Hans Halvorson - 2016 - Journal of Philosophical Logic 45 (5):467-483.
    Glymour and Quine propose two different formal criteria for theoretical equivalence. In this paper we examine the relationships between these criteria.
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  4. Morita Equivalence.Thomas William Barrett & Hans Halvorson - 2016 - Review of Symbolic Logic 9 (3):556-582.
    Logicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how these two well-known criteria are related to one another, we investigate an intermediate criterion called Morita equivalence.
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  5. What Do Symmetries Tell Us About Structure?Thomas William Barrett - 2017 - Philosophy of Science (4):617-639.
    Mathematicians, physicists, and philosophers of physics often look to the symmetries of an object for insight into the structure and constitution of the object. My aim in this paper is to explain why this practice is successful. In order to do so, I present a collection of results that are closely related to (and in a sense, generalizations of) Beth’s and Svenonius’ theorems.
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  6. On Einstein Algebras and Relativistic Spacetimes.Sarita Rosenstock, Thomas William Barrett & James Owen Weatherall - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):309-316.
    In this paper, we examine the relationship between general relativity and the theory of Einstein algebras. We show that according to a formal criterion for theoretical equivalence recently proposed by Halvorson and Weatherall, the two are equivalent theories.
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  7. On the Structure of Classical Mechanics.Thomas William Barrett - 2015 - British Journal for the Philosophy of Science 66 (4):801-828.
    The standard view is that the Lagrangian and Hamiltonian formulations of classical mechanics are theoretically equivalent. Jill North, however, argues that they are not. In particular, she argues that the state-space of Hamiltonian mechanics has less structure than the state-space of Lagrangian mechanics. I will isolate two arguments that North puts forward for this conclusion and argue that neither yet succeeds. 1 Introduction2 Hamiltonian State-space Has less Structure than Lagrangian State-space2.1 Lagrangian state-space is metrical2.2 Hamiltonian state-space is symplectic2.3 Metric > (...)
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  8. Mutual translatability, equivalence, and the structure of theories.Thomas William Barrett & Hans Halvorson - 2022 - Synthese 200 (3):1-36.
    This paper presents a simple pair of first-order theories that are not definitionally (nor Morita) equivalent, yet are mutually conservatively translatable and mutually 'surjectively' translatable. We use these results to clarify the overall geography of standards of equivalence and to show that the structural commitments that theories make behave in a more subtle manner than has been recognized.
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  9. From Geometry to Conceptual Relativity.Thomas William Barrett & Hans Halvorson - 2017 - Erkenntnis 82 (5):1043-1063.
    The purported fact that geometric theories formulated in terms of points and geometric theories formulated in terms of lines are “equally correct” is often invoked in arguments for conceptual relativity, in particular by Putnam and Goodman. We discuss a few notions of equivalence between first-order theories, and we then demonstrate a precise sense in which this purported fact is true. We argue, however, that this fact does not undermine metaphysical realism.
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  10.  72
    On automorphism criteria for comparing amounts of mathematical structure.Thomas William Barrett, J. B. Manchak & James Owen Weatherall - 2023 - Synthese 201 (6):1-14.
    Wilhelm (Forthcom Synth 199:6357–6369, 2021) has recently defended a criterion for comparing structure of mathematical objects, which he calls Subgroup. He argues that Subgroup is better than SYM \(^*\), another widely adopted criterion. We argue that this is mistaken; Subgroup is strictly worse than SYM \(^*\). We then formulate a new criterion that improves on both SYM \(^*\) and Subgroup, answering Wilhelm’s criticisms of SYM \(^*\) along the way. We conclude by arguing that no criterion that looks only to the (...)
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  11.  99
    Spacetime structure.Thomas William Barrett - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 51:37-43.
    This paper makes an observation about the ``amount of structure'' that different classical and relativistic spacetimes posit. The observation substantiates a suggestion made by Earman and yields a cautionary remark concerning the scope and applicability of structural parsimony principles.
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  12. Quine’s conjecture on many-sorted logic.Thomas William Barrett & Hans Halvorson - 2017 - Synthese 194 (9):3563-3582.
    Quine often argued for a simple, untyped system of logic rather than the typed systems that were championed by Russell and Carnap, among others. He claimed that nothing important would be lost by eliminating sorts, and the result would be additional simplicity and elegance. In support of this claim, Quine conjectured that every many-sorted theory is equivalent to a single-sorted theory. We make this conjecture precise, and prove that it is true, at least according to one reasonable notion of theoretical (...)
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  13.  50
    Structure and Equivalence.Thomas William Barrett - 2020 - Philosophy of Science 87 (5):1184-1196.
    It has been suggested that we can tell whether two theories are equivalent by comparing the structure that they ascribe to the world. If two theories posit different structures, then they must be i...
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  14.  17
    Heraclitus-Maximal Worlds.J. B. Manchak & Thomas William Barrett - 2024 - Journal of Philosophical Logic 53 (6):1519-1536.
    Within the context of general relativity, the Heraclitus asymmetry property requires that no distinct pair of spacetime events have the same local structure Manchak and Barrett (2023). Here, we explore Heraclitus-maximal worlds – those which are “as large as they can be” with respect to the Heraclitus property. Using Zorn’s lemma, we prove that such worlds exist and highlight a number of their properties. If attention is restricted to Heraclitus-maximal worlds, we show senses in which observers have the epistemic resources (...)
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  15.  54
    On Putnam’s Proof of the Impossibility of a Nominalistic Physics.Thomas William Barrett - 2020 - Erkenntnis 88 (1):1-28.
    In his book Philosophy of Logic, Putnam (1971) presents a short argument which reads like—and indeed, can be reconstructed as—a formal proof that a nominalistic physics is impossible. The aim of this paper is to examine Putnam’s proof and show that it is not compelling. The precise way in which the proof fails yields insight into the relation that a nominalistic physics should bear to standard physics and into Putnam’s indispensability argument.
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  16. Extension, Translation, and the Cantor-Bernstein Property.Thomas William Barrett & Hans Halvorson - manuscript
    The purpose of this paper is to examine in detail a particularly interesting pair of first-order theories. In addition to clarifying the overall geography of notions of equivalence between theories, this simple example yields two surprising conclusions about the relationships that theories might bear to one another. In brief, we see that theories lack both the Cantor-Bernstein and co-Cantor-Bernstein properties.
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  17.  49
    The curvature argument.Thomas William Barrett - 2021 - Studies in History and Philosophy of Science Part A 88:30-40.
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  18.  48
    Coordinates, Structure, and Classical Mechanics: A review of Jill North’s Physics, Structure, and Reality. [REVIEW]Thomas William Barrett - 2022 - Philosophy of Science 89 (3):644-653.
    This is an essay review of Jill North’s book Physics, Structure, and Reality. It focuses on two of the main topics of the book. The first is North’s idea that we can use coordinates as a window into the structure that a theory posits; the second is North’s argument for the inequivalence of Lagrangian and Newtonian mechanics.
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