Craig Callender

From Kant’s first published work to recent articles in the physics literature, philosophers and physicists have long sought an answer to the question, why does space have three dimensions. In this paper, I will flesh out Kant’s claim with a brief detour through Gauss’ law. I then describe Büchel’s version of the common argument that stable orbits are possible only if space is three-dimensional. After examining objections by Russell and van Fraassen, I develop three original criticisms of my own. These criticisms are relevant to both historical and contemporary proofs of the dimensionality of space (in particular, a recent one by Burgbacher, F. Lämmerzahl, C., and Macias). In general I argue that modern “proofs” of the dimensionality of space have gone off track.

Is the quantum state part of the furniture of the world? Einstein found such a position indigestible, but here I present a different understanding of the wavefunction that is easy to stomach. First, I develop the idea that the wavefunction is nomological in nature, showing how the quantum It or Bit debate gets subsumed by the corresponding It or Bit debate about laws of nature. Second, I motivate the nomological view by casting quantum mechanics in a “classical” formalism (Hamilton–Jacobi theory) and classical mechanics in a “quantum” formalism (Koopman–von Neumann theory) and then comparing and contrasting classical and quantum wave functions. I argue that Humeans about laws can treat classical and quantum wave functions on a par and that doing so yields many benefits.

This thesis is an attempt to accurately formulate and solve one of the problems associated with the direction of time. Processes in nature appear to be 'irreversible', for instance, heat flows from hot to cold but never from cold to hot. The problem of the direction of time, roughly put, is the difficulty of squaring this irreversible behavior with the apparent fact that the fundamental laws of physics are completely reversible. ;In the first three chapters I critically review the foundations of statistical mechanics. After arguing that entropy is an objective property of the thermodynamic world, I contrast the 'Boltzmannian' single-system approach to statistical mechanics with the 'Gibbsian' many-system approach. Based in part on its ability to handle irreversibility, I judge the Boltzmann approach to be superior from a philosophical perspective. I argue, however, that the statistical mechanical probabilities cannot be interpreted in such a way as to allow the theory to give the sort of explanation originally desired. ;The next four chapters are devoted to the direction of time. Chapters four and five attempt to provide the problem with the philosophically mature geography that has so far eluded it. Chapter six discusses the problem in the context of quantum mechanics, and chapter seven criticizes the problem's standard formulation. I show that the problem is really a much more general one than has previously been appreciated; indeed, I try to show that it is a problem afflicting all the special sciences. ;Finally, the remaining three chapters investigate three separate issues. Chapter eight discusses the tensed theory of time. I claim the best argument for the tensed theory relies on various temporal asymmetries, e.g., the asymmetry of causation. I provide reasons for not being persuaded by this argument. The tensed theory, I conclude, is not incoherent, as many have claimed, instead it is simply an implausible explanation of our experience. Chapter nine examines the possibility that quantum mechanics implies our world is temporally anisotropic, and chapter ten looks at some conceptual difficulties associated with our conception of time reversal invariance

This is the table of contents and first chapter of Physics Meets Philosophy at the Planck Scale (Cambridge University Press, 2001), edited by Craig Callender and Nick Huggett. The chapter discusses the question of why there should be a theory of quantum gravity. We tackle arguments that purport to show that the gravitational field *must* be quantized. We then introduce various programs in quantum gravity and discuss areas where quantum gravity and philosophy seem to have something to say to each other.