16-17 St Ebbe’s Street

Oxford OX1 1PT

teru dot thomas

at oxon dot org

I am a senior research fellow in philosophy at the University of Oxford, based at the Global Priorities Institute. My current work is mainly in normative ethics and decision theory, although I am also interested in the philosophy of mathematics, the philosophy of physics, formal epistemology, and many other areas.

I was previously a mathematician, working on some topics in representation theory and algebraic geometry. My PhD was from the University of Chicago, and I held research fellowships at Oxford and Edinburgh. Having collaborated on some interdisciplinary projects, I decided to retrain in philosophy, completing a second doctorate at Oxford in 2016.

I teach philosophy undergraduates at various Oxford colleges. I can offer tutorials in ethics, metaphysics, epistemology, philosophy of logic and language, philosophy of science, philosophy of mathematics, philosophy of physics, and other topics. I also supervise undergraduate and postgraduate theses in related areas. In the past I have taught mathematics as a tutor and course lecturer.

Recent Hand-Outs In winter 2017 I lectured on ‘Degrees of Belief’, a short introduction to Bayesian epistemology and decision theory.

Hand-outs >

In autumn 2017 I co-taught the graduate class ‘Topics in Ethics’ with Hilary Greaves.

Reading lists and notes >

Some Possibilities in Population Axiology

*Mind* (2018)

Abstract and links >

Separability

To appear in *The Oxford Handbook of Population Ethics*

Abstract (contact me for a draft!) >

Utilitarianism With and Without Expected Utility

(with David McCarthy and Kalle Mikkola)

Working paper (2016)

Abstract and links >

Representation of Strongly Independent Preorders by Sets of Scalar-Valued Functions

(with David McCarthy and Kalle Mikkola)

Working paper (2017)

Abstract and links >

Topics in Population Ethics

DPhil Thesis, University of Oxford (2016)

Link to archived copy >

On the CPT Theorem (with Hilary Greaves)

*Studies in History and Philosophy of Modern Physics* (2014)

Abstract and links >

Weil Representation and Transfer Factor

* Algebra and Number Theory* (2013)

Abstract and links >

Characteristic Cycle of the Theta Sheaf

Manuscript (2012)

Abstract and links >

Compatible Intertwiners for Representations of Finite Nilpotent Groups (with Masoud Kamgarpour)

*Representation Theory* (2011)

Abstract and links >

The Character of the Weil Representation*J. London Mathematical Society* (2008)

Abstract and links >

The Maslov Index as a Quadratic Space

*Mathematical Research Letters* (2006)

Abstract and links >

High-Spin States in ^{205}Rn: A New Shears Band Structure?

J. Novak et al., *Physical Review C* (1999)

Direct link >

See here for the research agenda of the Global Priorities Institute. Below is a list of some of my on-going projects. Please feel free to contact me for more information.

- Self-locating credence and objective chance
- Time-relative interests and personal identity
- Utilitarian and egalitarian aggregation theorems
- Vagueness and contingency of value
- Consequentialism and risk aversion
- Homotopy type theory, category theory, and structuralism

Notes on QFT and Geometric Quantization

Seminars at Edinburgh, c. 2012 >

Hecke Theory in the Language of Vector Bundles

Master’s thesis, 2003 >

Structure Constants of the Global Hecke Algebra

Research proposal, c. 2006 >

Structure Constants Formulary

Calculations with tamely ramified automorphic forms on the projective line, c. 2007 >

Cobordisms, Categories, and Quadratic Forms

Talk for Oxford Topology Seminar, 2008 >

Edinburgh Maslov Index Seminar

Lecture notes thanks to Thomas Koeppe, 2010 >

ORCID — Publons — PhilPapers

Some Possibilities in Population Axiology

*Mind* 127 (2018): 807-832

Abstract. It is notoriously difficult to find an intuitively satisfactory rule for evaluating populations based on the welfare of the people in them. Standard examples, like total utilitarianism, either entail the Repugnant Conclusion or in some other way contradict common and deeply felt intuitions about the relative value of populations. Several philosophers have presented formal arguments that seem to show that this happens of necessity: our core intuitions stand in contradiction. This paper assesses the state of play, focusing on the most powerful of these ‘impossibility theorems’, as developed by Gustaf Arrhenius. I highlight two ways in which these theorems fall short of their goal: some of them appeal to a supposedly egalitarian condition which, however, does not properly reflect egalitarian intuitions; the others rely on a background assumption about the structure of welfare which cannot be taken for granted. Nonetheless, the theorems remain important: they give insight into the difficulty, if perhaps not the impossibility, of constructing a satisfactory population axiology. We should aim for reflective equilibrium between intuitions and more theoretical considerations. I conclude by highlighting one possible ingredient in this equilibrium, which, I argue, leaves open a still wider range of acceptable theories: the possibility of vague or otherwise indeterminate value relations.

Keywords. Population ethics, impossibility theorems, egalitarianism, vagueness
Separability

To appear in*The Oxford Handbook of Population Ethics*

To appear in

Abstract. Separability is roughly the principle that, in comparing the value of two possible outcomes, one can ignore any people whose existence and welfare are unaffected. Separability is both antecedently plausible and surprisingly powerful; it is the key to some of the best positive arguments in population ethics (in particular: arguments for total utilitarianism). Besides surveying the motivations for and consequences of separability, I explore systematically how separable, anonymous population axiologies can respond to the Repugnant Conclusion.

Keywords. Population ethics, separability, utilitarianism
Representation of Strongly Independent Preorders by Sets of Scalar-Valued Functions

(with David McCarthy and Kalle Mikkola)

MPRA preprint (2017)

(with David McCarthy and Kalle Mikkola)

MPRA preprint (2017)

Abstract (Less Technical). This paper examines a foundational problem in decision theory. Standard expected utility theory assumes that an agent’s preferences (or, more objectively, the betterness relation) is complete; this, in conjunction with other axioms, entails that the agent can be represented as maximizing expected utility. A folk theorem (and in some cases a genuine theorem) claims that if the agent’s preferences are not complete, the agent can nonetheless be represented as maximizing expected utility as long as we supervaluate over a family of utility functions. We examine the conditions under which this claim is true.

Abstract. We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infinite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfies a condition that we call Polarization.

Keywords. Expected utility, multi-representation, incompleteness, mixture continuity
Utilitarianism With and Without Expected Utility

(with David McCarthy and Kalle Mikkola)

MPRA preprint (2016)

(with David McCarthy and Kalle Mikkola)

MPRA preprint (2016)

Abstract. We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The individual preorder then uniquely determines a social preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi's utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.

Keywords. Harsanyi, utilitarianism, expected utility, nonexpected utility, egalitarianism, variable populations.
On the CPT Theorem (with Hilary Greaves)

*Studies in History and Philosophy of Modern Physics* 45 (2014) 46-66
/
arXiv

Abstract. We provide a careful development and rigorous proof of the CPT theorem within the framework of mainstream (Lagrangian) quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches in the mainstream approach. We construct the CPT transformation for a general field directly, without appealing to the enumerative classification of representations, and in a manner that is clearly related to the requirements of our proof. Our approach applies equally in Minkowski spacetimes of any dimension at least three, and is in principle neutral between classical and quantum field theories: the quantum CPT theorem has a natural classical analogue. The key mathematical tool is that of complexification; this tool is central to the existing axiomatic proofs, but plays no overt role in the usual mainstream approaches to CPT.

Keywords. Quantum field theory; CPT theorem; Discrete symmetries; Spacetime symmetries.
Weil Representation and Transfer Factor

*Algebra and Number Theory* 7 (2013), 1535-1570
/
Preprint version

Abstract. This paper concerns the Weil representation of the semidirect product of the metaplectic and Heisenberg groups. First we present a canonical construction of the metaplectic group as a central extension of the symplectic group by a subquotient of the Witt group. This leads to simple formulas for the character, for the inverse Weyl transform, and for the transfer factor appearing in J. Adams’s work on character lifting. Along the way, we give formulas for outer automorphisms of the metaplectic group induced by symplectic similitudes. The approach works uniformly for finite and local fields.

Keywords. Metaplectic group, Weil representation, Weyl transform, transfer factor, Cayley transform, Maslov index.
Compatible Intertwiners for Representations of Finite Nilpotent Groups (with Masoud Kamgarpour)

*Represent. Theory* 15 (2011), 407-432
/
arXiv version

Abstract. We sharpen the orbit method for finite groups of small nilpotence class by associating representations to functionals on the corresponding Lie rings. This amounts to describing compatible intertwiners between representations parameterized by an additional choice of polarization. Our construction is motivated by the theory of the linearized Weil representation of the symplectic group. In particular, we provide generalizations of the Maslov index and the determinant functor to the context of finite abelian groups.

Keywords. Nilpotent groups, orbit method, Weil representation, Maslov index, determinants.
The Character of the Weil Representation

*J. LMS* (2) 77 (2008), 221-239. doi: 10.1112/jlms/jdm098 /
arXiv version

Abstract. Let V be a symplectic vector space over a finite or local field. We compute the character of the Weil representation of the metaplectic group Mp(V). The final formulas are overtly free of choices (for example, they do not involve the usual choice of a Lagrangian subspace of V). Along the way, in results similar to those of Maktouf, we relate the character to the Weil index of a certain quadratic form, which may be understood as a Maslov index. This relation also expresses the character as the pullback of a certain simple function from Mp(V\oplus V).

Keywords. Weil representation, Maslov index, character formula, metaplectic group.
Characteristic Cycle of the Theta Sheaf

Manuscript (2012)

Manuscript (2012)

Abstract. We extend from characteristic p to characteristic zero S. Lysenko’s theory of theta sheaves on the moduli stack of metaplectic bundles. The main tool is a Fourier transform for semi-homogeneous sheaves on vector bundles. We then calculate the characteristic cycles of the theta sheaves, showing that they lie in a small part of the global nilpotent cone.

Keywords. Metaplectic bundles, theta sheaf, characteristic cycles, Fourier transform.
The Maslov Index as a Quadratic Space

*Math. Res. Lett.* 13 no. 6 (2006), 985-999 /
arXiv (expanded version)

Abstract. Kashiwara defined the Maslov index (associated to a collection of Lagrangian subspaces of a symplectic vector space over a field F) as a class in the Witt group W(F) of quadratic forms. We construct a canonical quadratic vector space in this class and show how to understand the basic properties of the Maslov index without passing to W(F) – that is, more or less, how to upgrade Kashiwara’s equalities in W(F) to canonical isomorphisms between quadratic spaces. We also show how our canonical quadratic form occurs naturally in the context of the Weil representation. The quadratic space is defined using elementary linear algebra. On the other hand, it has a nice interpretation in terms of sheaf cohomology, due to A. Beilinson.

Keywords. Maslov index, quadratic forms, sheaf cohomology, Witt group.