Papers by James Owen Weatherall
This paper concerns the question of which collections of general relativistic spacetimes are dete... more This paper concerns the question of which collections of general relativistic spacetimes are deterministic relative to which definitions. We begin by considering a series of three definitions of increasing strength due to Belot (1995). The strongest of these definitions is particularly interesting for spacetime theories because it involves an asymmetry condition called "rigidity" that has been studied previously in a different context (Geroch 1969; Halvorson and Manchak 2022; Dewar 2024). We go on to explore other (stronger) asymmetry conditions that give rise to other (stronger) forms of determinism. We introduce a number of definitions of this type and clarify the relationships between them and the three considered by Belot. We go on to show that there are collections of general relativistic spacetimes that satisfy much stronger forms of determinism than previously known. We also highlight a number of open questions.
Determinism is the thesis that the past determines the future, but efforts to define it precisely... more Determinism is the thesis that the past determines the future, but efforts to define it precisely have exposed deep methodological disagreements. Standard possible-worlds formulations of determinism presuppose an "agreement" relation between worlds, but this relation can be understood in multiple ways -- none of which is particularly clear. We critically examine the proliferation of definitions of determinism in the recent literature, arguing that these definitions fail to deliver clear verdicts about actual scientific theories. We advocate a return to a formal approach, in the logical tradition of Carnap, that treats determinism as a property of scientific theories, rather than an elusive metaphysical doctrine.
We highlight two key distinctions: (1) the difference between qualitative and "full" determinism, as emphasized in recent discussions of physics and metaphysics, and (2) the distinction between weak and strong formal conditions on the uniqueness of world extensions. We argue that defining determinism in terms of metaphysical notions such as haecceities is unhelpful, whereas rigorous formal criteria -- such as Belot's D1 and D3 -- offer a tractable and scientifically relevant account. By clarifying what it means for a theory to be deterministic, we set the stage for a fruitful interaction between physics and metaphysics.
We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic v... more We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be “correct”, in the sense of formalizable in a formal proof system. We then present a view on the relationship between mathematics and logic that clarifies the role of formal correctness in mathematics. Finally, we discuss the significance of these arguments for recent discussions about automated theorem provers and applications of AI to mathematics.
This paper contends that Humeanism suffers from a major flaw: it is unable to explain why the pra... more This paper contends that Humeanism suffers from a major flaw: it is unable to explain why the practice of experimental science—i.e., the practice of creating novel circumstances and seeing what happens—should be expected to lead to scientific knowledge. In particular, it
is unclear how the Humean can make sense of local, concrete inquiry yielding knowledge which is global in scope, lawlike in character, and counterfactually robust. As a result, Humeanism is left without a plausible account of scientific epistemology.
Teleparallel gravity shares many qualitative features with general relativity, but differs from i... more Teleparallel gravity shares many qualitative features with general relativity, but differs from it in the following way: whereas in general relativity, gravitation is a manifestation of space-time curvature, in teleparallel gravity, spacetime is (always) flat. Gravitational effects in this theory arise due to spacetime torsion. It is often claimed that teleparallel gravity is
an equivalent reformulation of general relativity. In this paper we question that view. We argue that the theories are not equivalent, by the criterion of categorical equivalence and any stronger criterion, and that teleparallel gravity posits strictly more structure than general relativity.
We consider two simple criteria for when a physical theory should be said to be “generally covari... more We consider two simple criteria for when a physical theory should be said to be “generally covariant”, and we argue that these criteria are not met by Yang-Mills theory, even on geometric formulations of that theory. The reason, we show, is that the bundles encountered in Yang-Mills theory are not natural bundles; instead, they are gauge-natural. We then show how these observations relate to previous arguments about the significance of solder forms in assessing disanalogies between general relativity and Yang-Mills theory. We conclude by suggesting that general covariance is really about functoriality.
We consider conservation of momentum in AQUAL, a field-theoretic extension to Modified Newtonian ... more We consider conservation of momentum in AQUAL, a field-theoretic extension to Modified Newtonian Dynamics (MOND). We show that while there is a sense in which momentum is conserved, it is only if momentum is attributed to the gravitational field, and thus Newton's third law fails as usually understood. We contrast this situation with that of Newtonian gravitation on a field theoretic formulation. We then briefly discuss the situation in TeVeS, a relativistic theory that has AQUAL as a classical limit. I.
We review several topics of philosophical interest connected to misleading online content. First... more We review several topics of philosophical interest connected to misleading online content. First we consider proposed definitions of different types of misleading content. Then we consider the epistemology of misinformation, focusing on approaches from virtue epistemology and social epistemology. Finally we discuss how misinformation is related to belief polarization, and argue that models of rational polarization present special challenges for conceptualizing fake news and misinformation.
Synthese
Wilhelm (Forthcom Synth 199:6357–6369, 2021) has recently defended a criterion for comparing stru... more 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 automorphisms of mathematical objects to compare their structure can be fully satisfactory.
Philosophical Topics
Scientific curation, where scientific evidence is selected and shared, is essential to public bel... more Scientific curation, where scientific evidence is selected and shared, is essential to public belief formation about science. Yet common curation practices can distort the body of evidence the public sees. Focusing on science journalism, we employ computational models to investigate how such distortions influence public belief. We consider these effects for agents with and without confirmation bias. We find that standard journalistic practices can lead to significant distortions in public belief; that pre-existing errors in public belief can drive further distortions in reporting; that practices that appear relatively unobjectionable can produce serious epistemic harm; and that, in some cases, common curation practices related to fairness and extreme reporting can lead to polarization.
In this two-part essay, we distinguish several senses in which general relativity has been regard... more In this two-part essay, we distinguish several senses in which general relativity has been regarded as "locally special relativistic". In Part 1, we focused on senses in which a relativistic spacetime may be said to be "locally (approximately) Minkowskian". Here, in Part 2, we consider what it might mean to say that a matter theory is "locally special relativisitc". We isolate and evaluate three criteria in the literature and show that they are incompatible: matter theories satisfying one will generally violate others. We then consider what would happen if any of those criteria failed for a given theory.
In this two-part essay, we distinguish several senses in which general relativity has been regard... more In this two-part essay, we distinguish several senses in which general relativity has been regarded as "locally special relativistic". Here, in Part 1, we focus on senses in which a relativistic spacetime has been said to be "locally (approximately) Minkowskian". After critiquing several proposals in the literature, we present a result capturing a substantive sense in which every relativistic spacetime is locally approximately Minkowskian. We then show that Minkowski spacetime is not distinguished in this result: every relativistic spacetime is locally approximately every other spacetime in the same sense. In Part 2, we will consider "locally specially relativistic" matter theories.
Wilhelm (2021) has recently defended a criterion for comparing structure of mathematical objects,... more 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.
It is widely accepted by physicists and philosophers of physics alike that there are certain cont... more It is widely accepted by physicists and philosophers of physics alike that there are certain contexts in which general relativity will "break down". In such cases, one expects to need some as-yet undiscovered successor theory. This paper will discuss certain pathologies of general relativity that might be taken to signal that the theory is breaking down, and consider how one might expect a successor theory to do better. The upshot will be an unconventional interpretation of the "Strong Cosmic Censorship Hypothesis".
A classic result in the foundations of Yang-Mills theory, due to J. W. Barrett ["Holonomy an... more A classic result in the foundations of Yang-Mills theory, due to J. W. Barrett ["Holonomy and Path Structures in General Relativity and Yang-Mills Theory." Int. J. Th. Phys. 30(9), (1991)], establishes that given a "generalized" holonomy map from the space of piece-wise smooth, closed curves based at some point of a manifold to a Lie group, there exists a principal bundle with that group as structure group and a principal connection on that bundle such that the holonomy map corresponds to the holonomies of that connection. Barrett also provided one sense in which this "recovery theorem" yields a unique bundle, up to isomorphism. Here we show that something stronger is true: with an appropriate definition of isomorphism between generalized holonomy maps, there is an equivalence of categories between the category whose objects are generalized holonomy maps on a smooth, connected manifold and whose arrows are holonomy isomorphisms, and the category whose o...
In this paper, we examine the relationship between general relativity and the theory of Einstein ... more 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 (2012, 2015) and Weatherall (2015), the two are equivalent theories.
We provide a novel perspective on "regularity" as a property of representations of the ... more We provide a novel perspective on "regularity" as a property of representations of the Weyl algebra. We first critique a proposal by Halvorson [2004, "Complementarity of representations in quantum mechanics", Studies in History and Philosophy of Modern Physics 35(1), pp. 45--56], who argues that the non-regular "position" and "momentum" representations of the Weyl algebra demonstrate that a quantum mechanical particle can have definite values for position or momentum, contrary to a widespread view. We show that there are obstacles to such an intepretation of non-regular representations. In Part II, we propose a justification for focusing on regular representations, pace Halvorson, by drawing on algebraic methods.
Synthese, 2020
Why do people who disagree about one subject tend to disagree about other subjects as well? In th... more Why do people who disagree about one subject tend to disagree about other subjects as well? In this paper, we introduce a model to explore this phenomenon of "epistemic factionization". Agents attempt to discover the truth about multiple propositions by testing the world and sharing evidence gathered. But agents tend to mistrust evidence shared by those who do not hold similar beliefs. This mistrust leads to the endogenous emergence of factions of agents with multiple, highly correlated, polarized beliefs.
Towards a Theory of Spacetime Theories, 2017
I begin by reviewing some recent work on the status of the geodesic principle in general relativi... more I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to "explain" inertial motion. I argue that there is a sense in which both theories may be understood to explain inertial motion, but that the sense of "explain" is rather different from what one might have expected. This sense of explanation is connected with a view of theories-I call it the "puzzleball view"-on which the foundations of a physical theory are best understood as a network of mutually interdependent principles and assumptions.
Philosophy of Science, Feb 7, 2013
There is a venerable position in the philosophy of space and time that holds that the geometry of... more There is a venerable position in the philosophy of space and time that holds that the geometry of spacetime is conventional, provided one is willing to postulate a "universal force field". Here we ask a more focused question, inspired by this literature: in the context of our best classical theories of space and time, if one understands "force" in the standard way, can one accommodate different geometries by postulating a new force field? We argue that the answer depends on one's theory. In Newtonian gravitation the answer is "yes"; in relativity theory, it is "no".
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Papers by James Owen Weatherall
We highlight two key distinctions: (1) the difference between qualitative and "full" determinism, as emphasized in recent discussions of physics and metaphysics, and (2) the distinction between weak and strong formal conditions on the uniqueness of world extensions. We argue that defining determinism in terms of metaphysical notions such as haecceities is unhelpful, whereas rigorous formal criteria -- such as Belot's D1 and D3 -- offer a tractable and scientifically relevant account. By clarifying what it means for a theory to be deterministic, we set the stage for a fruitful interaction between physics and metaphysics.
is unclear how the Humean can make sense of local, concrete inquiry yielding knowledge which is global in scope, lawlike in character, and counterfactually robust. As a result, Humeanism is left without a plausible account of scientific epistemology.
an equivalent reformulation of general relativity. In this paper we question that view. We argue that the theories are not equivalent, by the criterion of categorical equivalence and any stronger criterion, and that teleparallel gravity posits strictly more structure than general relativity.
We highlight two key distinctions: (1) the difference between qualitative and "full" determinism, as emphasized in recent discussions of physics and metaphysics, and (2) the distinction between weak and strong formal conditions on the uniqueness of world extensions. We argue that defining determinism in terms of metaphysical notions such as haecceities is unhelpful, whereas rigorous formal criteria -- such as Belot's D1 and D3 -- offer a tractable and scientifically relevant account. By clarifying what it means for a theory to be deterministic, we set the stage for a fruitful interaction between physics and metaphysics.
is unclear how the Humean can make sense of local, concrete inquiry yielding knowledge which is global in scope, lawlike in character, and counterfactually robust. As a result, Humeanism is left without a plausible account of scientific epistemology.
an equivalent reformulation of general relativity. In this paper we question that view. We argue that the theories are not equivalent, by the criterion of categorical equivalence and any stronger criterion, and that teleparallel gravity posits strictly more structure than general relativity.
Scientists are generally subject to social pressures, including pressures to conform with others in their communities, that affect achievement of their epistemic goals. Here we analyze a network epistemology model in which agents, all else being equal, prefer to take actions that conform with those of their neighbors. This preference for conformity interacts with the agents' beliefs about which of two (or more) possible actions yields the better outcome. We find a range of possible outcomes, including stable polarization in belief and action. The model results are sensitive to network structure. In general, though, conformity has a negative effect on a community's ability to reach accurate consensus about the world.