Search results for 'Symmetry' (try it on Scholar)

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  1. Matt Farr & Alexander Reutlinger (2013). A Relic of a Bygone Age? Causation, Time Symmetry and the Directionality Argument. Erkenntnis 78 (2):215-235.score: 18.0
    Bertrand Russell famously argued that causation is not part of the fundamental physical description of the world, describing the notion of cause as “a relic of a bygone age” (Russell in Proc Aristot Soc 13:1–26, 1913). This paper assesses one of Russell’s arguments for this conclusion: the ‘Directionality Argument’, which holds that the time symmetry of fundamental physics is inconsistent with the time asymmetry of causation. We claim that the coherence and success of the Directionality Argument crucially depends on (...)
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  2. Bas C. Van Fraassen (1989). Laws and Symmetry. Oxford University Press.score: 18.0
    Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the (...)
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  3. Sebastian Lutz & Stephan Hartmann (2010). Conventional and Objective Invariance: Debs and Redhead on Symmetry. [REVIEW] Metascience 19:15-23.score: 18.0
    This review is a critical discussion of three main claims in Debs and Redhead’s thought-provoking book Objectivity, Invariance, and Convention. These claims are: (i) Social acts impinge upon formal aspects of scientific representation; (ii) symmetries introduce the need for conventional choice; (iii) perspectival symmetry is a necessary and sufficient condition for objectivity, while symmetry simpliciter fails to be necessary.
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  4. Dean Rickles (2013). Mirror Symmetry and Other Miracles in Superstring Theory. Foundations of Physics 43 (1):54-80.score: 18.0
    The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam’s ‘no miracles argument’ that, I argue, many string theorists in fact espouse in some form or other. String theory has generated many surprising, useful, and well-confirmed mathematical ‘predictions’—here I focus on mirror symmetry and the mirror theorem. These (...)
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  5. Elena Castellani (2002). Symmetry, Quantum Mechanics, and Beyond. Foundations of Science 7 (1-2):181-196.score: 18.0
    The relevance of symmetry to today's physics is a widely acknowledged fact. A significant part of recent physical inquiry – especially the physics concerned with investigating the fundamentalbuilding blocks of nature – is grounded on symmetry principles andtheir many and far-reaching consequences. But where these symmetries come from and what their real meaning is are open questions, at the center of a developing debate among physicists and philosophers of science. To tackle the problems arising in considering the (...) issue is the main purpose of this paper. Starting with briefly recalling the bases for the discussion – how symmetry enters and operates in physics, its special effectiveness in the quantum domain and the many relevant functions it performs (Sections 1–3), the paper then focus on the general interpretative questions that arise and the sorts of answers that have been given (Section 4). (shrink)
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  6. Simon Friederich (2013). Gauge Symmetry Breaking in Gauge Theories—in Search of Clarification. European Journal for Philosophy of Science 3 (2):157-182.score: 18.0
    The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle, taking into account the fact that the notion of a spontaneously broken local gauge symmetry, though widely employed in textbook expositions of the Higgs mechanism, is not supported by our leading theoretical frameworks of gauge quantum theories. In the context of lattice gauge theory, the statement that local gauge symmetry cannot be spontaneously broken can even be made rigorous in the form of (...)
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  7. Bert Schroer (2011). Bondi-Metzner-Sachs Symmetry, Holography on Null-Surfaces and Area Proportionality of “Light-Slice” Entropy. Foundations of Physics 41 (2):204-241.score: 18.0
    It is shown that certain kinds of behavior, which hitherto were expected to be characteristic for classical gravity and quantum field theory in curved spacetime, as the infinite dimensional Bondi-Metzner-Sachs symmetry, holography on event horizons and an area proportionality of entropy, have in fact an unnoticed presence in Minkowski QFT.This casts new light on the fundamental question whether the volume proportionality of heat bath entropy and the (logarithmically corrected) dimensionless area law obeyed by localization-induced thermal behavior are different geometric (...)
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  8. Errol Lord (2013). The Real Symmetry Problem(s) for Wide-Scope Accounts of Rationality. Philosophical Studies:1-22.score: 18.0
    You are irrational when you are akratic. On this point most agree. Despite this agreement, there is a tremendous amount of disagreement about what the correct explanation of this data is. Narrow-scopers think that the correct explanation is that you are violating a narrow-scope conditional requirement. You lack an intention to x that you are required to have given the fact that you believe you ought to x. Wide-scopers disagree. They think that a conditional you are required to make true (...)
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  9. Yaakov Friedman & Yuriy Gofman (2002). Relativistic Linear Spacetime Transformations Based on Symmetry. Foundations of Physics 32 (11):1717-1736.score: 18.0
    Usually the Lorentz transformations are derived from the conservation of the spacetime interval. We propose here a way of obtaining spacetime transformations between two inertial frames directly from symmetry, the isotropy of the space and principle of relativity. The transformation is uniquely defined except for a constant e, that depends only on the process of synchronization of clocks inside each system. Relativistic velocity addition is obtained, and it is shown that the set of velocities is a bounded symmetric domain. (...)
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  10. Ted Jacobson & Aron C. Wall (2010). Black Hole Thermodynamics and Lorentz Symmetry. Foundations of Physics 40 (8):1076-1080.score: 18.0
    Recent developments point to a breakdown in the generalized second law of thermodynamics for theories with Lorentz symmetry violation. It appears possible to construct a perpetual motion machine of the second kind in such theories, using a black hole to catalyze the conversion of heat to work. Here we describe and extend the arguments leading to that conclusion. We suggest the inference that local Lorentz symmetry may be an emergent property of the macroscopic world with origins in a (...)
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  11. Inge S. Helland (2008). Quantum Mechanics From Focusing and Symmetry. Foundations of Physics 38 (9):818-842.score: 18.0
    A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables—inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a definite interpretation. The Born formula is proved from weak (...)
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  12. Cheng-Shi Liu (2011). Trial Equation Method Based on Symmetry and Applications to Nonlinear Equations Arising in Mathematical Physics. Foundations of Physics 41 (5):793-804.score: 18.0
    To find exact traveling wave solutions to nonlinear evolution equations, we propose a method combining symmetry properties with trial polynomial solution to nonlinear ordinary differential equations. By the method, we obtain some exact traveling wave solutions to the Burgers-KdV equations and a kind of reaction-diffusion equations with high order nonlinear terms. As a result, we prove that the Burgers-KdV equation does not have the real solution in the form a 0+a 1tan ξ+a 2tan 2 ξ, which indicates that some (...)
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  13. Yusuf Sucu & Nuri Ünal (2012). Symmetry and Integrability in the Classical Model of Zitterbewegung. Foundations of Physics 42 (8):1067-1077.score: 18.0
    We extended the Barut’s classical model of zitterbewegung from 3+1 dimensional spacetime into 2+1 and 1+1 dimensional spacetimes and discussed the symmetry and integrability properties of the model in 2+1, 1+1 and 3+1 dimensions. In these cases, the free particle current or the velocity of the particle can be decomposed as a constant convection current and polarization currents.In 2+1 dimensional spacetime, a velocity of the particle and spin tensor are dependent to each other and the chirality can not be (...)
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  14. Timothy H. Boyer (2010). Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation. Foundations of Physics 40 (8):1102-1116.score: 18.0
    It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving (...)
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  15. S. Capozziello & M. De Laurentis (2010). A Review About Invariance Induced Gravity: Gravity and Spin From Local Conformal-Affine Symmetry. [REVIEW] Foundations of Physics 40 (7):867-899.score: 18.0
    In this review paper, we discuss how gravity and spin can be obtained as the realization of the local Conformal-Affine group of symmetry transformations. In particular, we show how gravitation is a gauge theory which can be obtained starting from some local invariance as the Poincaré local symmetry. We review previous results where the inhomogeneous connection coefficients, transforming under the Lorentz group, give rise to gravitational gauge potentials which can be used to define covariant derivatives accommodating minimal couplings (...)
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  16. Johan E. Gustafsson (2013). Value-Preference Symmetry and Fitting-Attitude Accounts of Value Relations. Philosophical Quarterly 63 (252):476–491.score: 18.0
    Joshua Gert and Wlodek Rabinowicz have developed frameworks for value relations that are rich enough to allow for non-standard value relations such as parity. Yet their frameworks do not allow for any non-standard preference relations. In this paper, I shall defend a symmetry between values and preferences, namely, that for every value relation, there is a corresponding preference relation, and vice versa. I claim that if the arguments that there are non-standard value relations are cogent, these arguments, mutatis mutandis, (...)
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  17. B. G. Sidharth (2008). Different Routes to Lorentz Symmetry Violations. Foundations of Physics 38 (1):89-95.score: 18.0
    Recent observations of ultra high energy cosmic rays and gamma rays suggest that there are small violations of Lorentz symmetry. If there were no such violations, then the GZK cut off would hold and cosmic rays with energy ∼1020 eV or higher would not be reaching the earth. However some such events seem to have been observed. This has lead to phenomenological models in which there is a small violation of the Lorentz symmetry or the velocity of light. (...)
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  18. Till D. Frank, Julia J. C. Blau & Michael T. Turvey (2012). Symmetry Breaking Analysis of Prism Adaptation's Latent Aftereffect. Cognitive Science 36 (4):674-697.score: 18.0
    The effect of prism adaptation on movement is typically reduced when the movement at test (prisms off) differs on some dimension from the movement at training (prisms on). Some adaptation is latent, however, and only revealed through further testing in which the movement at training is fully reinstated. Applying a nonlinear attractor dynamic model (Frank, Blau, & Turvey, 2009) to available data (Blau, Stephen, Carello, & Turvey, 2009), we provide evidence for a causal link between the latent (or secondary) aftereffect (...)
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  19. John Thrasher (2014). Uniqueness and Symmetry in Bargaining Theories of Justice. Philosophical Studies 167 (3):683-699.score: 18.0
    For contractarians, justice is the result of a rational bargain. The goal is to show that the rules of justice are consistent with rationality. The two most important bargaining theories of justice are David Gauthier’s and those that use the Nash’s bargaining solution. I argue that both of these approaches are fatally undermined by their reliance on a symmetry condition. Symmetry is a substantive constraint, not an implication of rationality. I argue that using symmetry to generate uniqueness (...)
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  20. Noah Moss Brender (2013). Sense-Making and Symmetry-Breaking. Symposium 17 (2):246-270.score: 18.0
    From his earliest work forward, Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own endogenous sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up Merleau-Ponty’s ontology (...)
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  21. Klaus Mainzer (1997). Symmetry and Complexity - Fundamental Concepts of Research in Chemistry. Hyle 3 (1):29 - 49.score: 18.0
    Molecules have more or less symmetric and complex structures which can be defined in the mathematical framework of topology, group theory, dynamical systems theory, and quantum mechanics. But symmetry and complexity are by no means only theoretical concepts of research. Modern computer aided visualizations show real forms of matter which nevertheless depend on the technical standards of observation, computation, and representation. Furthermore, symmetry and complexity are fundamental interdisciplinary concepts of research inspiring the natural sciences since the antiquity.
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  22. A. Zee (1986/1999). Fearful Symmetry: The Search for Beauty in Modern Physics. Princeton University Press.score: 18.0
    Fearful Symmetry brings the incredible discoveries of contemporary physics within everyone's grasp. A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how today's theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, the book describes the majestic sweep and accomplishments of twentieth-century physics. In the end, we stand in awe before the grand vision of modern physics--one of the greatest chapters in (...)
     
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  23. Francis Heylighen (2011). Symmetry, Potentiality and Reversibility. Foundations of Science 16 (4):335-336.score: 16.0
    This short comment confirms Longo’s observation about the importance of symmetries for understanding space and time, but raises the additional issue of the transition from reversible to irreversible transformations.
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  24. J. B. Paris & A. Vencovská (2012). Symmetry in Polyadic Inductive Logic. Journal of Logic, Language and Information 21 (2):189-216.score: 16.0
    A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived.
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  25. Roger Vergauwen (2010). Will Science and Consciousness Ever Meat? Complexity, Symmetry and Qualia. Symmetry 2 (3):1250-1269.score: 15.0
    Within recent discussions in the Philosophy of Mind, the nature of conscious phenomenal states or qualia (also called ‘raw feels’ or the feel of ‘what it is like to be’) has been an important focus of interest. Proponents of Mind-Body Type-Identity theories have claimed that mental states can be reduced to neurophysiological states of the brain. Others have denied that such a reduction is possible; for them, there remains an explanatory gap. In this paper, functionalist, physicalist, epiphenomenalist, and biological models (...)
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  26. John Brunero (2012). Instrumental Rationality, Symmetry and Scope. Philosophical Studies 157 (1):125-140.score: 15.0
    Instrumental rationality prohibits one from being in the following state: intending to pass a test, not intending to study, and believing one must intend to study if one is to pass. One could escape from this incoherent state in three ways: by intending to study, by not intending to pass, or by giving up one’s instrumental belief. However, not all of these ways of proceeding seem equally rational: giving up one’s instrumental belief seems less rational than giving up an end, (...)
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  27. Andrea Busch & Sabine Zachgo (2009). Flower Symmetry Evolution: Towards Understanding the Abominable Mystery of Angiosperm Radiation. Bioessays 31 (11):1181-1190.score: 15.0
  28. N. Jack Kanak & Sharon D. Neuner (1970). Associative Symmetry and Item Availablity as a Function of Five Methods of Paired-Associate Acquisition. Journal of Experimental Psychology 86 (2):288.score: 15.0
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  29. G. A. Kelly (1935). Some Observations on the Relation of the Principle of Physiological Polarity and Symmetry and the Doctrine of Cerebral Dominance to the Perception of Symbols. Journal of Experimental Psychology 18 (2):202.score: 15.0
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  30. Sundar Sarukkai (2004). Philosophy of Symmetry. Indian Institute of Advanced Study.score: 15.0
     
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  31. Keith A. Wollen (1968). Effects of Maximizing Availability and Minimizing Rehearsal Upon Associative Symmetry in Two Modalities. Journal of Experimental Psychology 77 (4):626.score: 15.0
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  32. Yuri Balashov (2002). What is a Law of Nature? The Broken-Symmetry Story. Southern Journal of Philosophy 40 (4):459-473.score: 12.0
    I argue that the contemporary interplay of cosmology and particle physics in their joint effort to understand the processes at work during the first moments of the big bang has important implications for understanding the nature of lawhood. I focus on the phenomenon of spontaneous symmetry breaking responsible for generating the masses of certain particles. This phenomenon presents problems for the currently fashionable Dretske-Tooley-Armstrong theory and strongly favors a rival nomic ontology of causal powers.
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  33. John Earman (2004). Laws, Symmetry, and Symmetry Breaking: Invariance, Conservation Principles, and Objectivity. Philosophy of Science 71 (5):1227--1241.score: 12.0
    Given its importance in modern physics, philosophers of science have paid surprisingly little attention to the subject of symmetries and invariances, and they have largely neglected the subtopic of symmetry breaking. I illustrate how the topic of laws and symmetries brings into fruitful interaction technical issues in physics and mathematics with both methodological issues in philosophy of science, such as the status of laws of physics, and metaphysical issues, such as the nature of objectivity.
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  34. Aaron J. Cotnoir (2010). Anti-Symmetry and Non-Extensional Mereology. Philosophical Quarterly 60 (239):396-405.score: 12.0
    I examine the link between extensionality principles of classical mereology and the anti-symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti-symmetry. I examine the notions of proper parthood, weak supplementation and non-well-foundedness. By rejecting anti-symmetry, the anti-extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non-extensional mereology in which anti-symmetry fails. If the notion of 'mereological equivalence' is made explicit, this non-anti-symmetric mereology recaptures (...)
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  35. David J. Baker & Hans Halvorson, How is Spontaneous Symmetry Breaking Possible?score: 12.0
    We pose and resolve a seeming paradox about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator. But Wigner's theorem guarantees that every symmetry is implemented by a unitary operator that preserves transition probabilities between pure states. We show how it is possible for a unitary operator of this sort to connect the folia of unitarily inequivalent representations. This result undermines (...)
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  36. David Baker (2011). Broken Symmetry and Spacetime. Philosophy of Science 78 (1):128-148.score: 12.0
    The phenomenon of broken spacetime symmetry in the quantum theory of infinite systems forces us to adopt an unorthodox ontology. We must abandon the standard conception of the physical meaning of these symmetries, or else deny the attractive “liberal” notion of which physical quantities are significant. A third option, more attractive but less well understood, is to abandon the existing (Halvorson-Clifton) notion of intertranslatability for quantum theories.
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  37. Roger White (2009). Evidential Symmetry and Mushy Credence. In T. Szabo Gendler & J. Hawthorne (eds.), Oxford Studies in Epistemology. Oxford University Press. 161-186.score: 12.0
    the symmetry of our evidential situation. If our confidence is best modeled by a standard probability function this means that we are to distribute our subjective probability or credence sharply and evenly over possibilities among which our evidence does not discriminate. Once thought to be the central principle of probabilistic reasoning by great..
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  38. Joseph Diekemper (2005). Presentism and Ontological Symmetry. Australasian Journal of Philosophy 83 (2):223 – 240.score: 12.0
    In this paper, I argue that there is an inconsistency between two presentist doctrines: that of ontological symmetry and asymmetry of fixity. The former refers to the presentist belief that the past and future are equally unreal. The latter refers to the A-Theoretic intuition that the past is closed or actual, and the future is open or potential. My position in this paper is that the presentist is unable to account for the temporal asymmetry that is so fundamentally a (...)
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  39. John Earman (2004). Curie's Principle and Spontaneous Symmetry Breaking. International Studies in the Philosophy of Science 18 (2 & 3):173 – 198.score: 12.0
    In 1894 Pierre Curie announced what has come to be known as Curie's Principle: the asymmetry of effects must be found in their causes. In the same publication Curie discussed a key feature of what later came to be known as spontaneous symmetry breaking: the phenomena generally do not exhibit the symmetries of the laws that govern them. Philosophers have long been interested in the meaning and status of Curie's Principle. Only comparatively recently have they begun to delve into (...)
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  40. Alexandre Guay, Geometrical Aspects of Local Gauge Symmetry.score: 12.0
    This paper is an analysis of the geometrical interpretation of local gauge symmetry for theories of the Yang-Mills type.
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  41. Katherine Brading & Harvey R. Brown (2004). Are Gauge Symmetry Transformations Observable? British Journal for the Philosophy of Science 55 (4):645-665.score: 12.0
    In a recent paper in the British Journal for the Philosophy of Science, Kosso discussed the observational status of continuous symmetries of physics. While we are in broad agreement with his approach, we disagree with his analysis. In the discussion of the status of gauge symmetry, a set of examples offered by ’t Hooft has influenced several philosophers, including Kosso; in all cases the interpretation of the examples is mistaken. In this paper we present our preferred approach to the (...)
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  42. James Warren (2001). Lucretius, Symmetry Arguments, and Fearing Death. Phronesis 46 (4):466-491.score: 12.0
    This paper identifies two possible versions of the Epicurean 'Symmetry argument', both of which claim that post mortem non-existence is relevantly like prenatal non-existence and that therefore our attitude to the former should be the same as that towards the latter. One version addresses the fear of the state of being dead by making it equivalent to the state of not yet being born; the other addresses the prospective fear of dying by relating it to our present retrospective attitude (...)
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  43. Richard Healey (2010). Gauge Symmetry and the Theta Vacuum. In Mauricio Suarez, Mauro Dorato & Miklos Redei (eds.), EPSA Philosophical Issues in the Sciences. Springer. 105--116.score: 12.0
    According to conventional wisdom, local gauge symmetry is not a symmetry of nature, but an artifact of how our theories represent nature. But a study of the so-called theta-vacuum appears to refute this view. The ground state of a quantized non-Abelian Yang-Mills gauge theory is characterized by a real-valued, dimensionless parameter theta—a fundamental new constant of nature. The structure of this vacuum state is often said to arise from a degeneracy of the vacuum of the corresponding classical theory, (...)
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  44. Noah Moss Brender (2013). Sense-Making and Symmetry-Breaking: Merleau-Ponty, Cognitive Science, and Dynamic Systems Theory. Symposium 17 (2):247-273.score: 12.0
    From his earliest work forward, phenomenologist Maurice Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own intrinsic sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up (...)
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  45. Sorin Bangu (2008). Reifying Mathematics? Prediction and Symmetry Classification. Studies in History and Philosophy of Science Part B 39 (2):239-258.score: 12.0
    In this paper I reconstruct and critically examine the reasoning leading to the famous prediction of the ‘omega minus’ particle by M. Gell-Mann and Y. Ne’eman (in 1962) on the basis of a symmetry classification scheme. While the peculiarity of this prediction has occasionally been noticed in the literature, a detailed treatment of the methodological problems it poses has not been offered yet. By spelling out the characteristics of this type of prediction, I aim to underscore the challenges raised (...)
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  46. Katherine A. Brading & Elena Castellani (eds.) (2003). Symmetries in Physics: Philosophical Reflections. Cambridge University Press.score: 12.0
    Highlighting main issues and controversies, this book brings together current philosophical discussions of symmetry in physics to provide an introduction to the subject for physicists and philosophers. The contributors cover all the fundamental symmetries of modern physics, such as CPT and permutation symmetry, as well as discussing symmetry-breaking and general interpretational issues. Classic texts are followed by new review articles and shorter commentaries for each topic. Suitable for courses on the foundations of physics, philosophy of physics and (...)
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  47. Alexandre Guay, The Arbitrariness of Local Gauge Symmetry.score: 12.0
    This paper shows how the study of surpluses of structure is an interesting philosophical task. In particular I explore how local gauge symmetry in quantized Yang-Mills theories is the by-product of the specific dynamical structure of interaction. It is shown how in non relativistic quantum mechanics gauge symmetry corresponds to the freedom to locally define global features of gauge potentials. Also discussed is how in quantum field theory local gauge symmetry is replaced by BRST symmetry. This (...)
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  48. Dean Rickles, Symmetry & Possibility: To Reduce or Not Reduce?score: 12.0
    In this paper I examine the connection between symmetry and modality from the perspective of `reduction' methods in geometric mechanics. I begin by setting the problem up as a choice between two opposing views: reduction and non-reduction. I then discern four views on the matter in the literature; they are distinguished by their advocation of distinct geometric spaces as representing `reality'. I come down in favour of non-reductive methods.
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  49. Jeremy Butterfield, On Symmetry and Conserved Quantities in Classical Mechanics.score: 12.0
    This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem's main ``ingredient'', apart from cyclic (...)
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  50. Domenico Giulini, Concepts of Symmetry in the Work of Wolfgang Pauli.score: 12.0
    "Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which differ in meaning as well as their mathematical consequences. Symmetries of crystals, for example, generally express a different kind of invariance than gauge symmetries, though in specific situations the distinctions may become quite subtle. I will review some of the (...)
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