Hans Halvorson

University of Pittsburgh
Department of Philosophy
PhD, 2001
Princeton, New Jersey, United States of America
Areas of Specialization
PhilPapers Editorships
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Closing the Hole Argument with J. B. Manchak
The hole argument purportedly shows that spacetime substantivalism implies a pernicious form of indeterminism. We show that the argument is seductive only because it mistakes a trivial claim (viz. there are isomorphic models) for a significant claim (viz. there are hole isomorphisms). We prove that the latter claim is false -- thereby closing the debate about whether substantivalism implies indeterminism.
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John Bell on 'Subject and Object': an Exchange with Jeremy Butterfield
This three-part paper comprises: (i) a critique by Halvorson of Bell’s (1973) paper ‘Subject and Object’; (ii) a comment by Butterfield; (iii) a reply by Halvorson. An Appendix gives the passage from Bell that is the focus of Halvorson's critique.
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What hole argument? with J. B. Manchak
The hole argument is supposed to show that spacetime substantivalism implies indeterminism. Here we attempt to answer the question: what is the mathematical fact that is supposed to generate the hole argument? We identify two potential mathematical facts. The first fact is trivial -- as argued by Weatherall -- and so cannot support the hole argument. The second fact would be non-trivial, but we prove that it is false. We conclude that there is no basis for the hole argument.
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John Bell on Subject and Object
A critical examination of John Bell's article "Subject and object"
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Momentum and Context
A sentence's meaning may depend on the state of motion of the speaker. I argue that this context-sensitivity blocks the inference from special relativity to four-dimensionalism.
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How Logic Works: A User's Guide Princeton University Press. 2020.
How Logic Works is an introductory logic textbook that is different by design. Rather than teaching elementary symbolic logic as an abstract or rote mathematical exercise divorced from ordinary thinking, Hans Halvorson presents it as the skill of clear and rigorous reasoning, which is essential in all fields and walks of life, from the sciences to the humanities—anywhere that making good arguments, and spotting bad ones, is critical to success. Instead of teaching how to apply algorithms using …Read more
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Concluding Unscientific Image (review) Metascience 29 175-185. 2020.
40-year anniversary review of van Fraassen's Scientific Image
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Theories are not partially ordered with Thomas William Barrett
This paper presents a simple example of first-order theories T1 and T2 such that i) T1 can be embedded in T2 and vice versa, ii) T1 posits all of the structure of T2 and vice versa, but iii) T1 and T2 are not equivalent. This shows that theories lack both the Cantor-Bernstein and co-Cantor-Bernstein properties and are neither partially ordered by the relation 'is embeddable in' nor by 'posits all of the structure of'. In addition, these results clarify the overall geography of notions of equiv…Read more
•  190
Extension, Translation, and the Cantor-Bernstein Property with Thomas William Barrett
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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Deep Beauty: Understanding the Quantum World through Mathematical Innovation (edited book) Cambridge University Press. 2011.
No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts, at the cutting edge of future physics. These creative d…Read more
•  36
It Keeps me Seeking: The Invitation from Science, Philosophy and Religion with Andrew Briggs and Andrew Steane Oxford University Press. 2018.
Here is a fresh look at how science contributes to the bigger picture of human flourishing, through a collage of science and philosophy, richly illustrated by the authors' own experience and personal reflection. They survey the territory of fundamental physics, machine learning, philosophy of human identity, evolutionary biology, miracles, arguments from design, naturalism, the history of ideas, and more. The natural world can be appreciated not only for itself, but also as an eloquent gesture, …Read more
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There is no invariant, four-dimensional stuff
Some philosophers say that in special relativity, four-dimensional stuff is invariant in some sense that three-dimensional stuff is not. I show that this claim is false.
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Quantum Entanglements: Selected Papers (edited book) with Jeremy Butterfield Clarendon Press. 2004.
This volume gathers together ground-breaking work on the foundations and philosophy of quantum physics, by one of the most brilliant and productive researchers in the field. Rob Clifton died tragically in 2002 at the age of 38; two of his colleagues, themselves leading philosophers of physics, present fourteen of his finest papers here, all of which combine exciting philosophical discussion with rigorous mathematical results. Quantum Entanglements offers inspiration and substantial reward to any…Read more
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Glymour and Quine on Theoretical Equivalence with Thomas William Barrett Journal of Philosophical Logic 45 (5): 467-483. 2016.
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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Quine’s conjecture on many-sorted logic with Thomas William Barrett Synthese 194 (9): 3563-3582. 2017.
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 the…Read more
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The Logic in Philosophy of Science Cambridge University Press. 2019.
Major figures of twentieth-century philosophy were enthralled by the revolution in formal logic, and many of their arguments are based on novel mathematical discoveries. Hilary Putnam claimed that the Löwenheim-Skølem theorem refutes the existence of an objective, observer-independent world; Bas van Fraassen claimed that arguments against empiricism in philosophy of science are ineffective against a semantic approach to scientific theories; W. V. O. Quine claimed that the distinction between ana…Read more
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Morita Equivalence with Thomas William Barrett Review of Symbolic Logic 9 (3): 556-582. 2016.
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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Foundations and Philosophy with Dimitris Tsementzis Philosophers' Imprint 18. 2018.
The Univalent Foundations of mathematics take the point of view that all of mathematics can be encoded in terms of spatial notions like "point" and "path". We will argue that this new point of view has important implications for philosophy, and especially for those parts of analytic philosophy that take set theory and first-order logic as their benchmark of rigor. To do so, we will explore the connection between foundations and philosophy, outline what is distinctive about the logic of the Univa…Read more
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From Geometry to Conceptual Relativity with Thomas William Barrett Erkenntnis 82 (5): 1043-1063. 2017.
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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How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence with David John Baker Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4): 464-469. 2013.
We pose and resolve a puzzle about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator in a ground state's GNS representation. But Wigner's theorem guarantees that any symmetry's action on states is given by a unitary operator. How can this unitary operator fail to implement the symmetry in the GNS representation? We show how it is possible for a unitary operator of this sort to con…Read more
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To be a realist about quantum theory In Olimpia Lombardi (ed.), Quantum Worlds: Perspectives on the Ontology of Quantum Mechanics, . 2019.
I look at the distinction between between realist and antirealist views of the quantum state. I argue that this binary classification should be reconceived as a continuum of different views about which properties of the quantum state are representationally significant. What's more, the extreme cases -- all or none --- are simply absurd, and should be rejected by all parties. In other words, no sane person should advocate extreme realism or antirealism about the quantum state. And if we focus on …Read more
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A Theological Critique of the Fine-Tuning Argument In Matthew A. Benton, John Hawthorne & Dani Rabinowitz (eds.), Knowledge, Belief, and God: New Insights in Religious Epistemology, Oxford University Press. pp. 122-135. 2018.
According to the premises of the fine-tuning argument, most nomologically possible universes lack intelligent life; and the fact that ours has intelligent life is best explained by supposing it was created. However, if our universe was created, then the creator chose the laws of nature, and hence chose in favor of lifeless universes. In other words, the fine-tuning argument shows that God prefers universes without intelligent life; and the fact that our universe has intelligent life provides n…Read more
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Scientific Theories In Paul Humphreys (ed.), The Oxford Handbook of Philosophy of Science, Oxford University Press. pp. 585-608. 2016.
Since the beginning of the 20th century, philosophers of science have asked, "what kind of thing is a scientific theory?" The logical positivists answered: a scientific theory is a mathematical theory, plus an empirical interpretation of that theory. Moreover, they assumed that a mathematical theory is specified by a set of axioms in a formal language. Later 20th century philosophers questioned this account, arguing instead that a scientific theory need not include a mathematical component; or t…Read more
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Complementarity of representations in quantum mechanics Studies in History and Philosophy of Modern Physics 35 (1): 45-56. 2001.
We show that Bohr's principle of complementarity between position and momentum descriptions can be formulated rigorously as a claim about the existence of representations of the canonical commutation relations. In particular, in any representation where the position operator has eigenstates, there is no momentum operator, and vice versa. Equivalently, if there are nonzero projections corresponding to sharp position values, all spectral projections of the momentum operator map onto the zero eleme…Read more
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Characterizing quantum theory in terms of information-theoretic constraints with Rob Clifton and Jeffrey Bub Foundations of Physics 33 (11): 1561-1591. 2002.
We show that three fundamental information-theoretic constraints -- the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment -- suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, a…Read more