Boolean Coverings of Quantum Observable Structure: A Setting for an Abstract Differential Geometric Mechanism

We develop the idea of employing localization systems of Boolean coverings, associated with measurement situations, in order to comprehend structures of Quantum Observables. In this manner, Boolean domain observables constitute structure sheaves of coordinatization coefficients in the attempt to probe the Quantum world. Interpretational aspects of the proposed scheme are discussed with respect to a functorial formulation of information exchange, as well as, quantum logical considerations. Finally, the sheaf theoretical construction suggests an opearationally intuitive method to develop differential geometric concepts in the quantum regime.Comment: 25 pages, Late

Against Pointillisme about Mechanics

This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the concept of velocity in classical mechanics; especially against proposals by Tooley, Robinson and Lewis. A companion paper argues against pointillisme about (chrono)-geometry, as proposed by Bricker. To avoid technicalities, I conduct the argument almost entirely in the context of ``Newtonian'' ideas about space and time, and the classical mechanics of point-particles, i.e. extensionless particles moving in a void. But both the debate and my arguments carry over to relativistic physics.Comment: 41 pages Late

Against Pointillisme about Geometry

This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the structure of space and-or spacetime itself, especially a paper by Bricker (1993). A companion paper argues against pointillisme in mechanics, especially about velocity; it focusses on Tooley, Robinson and Lewis. To avoid technicalities, I conduct the argument almost entirely in the context of ``Newtonian'' ideas about space and time. But both the debate and my arguments carry over to relativistic, and even quantum, physics.Comment: 37 pages Late

Laws, Causation and Dynamics at Different Levels

I have two main aims. The first is general, and more philosophical (Section 2). The second is specific, and more closely related to physics (Sections 3 and 4). The first aim is to state my general views about laws and causation at different `levels'. The main task is to understand how the higher levels sustain notions of law and causation that `ride free' of reductions to the lower level or levels. I endeavour to relate my views to those of other symposiasts. The second aim is to give a framework for describing dynamics at different levels, emphasising how the various levels' dynamics can mesh or fail to mesh. This framework is essentially that of elementary dynamical systems theory. The main idea will be, for simplicity, to work with just two levels, dubbed `micro' and `macro' which are related by coarse-graining. I use this framework to describe, in part, the first four of Ellis' five types of top-down causation

UTP2: Higher-Order Equational Reasoning by Pointing

We describe a prototype theorem prover, UTP2, developed to match the style of hand-written proof work in the Unifying Theories of Programming semantical framework. This is based on alphabetised predicates in a 2nd-order logic, with a strong emphasis on equational reasoning. We present here an overview of the user-interface of this prover, which was developed from the outset using a point-and-click approach. We contrast this with the command-line paradigm that continues to dominate the mainstream theorem provers, and raises the question: can we have the best of both worlds?Comment: In Proceedings UITP 2014, arXiv:1410.785

Between Laws and Models: Some Philosophical Morals of Lagrangian Mechanics

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 moral concerns methodology: Lagrangian mechanics provides a level of description of phenomena which has been largely ignored by philosophers, since it falls between their accustomed levels--``laws of nature'' and ``models''. Another main moral concerns ontology: the ontology of Lagrangian mechanics is both more subtle and more problematic than philosophers often realize. The treatment of Lagrangian mechanics provides an introduction to the subject for philosophers, and is technically elementary. In particular, it is confined to systems with a finite number of degrees of freedom, and for the most part eschews modern geometry. But it includes a presentation of Routhian reduction and of Noether's ``first theorem''.Comment: 106 pages, no figure