Conceptual strategies and inter-theory relations: The case of nanoscale cracks

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Abstract

This paper introduces a new account of inter-theory relations in physics, which I call the conceptual strategies account. Using the example of a multiscale computer simulation model of nanoscale crack propagation in silicon, I illustrate this account and contrast it with existing reductive, emergent, and handshaking approaches. The conceptual strategies account develops the notion that relations among physical theories, and among their models, are constrained but not dictated by limitations from physics, mathematics, and computation, and that conceptual reasoning within those limits is required both to generate and to understand the relations between theories. Conceptual strategies result in a variety of types of relations between theories and models. These relations are themselves epistemic objects, like theories and models, and as such are an under-recognized part of the epistemic landscape of science.

Original languageEnglish
Pages (from-to)158-165
Number of pages8
JournalStudies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
Volume62
DOIs
StatePublished - May 2018

Bibliographical note

Funding Information:
It is not merely logical relations that undergird inter-theory relations in physics. It is both possible and, for the purposes of multi-scale modeling, necessary, to develop accounts of how different theories at different scales can be constructively combined to model material behavior. The conceptual-strategies account of inter-theory relations that I have presented here is offered as an alternative both to standard views of inter-theory relations—which fail to offer a satisfactory account of the conceptual transition, in a given explanation, prediction, or simulation, from one theory to another—and to Winsberg's handshaking account of physical relations between component models in a multiscale model. I have argued that relations between theories in physics, such as between continuum and molecular classical mechanics, and between classical and quantum mechanics, rely on conceptual strategizing, a practice of reasoning within computational, mathematical, and physical constraints, which is exemplified by techniques such as the MNRF and silogen strategies used in this paper's central example of a nanoscale crack propagating through a block of silicon. These techniques, called handshaking algorithms, are instances of a few common conceptual strategies; other conceptual strategies include idealization and abstraction, among others. In philosophy of science, these strategies have been discussed primarily in the context of the epistemology of models, and one aim of this essay has been to show that these strategies are relevant to a wider variety of debates and contexts. By modeling (if you will) an account of inter-theory relations after successful strategies for constructing multiscale models, I have uncovered a more robust picture of how theories can collaborate to generation predictions and explanations in physics. The example used throughout this essay to motivate this account has been a multiscale computer simulation of a nanoscale crack propagating through a block of silicon. This example is particularly salient because of its use of two distinct strategies for connecting theories across widely differing length scales. The first strategy, used to connect the models of the mesoscopic and microscopic length scales of the system, was to construct a fictional entity on which calculations from both contributing models could be performed, and the results averaged. This entity, the silogen, is neither an idealization of any realistic atom, nor is it a straightforward abstraction. As a piece of epistemic equipment, it is more closely akin to the construction of an explicitly un-physical fiction, such as the classical trajectories ascribed to electrons in quantum dots discussed by Bokulich ( Bokulich, 2008; Bokulich, 2012 ). The second strategy, used to connect the macroscopic and mesoscopic length scales of the system, was to manipulate a non-representational mathematical feature of the macroscopic model, namely the distribution in space of the mesh points used to discretize the continuum model of the system, in order to license the algorithm that was used to bridge the models of the macroscopic and mesoscopic scales. I have suggested that this strategy, which I called MNRF, is a more general one that may be found in many instances of modeling across length, time, and energy scales in physics, and likely in other sciences as well. In the modeling of critical phenomena via the renormalization group, for instance, Kadanoff's block-spin parameterization manipulates features of the model—the blocks—that are not meant to be representational of any physical phenomenon or behavior; it is another instance of the MNRF strategy. This conceptual strategy is distinct from abstraction, idealization, and constructing a fiction, which are nonetheless additional means of connecting theories across scales. More broadly, my aim has been to show that conceptual strategies such as these are sometimes necessary to bridge scales, and that when they are used in this context they should be studied in the same ways that they are studied in more general modeling contexts; fictions, for instance, do not stop being fictions when they are called upon to ground an inter-theory relation, and what we know of fictions can help us to understand their uses as inter-theory relations. Importantly, this panoply of strategies is not reducible to the articulation of logical relations. These strategies are the tools used to justify inferences, predictions, and explanations that require contributions from across multiple scales or theoretical frameworks. Consequently, these strategies are an essential epistemic feature of inter-theory relations, and they have, with a few exceptions, been largely overlooked as a means of unpacking relationships among theories in physics and beyond. By correcting course and re-examining inter-theory relations in the richer context of conceptual strategizing across scales, I have laid the groundwork for a more robust and realistic account of how scientific theories work—and how they work together—in physics and beyond. 4 4 This article is the product of many long, productive discussions with many people who have been generous with their time and energy. I am deeply grateful to Robert Batterman, Alisa Bokulich, Daniel Burnston, Nora Mills Boyd, Margaret Morrison, Jeff Sykora, Eric Winsberg, James Woodward, and two anonymous reviewers for their comments, and to audiences at the Bay Area Philosophy of Science Colloquium, the Society for Philosophy of Science in Practice, the Southern California Philosophy of Physics Group, the Philosophy of Science Association, the Boston Colloquium for the Philosophy of Science, and the TU–Darmstadt CompuGene Winter School. As always, thanks to STARS. This article was developed from research supported by the National Science Foundation under grant number 1247842.

Publisher Copyright:
© 2017 Elsevier Ltd

Keywords

  • Classical physics
  • Conceptual strategies
  • Emergence
  • Inter-theory relations
  • Models in physics
  • Nanoscience
  • Quantum physics
  • Reductionism

ASJC Scopus subject areas

  • History
  • Physics and Astronomy (all)
  • History and Philosophy of Science

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