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  1. Approximation and Idealization: Why the Difference Matters.John D. Norton - 2012 - Philosophy of Science 79 (2):207-232.
    It is proposed that we use the term “approximation” for inexact description of a target system and “idealization” for another system whose properties also provide an inexact description of the target system. Since systems generated by a limiting process can often have quite unexpected, even inconsistent properties, familiar limit systems used in statistical physics can fail to provide idealizations, but are merely approximations. A dominance argument suggests that the limiting idealizations of statistical physics should be demoted to approximations.
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  • Physical Emergence, Diachronic and Synchronic.Alexander Rueger - 2000 - Synthese 124 (3):297-322.
    This paper explicates two notions of emergencewhich are based on two ways of distinguishinglevels of properties for dynamical systems.Once the levels are defined, the strategies ofcharacterizing the relation of higher level to lower levelproperties as diachronic and synchronic emergenceare the same. In each case, the higher level properties aresaid to be emergent if they are novel or irreducible with respect to the lower level properties. Novelty andirreducibility are given precise meanings in terms of the effectsthat the change of a bifurcation (...)
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  • Approximations, Idealizations, and Models in Statistical Mechanics.Chuang Liu - 2004 - Erkenntnis 60 (2):235-263.
    In this paper, a criticism of the traditional theories of approximation and idealization is given as a summary of previous works. After identifying the real purpose and measure of idealization in the practice of science, it is argued that the best way to characterize idealization is not to formulate a logical model – something analogous to Hempel's D-N model for explanation – but to study its different guises in the praxis of science. A case study of it is then made (...)
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  • Mathematical Rigor in Physics: Putting Exact Results in Their Place.Axel Gelfert - 2005 - Philosophy of Science 72 (5):723-738.
    The present paper examines the role of exact results in the theory of many‐body physics, and specifically the example of the Mermin‐Wagner theorem, a rigorous result concerning the absence of phase transitions in low‐dimensional systems. While the theorem has been shown to hold for a wide range of many‐body models, it is frequently ‘violated’ by results derived from the same models using numerical techniques. This raises the question of how scientists regulate their theoretical commitments in such cases, given that the (...)
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  • How Models Represent.James Nguyen - 2016 - Dissertation,
    Scientific models are important, if not the sole, units of science. This thesis addresses the following question: in virtue of what do scientific models represent their target systems? In Part i I motivate the question, and lay out some important desiderata that any successful answer must meet. This provides a novel conceptual framework in which to think about the question of scientific representation. I then argue against Callender and Cohen’s attempt to diffuse the question. In Part ii I investigate the (...)
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  • Coordination of Space and Unity of Science.Chuang Liu - unknown
    In this essay, I explore a metaphor in geometry for the debate between the unity and the disunity of science, namely, the possibility of putting a global coordinate system (or a chart) on a manifold. I explain why the former is a good metaphor that shows what it means (and takes in principle) for science to be unified. I then go through some of the existing literature on the unity/disunity debate and show how the metaphor sheds light on some of (...)
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  • Hierarchy, Form, and Reality.Gang Chen - 2009 - Frontiers of Philosophy in China 4 (3):437-453.
    Scientific progress in the 20th century has shown that the structure of the world is hierarchical. A philosophical analysis of the hierarchy will bear obvious significance for metaphysics and philosophy in general. Jonathan Schaffer’s paper, “Is There a Fundamental Level?”, provides a systematic review of the works in the field, the difficulties for various versions of fundamentalism, and the prospect for the third option, i.e., to treat each level as ontologically equal. The purpose of this paper is to provide an (...)
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  • La representación del espacio mediante coordenadas cartesianas y la unidad de la ciencia.Chuang Liu - 2006 - Discusiones Filosóficas 7 (10):17-32.
    En este artículo, exploro una metáfora engeometría que nos ayuda a entender mejorel debate sobre la unidad y la desunidad dela ciencia, a saber, la posibilidad de poner unsistema global de coordenadascartesianas sobreuna variedad .Explicaré las razones por las que ésta es unabuena metáfora capaz de mostrar lo quesignifica launificación para la ciencia. Posteriormente,examinaré una parte de la literatura sobre eldebate unidad/desunidad y mostraré cómoesta metáfora puede iluminar algunos de losargumentos y puntos de vista.n this essay, I explore a metaphor (...)
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  • Compendium of the Foundations of Classical Statistical Physics.Jos Uffink - unknown
    Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their central concepts. (...)
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  • Turn and Face the Strange... Ch-Ch-Changes: Philosophical Questions Raised by Phase Transitions.Tarun Menon & Craig Callender - 2013 - In Robert W. Batterman (ed.), The Oxford Handbook of Philosophy of Physics. Oxford University Press.
    Phase transitions are an important instance of putatively emergent behavior. Unlike many things claimed emergent by philosophers, the alleged emergence of phase transitions stems from both philosophical and scientific arguments. Here we focus on the case for emergence built from physics, in particular, arguments based upon the infinite idealization invoked in the statistical mechanical treatment of phase transitions. After teasing apart several challenges, we defend the idea that phase transitions are best thought of as conceptually novel, but not ontologically or (...)
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  • History of the Lenz-Ising Model 1920–1950: From Ferromagnetic to Cooperative Phenomena.Martin Niss - 2005 - Archive for History of Exact Sciences 59 (3):267-318.
    .I chart the considerable changes in the status and conception of the Lenz-Ising model from 1920 to 1950 in terms of three phases: In the early 1920s, Lenz and Ising introduced the model in the field of ferromagnetism. Based on an exact derivation, Ising concluded that it is incapable of displaying ferromagnetic behavior, a result he erroneously extended to three dimensions. In the next phase, Lenz and Ising’s contemporaries rejected the model as a representation of ferromagnetic materials because of its (...)
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  • Combining Finite and Infinite Elements: Why Do We Use Infinite Idealizations in Engineering?Silvia De Bianchi - 2019 - Synthese 196 (5):1733-1748.
    This contribution sheds light on the role of infinite idealization in structural analysis, by exploring how infinite elements and finite element methods are combined in civil engineering models. This combination, I claim, should be read in terms of a ‘complementarity function’ through which the representational ideal of completeness is reached in engineering model-building. Taking a cue from Weisberg’s definition of multiple-model idealization, I highlight how infinite idealizations are primarily meant to contribute to the prediction of structural behavior in Multiphysics approaches.
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  • The Modular Structure of Physical Theories.Olivier Darrigol - 2008 - Synthese 162 (2):195 - 223.
    Any advanced theory of physics contains modules defined as essential components that are themselves theories with different domains of application. Different kinds of modules can be distinguished according to the way in which they fit in the symbolic and interpretive apparatus of a theory. The number and kind of the modules of a given theory vary as the theory evolves in time. The relative stability of modules and the variability of their insertion in other theories play a vital role in (...)
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  • Chaos and Fundamentalism.Gordon Belot - 2000 - Philosophy of Science 67 (3):465.
    1. It is natural to wonder what our multitude of successful physical theories tell us about the world—singly, and as a body. What are we to think when one theory tells us about a flat Newtonian spacetime, the next about a curved Lorentzian geometry, and we have hints of others, portraying discrete or higher-dimensional structures which look something like more familiar spacetimes in appropriate limits?
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  • Spontaneous Symmetry Breaking (II): Variations in Complex Models.Chuang Liu - unknown
    This paper, part II of a two-part project, continues to explore the meaning of spontaneous symmetry breaking (SSB) by applying and expanding the general notion we obtained in part I to some more complex and, from the physics point of view, more important models (in condensed matter physics and in quantum field theories).
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  • Critical Phenomena and Breaking Drops: Infinite Idealizations in Physics.Robert Batterman - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (2):225-244.
    Thermodynamics and Statistical Mechanics are related to one another through the so-called "thermodynamic limit'' in which, roughly speaking the number of particles becomes infinite. At critical points (places of physical discontinuity) this limit fails to be regular. As a result, the "reduction'' of Thermodynamics to Statistical Mechanics fails to hold at such critical phases. This fact is key to understanding an argument due to Craig Callender to the effect that the thermodynamic limit leads to mistakes in Statistical Mechanics. I discuss (...)
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  • Abstraction and its Limits: Finding Space For Novel Explanation.Eleanor Knox - 2016 - Noûs 50 (1):41-60.
    Several modern accounts of explanation acknowledge the importance of abstraction and idealization for our explanatory practice. However, once we allow a role for abstraction, questions remain. I ask whether the relation between explanations at different theoretical levels should be thought of wholly in terms of abstraction, and argue that changes of the quantities in terms of which we describe a system can lead to novel explanations that are not merely abstractions of some more detailed picture. I use the example of (...)
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  • Taking Thermodynamics Too Seriously.Craig Callender - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (4):539-553.
    This paper discusses the mistake of understanding the laws and concepts of thermodynamics too literally in the foundations of statistical mechanics. Arguing that this error is still made in subtle ways, the article explores its occurrence in three examples: the Second Law, the concept of equilibrium and the definition of phase transitions.
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  • Infinite Idealizations in Physics.Elay Shech - 2018 - Philosophy Compass 13 (9):e12514.
    In this essay, I provide an overview of the debate on infinite and essential idealizations in physics. I will first present two ostensible examples: phase transitions and the Aharonov– Bohm effect. Then, I will describe the literature on the topic as a debate between two positions: Essentialists claim that idealizations are essential or indispensable for scientific accounts of certain physical phenomena, while dispensabilists maintain that idealizations are dispensable from mature scientific theory. I will also identify some attempts at finding a (...)
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  • Model Templates Within and Between Disciplines: From Magnets to Gases – and Socio-Economic Systems.Tarja Knuuttila & Andrea Loettgers - 2016 - European Journal for Philosophy of Science 6 (3):377-400.
    One striking feature of the contemporary modelling practice is its interdisciplinary nature. The same equation forms, and mathematical and computational methods, are used across different disciplines, as well as within the same discipline. Are there, then, differences between intra- and interdisciplinary transfer, and can the comparison between the two provide more insight on the challenges of interdisciplinary theoretical work? We will study the development and various uses of the Ising model within physics, contrasting them to its applications to socio-economic systems. (...)
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