Isaac Wilhelm

If a proposition is typically true, given your evidence, then you should believe that proposition; or so I argue here. In particular, in this paper, I propose and defend a principle of rationality---call it the `Typical Principle'---which links rational belief to facts about what is typical. As I show, this principle avoids several problems that other, seemingly similar principles face. And as I show, in many cases, this principle implies the verdicts of the Principal Principle: so ultimately, the Typical Principle may be the more fundamental of the two.

According to the Best System Account of lawhood, laws of nature are theorems of the deductive systems that best balance simplicity and strength. In this paper, I advocate a different account of lawhood which is related, in spirit, to the BSA: according to my account, laws are theorems of deductive systems that best balance simplicity, strength, and also calculational tractability. I discuss two problems that the BSA faces, and I show that my account solves them. I also use my account to illuminate the nomological character of special science laws.

I formulate a theory of groups based on pluralities and counterparts: roughly put, a group is a plurality of entities at a time. This theory comes with counterpart-theoretic semantics for modal and temporal sentences about groups. So this theory of groups is akin to the stage theory of material objects: both take the items they analyze to exist at a single time, and both use counterparts to satisfy certain conditions relating to the modal properties, temporal properties, and coincidence properties of those items.

I explore the relationship between a prominent analysis of intrinsic properties, due to Langton and Lewis, and the phenomenon of quantum entanglement. As I argue, the analysis faces a puzzle. The full analysis classifies certain properties of entangled particles as intrinsic. But when combined with an extremely plausible assumption about duplication, the main part of the analysis classifies those properties as non-intrinsic instead. I conclude that much of Lewis’s metaphysics is in trouble: Lewis based many of his metaphysical views—his thesis of Humean supervenience, for instance, and his account of recombination—on an analysis of intrinsicality which does not sit well with quantum phenomena.

Philosophers have developed several detailed accounts of what makes some mathematical proofs explanatory. Significantly less attention has been paid, however, to what makes some proofs more explanatory than other proofs. That is problematic, since the reasons for thinking that some proofs explain are also reasons for thinking that some proofs are more explanatory than others. So in this paper, I develop an account of comparative explanation in mathematics. I propose a theory of the `at least as explanatory as' relation among mathematical proofs.

A popular method for comparing the structures of mathematical objects, which I call the ‘subset approach’, says that X has more structure than Y just in case X’s automorphisms form a proper subset of Y’s automorphisms. This approach is attractive, in part, because it seems to yield the right results in some comparisons of spacetime structure. But as I show, it yields the wrong results in a number of other cases. The problem is that the subset approach compares structure using automorphism sets. So a different approach is needed: structure should be compared using automorphism groups.

I show that centered propositions—also called de se propositions, and usually modeled as sets of centered worlds—pose a serious problem for various versions of Lewis's Principal Principle. The problem, put roughly, is that in scenarios like Elga's `Sleeping Beauty' case, those principles imply that rational agents ought to have obviously irrational credences. To solve the problem, I propose a centered version of the Principal Principle. My version allows centered propositions to be objectively chancy.

Typicality is routinely invoked in everyday contexts: bobcats are typically short-tailed; people are typically less than seven feet tall. Typicality is invoked in scientific contexts as well: typical gases expand; typical quantum systems exhibit probabilistic behaviour. And typicality facts like these support many explanations, both quotidian and scientific. But what is it for something to be typical? And how do typicality facts explain? In this paper, I propose a general theory of typicality. I analyse the notion of a typical property. I provide a formalism for typicality explanations, and I give an account of why typicality explanations are explanatory. Along the way, I show how typicality facts explain a variety of phenomena, from everyday phenomena to the statistical mechanical behaviour of gases. Finally, I argue that typicality is not the same thing as probability.

I explore how the nature, scope, and limits of the knowledge obtained in orbital dynamics has changed in recent years. Innovations in the design of spacecraft trajectories, as well as in astronomy, have led to new logics of theory-testing—that is, new research methodologies—in orbital dynamics. These methodologies—which combine resonance overlap theories, numerical experiments, and the implementation of space missions—were developed in response to the discovery of chaotic dynamical systems in our solar system. In the past few decades, they have replaced the methodology that dominated orbital research in the centuries following Newton's Principia. As a result, the kind of knowledge achieved by orbital research has changed: we can know how orbiting bodies in chaotic systems behave, but only over sufficiently short time scales; and we can reliably measure those temporal limitations, using Lyapunov time.

This paper presents new data on the representation of women who publish in 25 top philosophy journals as ranked by the Philosophical Gourmet Report for the years 2004, 2014, and 2015. It also provides a new analysis of Schwitzgebel’s 1955–2015 journal data. The paper makes four points while providing an overview of the current state of women authors in philosophy. In all years and for all journals, the percentage of female authors was extremely low, in the range of 14–16%. The percentage of women authors is less than the percentage of women faculty in different ranks and at different kinds of institutions. In addition, there is great variation across individual journals, and the discrepancy between women authors and women faculty appears to be different in different subfields. Interestingly, journals which do not practice anonymous review seem to have a higher percentage of women authors than journals which practice double anonymous or triple anonymous review. This paper also argues that we need more data on academic publishing to better understand whether this can explain why there are so few full-time female faculty in philosophy, since full-time hiring and tenuring practices presumably depend on a candidate’s academic publishing.