Methodological Fundamentalism: or why Batterman’s Different Notions of ‘Fundamentalism’ may not make a Difference

I argue that the distinctions Robert Batterman (2004) presents between ‘epistemically fundamental’ versus ‘ontologically fundamental’ theoretical approaches can be subsumed by methodologically fundamental procedures. I characterize precisely what is meant by a methodologically fundamental procedure, which involves, among other things, the use of multilinear graded algebras in a theory’s formalism. For example, one such class of algebras I discuss are the Clifford (or Geometric) algebras. Aside from their being touted by many as a “unified mathematical language for physics,” (Hestenes (1984, 1986) Lasenby, et. al. (2000)) Finkelstein (2001, 2004) and others have demonstrated that the techniques of multilinear algebraic ‘expansion and contraction’ exhibit a robust regularizablilty. That is to say, such regularization has been demonstrated to remove singularities, which would otherwise appear in standard field-theoretic, mathematical characterizations of a physical theory. I claim that the existence of such methodologically fundamental procedures calls into question one of Batterman’s central points, that “our explanatory physical practice demands that we appeal essentially to (infinite) idealizations” (2003, 7) exhibited, for example, by singularities in the case of modeling critical phenomena, like fluid droplet formation. By way of counterexample, in the field of computational fluid dynamics (CFD), I discuss the work of Mann & Rockwood (2003) and Gerik Scheuermann, (2002). In the concluding section, I sketch a methodologically fundamental procedure potentially applicable to more general classes of critical phenomena appearing in fluid dynamics

On the second law of thermodynamics

The key purpose of this article is to clarify the foundations of classical statistical mechanics. It is argued that the relevant concepts and laws, e.g. probability, ergodicity, entropy and the second law of thermodynamics as well as the arrow of time, all follow directly from the Gibbs-Liouville theorem in combination with the fact that any given observer of a system do not possess infinite knowledge about the initial conditions of the system. The point of view taken is thus that statistical mechanics is a theoretical framework applicable when it is not possible to determine the state of a system completely objectively. This is in contrast to classical mechanics where, by assumption, it is possible for any given observer to know the state of the system with infinite precision. For this reason, i.e. the subjectivity of the observer, the foundational concepts and laws are phrased in terms of the information possessed by the observer about the system studied

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

On Time chez Dummett

I discuss three connections between Dummett's writings about time and philosophical aspects of physics. The first connection (Section 2) arises from remarks of Dummett's about the different relations of observation to time and to space. The main point is uncontroversial and applies equally to classical and quantum physics. It concerns the fact that perceptual processing is so rapid, compared with the typical time-scale on which macroscopic objects change their observable properties, that it engenders the idea of a 'common now', spread across space. The other two connections are specific to quantum theory, as interpreted along the lines of Everett. So for these two connections, the physics side is controversial, just as the philosophical side is. In Section 3, I connect the subjective uncertainty before an Everettian 'splitting' of the multiverse to Dummett's suggestion, inspired by McTaggart, that a complete, i.e. indexical-free description of a temporal reality is impossible. And in Section 4, I connect Barbour's denial that time is real---a denial along the lines of Everett, rather than McTaggart---to Dummett's suggestion that statements about the past are not determinately true or false, because they are not effectively decidable.Comment: 25 pages; no figure

Dynamical Emergence of FRW Cosmological Models

Recent astronomical observations strongly indicate that the current Universe is undergoing an accelerated phase of expansion. The discovery of this fact was unexpected and resulted in the comeback of cosmological constant. The conception of standard cosmological model has its roots in this context. The paper relates to the methodological status of effective theories in the context of cosmological investigations. We argue that the standard cosmological model (LCDM model) as well as the CDM have a status of effective theories only, similarly to the standard model of particle physics. The LCDM model is studied from the point of view of the methodological debate on reductionism and epistemological emergence in the science. It is shown in the paper that bifurcation as well as structural instability notion can be useful in the detection of emergence the LCDM model from the CDM model. We demonstrate that the structural stability of the LCDM model can explain the flexibility of the model to accommodation of the observational data. We show that LCDM model can be derived from CDM as the bifurcation. It is an example of acausal derivation of Lambda term. The case study of emergence of LCDM model suggests that it can be understood in terms of bifurcation and structural stability issue. The reduction from the upper models represented in terms of dynamical system to low-level ones can be realized in any case by application of a mathematical limit (boundary crossing) with respect to the model parameter. It is a simple consequence of mathematical theorem about smooth dependence solutions with respect to time, initial condition and the parameters.Comment: 8ssmmp.cls, 14 pages, 3 figures; rev. 2: added section on emergence from bifurcation; rev. 3: reorganized and shortened text; transition from the LCDM to CDM model was explicitly shown, for this aim it was used the theorem on smooth dependence of solution on initial conditions and change of parameters. In: B. Dragovich, I. Salom (eds) Proceedings of the 8th Mathematical Physics Meeting: Summer School and Conference on Modern Mathematical Physics. August 24-31, 2014, Belgrade, Serbia. Institute of Physics, Belgrade, 201

A Loophole in Bell's Theorem? Parameter Dependence in the Hess-Philipp Model

The hidden-variables model constructed by Karl Hess and Walter Philipp is claimed by its authors to exploit a "loophole" in Bell's theorem; the claim is made by Hess and Philipp that the parameters employed in their model extend beyond those considered by Bell. Furthermore, they claim that their model satisfies Einstein locality and is free of any "suspicion of spooky action at a distance." Both of these claims are false; the Hess-Philipp model achieves agreement with the quantum-mechanical predictions, not by circumventing Bell's theorem, but via Parameter Dependence.Comment: 18 pages, 1 figure, 1 table. In this version, remarks have been added to make clearer the relation between the Hess-Philipp model and the simpler model presented herein. References to related criticisms of Hess and Philipp, by Gill et al, (quant-ph/0204169) and Mermin (quant-ph/0206118) have also been added. To be presented at the 18th Biennial Meeting of the Philosophy of Science Association, Milwaukee, Nov. 7-10, 2002. This version matches that deposited on the PhilSci archive at http://philsci-archive.pitt.edu/, PITT-PHIL-SCI0000069