In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. Theâ€¦ (More)

We discuss from a philosophical perspective the way in which the normal concept of time might be said to â€˜emergeâ€™ in a quantum theory of gravity. After an introduction, we briefly discuss the notionâ€¦ (More)

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. Theâ€¦ (More)

We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Section 1, we introduce these problems. Inâ€¦ (More)

This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation inâ€¦ (More)

Using the Hilbertâ€“Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned.â€¦ (More)

1. Introduction In this paper, I shall sketch some of the issues that arise in the interpretation of quantum theory, from the perspective of a philosopher of physics. I will emphasise the measurementâ€¦ (More)

This Chapter expounds the modern theory of symplectic reduction in finitedimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries andâ€¦ (More)

The twentieth century saw two fundamental revolutions in physics-relativity and quantum. Daily use of these theories can numb the sense of wonder at their immense empirical success. Does theirâ€¦ (More)

I extract some philosophical morals from some aspects of Lagrangian mechanics. (A companion paper will present similar morals from Hamiltonian mechanics and Hamilton-Jacobi theory.) One main moralâ€¦ (More)