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Categories and the Foundations of Classical Field Theories

In Elaine Landry (ed.), Categories for the Working Philosopher. Oxford, UK: Oxford University Press (forthcoming)

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  1. What Can Categories Tell Us About Space-Time?Ko Sanders - unknown
    It is widely believed that in quantum theories of gravity, the classical description of space-time as a manifold is no longer viable as a fundamental concept. Instead, space-time emerges as an approximation in appropriate regimes. In order to understand what is required to explain this emergence, it is necessary to have a good understanding of the classical structure of space-time. In this essay I will focus on the concept of space-time as it appears in locally covariant quantum field theory, an (...)
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  • Duality and Ontology.Baptiste Le Bihan & James Read - 2018 - Philosophy Compass 13 (12):e12555.
    A ‘duality’ is a formal mapping between the spaces of solutions of two empirically equivalent theories. In recent times, dualities have been found to be pervasive in string theory and quantum field theory. Naïvely interpreted, duality-related theories appear to make very different ontological claims about the world—differing in e.g. space-time structure, fundamental ontology, and mereological structure. In light of this, duality-related theories raise questions familiar from discussions of underdetermination in the philosophy of science: in the presence of dual theories, what (...)
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  • 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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  • Spacetime and Physical Equivalence.Sebastian De Haro - unknown
    In this essay I begin to lay out a conceptual scheme for: analysing dualities as cases of theoretical equivalence; assessing when cases of theoretical equivalence are also cases of physical equivalence. The scheme is applied to gauge/gravity dualities. I expound what I argue to be their contribution to questions about: the nature of spacetime in quantum gravity; broader philosophical and physical discussions of spacetime. - proceed by analysing duality through four contrasts. A duality will be a suitable isomorphism between models: (...)
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  • Deduction and Definability in Infinite Statistical Systems.Benjamin Feintzeig - 2017 - Synthese:1-31.
    Classical accounts of intertheoretic reduction involve two pieces: first, the new terms of the higher-level theory must be definable from the terms of the lower-level theory, and second, the claims of the higher-level theory must be deducible from the lower-level theory along with these definitions. The status of each of these pieces becomes controversial when the alleged reduction involves an infinite limit, as in statistical mechanics. Can one define features of or deduce the behavior of an infinite idealized system from (...)
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  • On Representational Redundancy, Surplus Structure, and the Hole Argument.Clara Bradley & James Owen Weatherall - 2020 - Foundations of Physics 50 (4):270-293.
    We address a recent proposal concerning ‘surplus structure’ due to Nguyen et al.. We argue that the sense of ‘surplus structure’ captured by their formal criterion is importantly different from—and in a sense, opposite to—another sense of ‘surplus structure’ used by philosophers. We argue that minimizing structure in one sense is generally incompatible with minimizing structure in the other sense. We then show how these distinctions bear on Nguyen et al.’s arguments about Yang-Mills theory and on the hole argument.
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  • 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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  • A Schema for Duality, Illustrated by Bosonization.Sebastian De Haro & Jeremy Butterfield - unknown
    In this paper we present a schema for describing dualities between physical theories, and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory. The schema develops proposals in De Haro : these proposals include construals of notions related to duality, like representation, model, symmetry and interpretation. The aim of the schema is to give a more precise criterion for duality than has so far been considered. The bosonization example, or boson-fermion duality, has (...)
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  • 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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  • Categories of Scientific Theories.Hans Halvorson & Dimitris Tsementzis - 2018 - In Elaine Landry (ed.), Categories for the Working Philosopher. Oxford University Press.
    We discuss ways in which category theory might be useful in philosophy of science, in particular for articulating the structure of scientific theories. We argue, moreover, that a categorical approach transcends the syntax-semantics dichotomy in 20th century analytic philosophy of science.
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  • Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent?James Weatherall - 2016 - Erkenntnis 81 (5):1073-1091.
    I argue that a criterion of theoretical equivalence due to Glymour :227–251, 1977) does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is “yes”, at least on one natural understanding of Newtonian gravitation.
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  • On the Time Reversal Invariance of Classical Electromagnetic Theory.David B. Malament - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (2):295-315.
    David Albert claims that classical electromagnetic theory is not time reversal invariant. He acknowledges that all physics books say that it is, but claims they are ``simply wrong" because they rely on an incorrect account of how the time reversal operator acts on magnetic fields. On that account, electric fields are left intact by the operator, but magnetic fields are inverted. Albert sees no reason for the asymmetric treatment, and insists that neither field should be inverted. I argue, to the (...)
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  • 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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  • Definable Categorical Equivalence.Laurenz Hudetz - 2019 - Philosophy of Science 86 (1):47-75.
    This article proposes to explicate theoretical equivalence by supplementing formal equivalence criteria with preservation conditions concerning interpretation. I argue that both the internal structure of models and choices of morphisms are aspects of formalisms that are relevant when it comes to their interpretation. Hence, a formal criterion suitable for being supplemented with preservation conditions concerning interpretation should take these two aspects into account. The two currently most important criteria—gener-alized definitional equivalence and categorical equivalence—are not optimal in this respect. I put (...)
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  • The Status of Scaling Limits as Approximations in Quantum Theories.Benjamin Feintzeig - unknown
    This paper attempts to make sense of a notion of ``approximation on certain scales'' in physical theories. I use this notion to understand the classical limit of ordinary quantum mechanics as a kind of scaling limit, showing that the mathematical tools of strict quantization allow one to make the notion of approximation precise. I then compare this example with the scaling limits involved in renormalization procedures for effective field theories. I argue that one does not yet have the mathematical tools (...)
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  • Classical Spacetime Structure.James Owen Weatherall - unknown
    I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students in philosophy; the presentation avoids mathematical formalism as much as possible.
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