About

Thomas Barrett is an Associate Professor in the Department of Philosophy at the University of California, Santa Barbara. He serves as the Graduate Admissions Committee Chair. His areas of specialization include the philosophy of physics, philosophy of science, and logic. Dr. Barrett holds a PhD from Princeton University and is actively involved in teaching and mentoring students within the department. His research focuses on foundational issues in philosophy of physics and science, contributing to the understanding of these fields through his academic work and teaching.

Research topics

• Data Mining
• Computer Science
• Pure mathematics
• Epistemology
• Mathematics
• Philosophy
• Mathematical economics
• Linguistics

Selected publications

• Classical Heraclitus Spacetimes and the Equivalence of Local and Global Structure

  PhilSci-Archive (University of Pittsburgh) · 2026-01-01

  otherOpen accessSenior author

  In any spacetime theory, a model is Heraclitus if no distinct points share the same local structure. Heraclitus models are known to exist in general relativity. Here, we present three examples of Heraclitus models within the classical spacetime context: (i) a geometrized classical spacetime (with curved derivative operator), (ii) a classical cosmological model whose underlying spacetime is Galilean (with flat derivative operator), and (iii) a classical cosmological model whose underlying spacetime is Leibnizian (with no derivative operator). The third example is of special interest since it shows a sense in which non-rigid Leibnizian spacetime can be "rigidified" by adding matter. This means Leibnizian spacetime+matter can be more deterministic than Leibnizian spacetime itself. We close with a general theorem which holds in any spacetime theory: Heraclitus models have the same local structure if and only if they have the same global structure.

  OA PDF

• On Coordinates and Spacetime Structure

  Philosophy of Physics · 2024-07-19 · 3 citations

  articleOpen access1st authorCorresponding

  Philosophers and physicists often claim that the “privileged coordinates” of a physical theory provide a window into its structure. The purpose of this paper is to examine whether this is the case. We show that there are general relativistic spacetimes that admit the same privileged coordinates but have different structure, and we infer from this that privileged coordinates do not provide a perfect guide to underlying structure. We conclude by isolating the conditions under which privileged coordinates do perfectly reflect structure.

  PublisherDOI

• On Privileged Coordinates and Kleinian Methods

  Erkenntnis · 2024-12-15

  articleOpen access1st authorCorresponding

  Abstract This paper examines two ways in which the ‘privileged coordinates’ of a geometric space might have significance. First, the structure of the space might be ‘determined by its privileged coordinates’. Second, the space might be presentable using ‘Kleinian methods’. We examine the geometric spaces for which these two conditions hold. Along the way, we investigate the relationship between these two conditions.

  PublisherOA PDFDOI

• Heraclitus-Maximal Worlds

  Journal of Philosophical Logic · 2024-08-29

  articleOpen accessSenior author
  PublisherOA PDFDOI

• What Do Privileged Coordinates Tell Us about Structure?

  Philosophy of Science · 2024-11-27 · 1 citations

  articleOpen access1st authorCorresponding

  Abstract We examine whether the “privileged coordinates” of a geometric space encode its “amount of structure.” In doing so, we compare this coordinate approach to comparing amounts of structure to the more familiar automorphism approach. We first show that on a natural understanding of the former, it faces one of the same well-known problems as the latter. We then capture a precise sense in which the two approaches are closely related to one another, and we conclude by discussing whether they might still prove useful in cases of philosophical interest, despite their shortcomings.

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• On automorphism criteria for comparing amounts of mathematical structure

  Synthese · 2023-05-25 · 6 citations

  articleOpen access1st authorCorresponding

  Abstract 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 $$^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mo>∗</mml:mo></mml:msup></mml:math> , another widely adopted criterion. We argue that this is mistaken; Subgroup is strictly worse than SYM $$^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mo>∗</mml:mo></mml:msup></mml:math> . We then formulate a new criterion that improves on both SYM $$^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mo>∗</mml:mo></mml:msup></mml:math> and Subgroup, answering Wilhelm’s criticisms of SYM $$^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mo>∗</mml:mo></mml:msup></mml:math> along the way. We conclude by arguing that no criterion that looks only to the automorphisms of mathematical objects to compare their structure can be fully satisfactory.

  PublisherOA PDFDOI

• Coordinates, Structure, and Classical Mechanics: A review of Jill North’s <i>Physics, Structure, and Reality</i>

  Philosophy of Science · 2022-07-01 · 5 citations

  reviewOpen access1st authorCorresponding

  Abstract 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.

  PublisherOA PDFDOI

• On Automorphism Criteria for Comparing Amounts of Mathematical Structure

  PhilSci-Archive (University of Pittsburgh) · 2022-04-25 · 2 citations

  preprintOpen access1st authorCorresponding

  Wilhelm (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 automorphisms of mathematical objects to compare their structure can be fully satisfactory.

  OA PDFDOI

• Mutual translatability, equivalence, and the structure of theories

  Synthese · 2022 · 6 citations

  1st authorCorresponding
  • Epistemology
  • Mathematics
  • Philosophy
  PublisherOA PDFDOI

• The curvature argument

  Studies in History and Philosophy of Science Part A · 2021-05-14 · 1 citations

  articleOpen access1st authorCorresponding

  Dasgupta (2015) has recently put forward a novel argument, which he calls the 'curvature argument', that aims to show that Galilean spacetime is not an ideal setting for our classical theory of motion. This paper examines the curvature argument and argues that it is not sound. The discussion yields a remark about the conditions under which a 'symmetry argument' demonstrates that a particular spacetime is a non-ideal setting for our theory of motion.

  PublisherDOI

Frequent coauthors

• James Owen Weatherall

  University of Edinburgh

  5 shared

• J. B. Manchak

  University of California, Irvine

  5 shared

• Hans Halvorson

  5 shared

• Sarita Rosenstock

  3 shared

• JB Manchak

  1 shared