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John D. Norton [123]John Norton [38]John Douglas Norton [1]
  1. A Material Theory of Induction.John D. Norton - 2003 - Philosophy of Science 70 (4):647-670.
    Contrary to formal theories of induction, I argue that there are no universal inductive inference schemas. The inductive inferences of science are grounded in matters of fact that hold only in particular domains, so that all inductive inference is local. Some are so localized as to defy familiar characterization. Since inductive inference schemas are underwritten by facts, we can assess and control the inductive risk taken in an induction by investigating the warrant for its underwriting facts. In learning more facts, (...)
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  2. 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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  3. What Price Spacetime Substantivalism? The Hole Story.John Earman & John Norton - 1987 - British Journal for the Philosophy of Science 38 (4):515-525.
    Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.
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  4. The Dome: An Unexpectedly Simple Failure of Determinism.John Norton - 2008 - Philosophy of Science 75 (5):786-798.
    Newton’s equations of motion tell us that a mass at rest at the apex of a dome with the shape specified here can spontaneously move. It has been suggested that this indeterminism should be discounted since it draws on an incomplete rendering of Newtonian physics, or it is “unphysical,” or it employs illicit idealizations. I analyze and reject each of these reasons. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, PA (...)
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  5.  62
    Causation as Folk Science.John D. Norton - 2007 - In Huw Price & Richard Corry (eds.), Philosophers' Imprint. Oxford University Press.
    I deny that the world is fundamentally causal, deriving the skepticism on non-Humean grounds from our enduring failures to find a contingent, universal principle of causality that holds true of our science. I explain the prevalence and fertility of causal notions in science by arguing that a causal character for many sciences can be recovered, when they are restricted to appropriately hospitable domains. There they conform to a loose collection of causal notions that form a folk science of causation. This (...)
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  6. Ignorance and Indifference.John Norton - 2008 - Philosophy of Science 75 (1):45-68.
    The epistemic state of complete ignorance is not a probability distribution. In it, we assign the same, unique, ignorance degree of belief to any contingent outcome and each of its contingent, disjunctive parts. That this is the appropriate way to represent complete ignorance is established by two instruments, each individually strong enough to identify this state. They are the principle of indifference (PI) and the notion that ignorance is invariant under certain redescriptions of the outcome space, here developed into the (...)
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  7.  53
    Is There an Independent Principle of Causality in Physics?John Norton - 2009 - British Journal for the Philosophy of Science 60 (3):475-486.
    Mathias Frisch has argued that the requirement that electromagnetic dispersion processes are causal adds empirical content not found in electrodynamic theory. I urge that this attempt to reconstitute a local principle of causality in physics fails. An independent principle is not needed to recover the results of dispersion theory. The use of ‘causality conditions’ proves to be the mere adding of causal labels to an already presumed fact. If instead one seeks a broader, independently formulated grounding for the conditions, that (...)
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  8. Are Thought Experiments Just What You Thought?John Norton - 1996 - Canadian Journal of Philosophy 26 (3):333 - 366.
    Canadian Journal of Philosophy, 26, pp. 333-66. 1996.
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  9.  72
    Why Thought Experiments Do Not Transcend Empiricism.John D. Norton - 2004 - In Christopher Hitchcock (ed.), Contemporary Debates in the Philosophy of Science. Blackwell. pp. 44-66.
    Thought experiments are ordinary argumentation disguised in a vivid pictorial or narrative form. This account of their nature will allow me to show that empiricism has nothing to fear from thought experiments. They perform no epistemic magic. In so far as they tell us about the world, thought experiments draw upon what we already know of it, either explicitly or tacitly; they then transform that knowledge by disguised argumentation. They can do nothing more epistemically than can argumentation. I defend my (...)
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  10. How the Formal Equivalence of Grue and Green Defeats What is New in the New Riddle of Induction.John D. Norton - 2006 - Synthese 150 (2):185-207.
    That past patterns may continue in many different ways has long been identified as a problem for accounts of induction. The novelty of Goodman’s ”new riddle of induction” lies in a meta-argument that purports to show that no account of induction can discriminate between incompatible continuations. That meta-argument depends on the perfect symmetry of the definitions of grue/bleen and green/blue, so that any evidence that favors the ordinary continuation must equally favor the grue-ified continuation. I argue that this very dependence (...)
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  11.  64
    Exorcist XIV: The Wrath of Maxwell's Demon. Part I. From Maxwell to Szilard.John Earman & John D. Norton - 1998 - Studies in History and Philosophy of Modern Physics 29 (4):435-471.
    In this first part of a two-part paper, we describe efforts in the early decades of this century to restrict the extent of violations of the Second Law of thermodynamics that were brought to light by the rise of the kinetic theory and the identification of fluctuation phenomena. We show how these efforts mutated into Szilard’s proposal that Maxwell’s Demon is exorcised by proper attention to the entropy costs associated with the Demon’s memory and information acquisition. In the second part (...)
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  12.  74
    Waiting for Landauer.John D. Norton - 2011 - Studies in History and Philosophy of Science Part B 42 (3):184-198.
    Landauer's Principle asserts that there is an unavoidable cost in thermodynamic entropy creation when data is erased. It is usually derived from incorrect assumptions, most notably, that erasure must compress the phase space of a memory device or that thermodynamic entropy arises from the probabilistic uncertainty of random data. Recent work seeks to prove Landauer’s Principle without using these assumptions. I show that the processes assumed in the proof, and in the thermodynamics of computation more generally, can be combined to (...)
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  13. Eaters of the Lotus: Landauer's Principle and the Return of Maxwell's Demon.John D. Norton - 2005 - Studies in History and Philosophy of Science Part B 36 (2):375-411.
    Landauer’s principle is the loosely formulated notion that the erasure of n bits of information must always incur a cost of k ln n in thermodynamic entropy. It can be formulated as a precise result in statistical mechanics, but by erasure processes that use a thermodynamically irreversible phase space expansion, which is the real origin of the law’s entropy cost. General arguments that purport to establish the unconditional validity of the law (erasure maps many physical states to one; erasure compresses (...)
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  14. Must Evidence Underdetermine Theory.John D. Norton - forthcoming - The Challenge of the Social and the Pressure of Practice:17--44.
    According to the underdetermination thesis, all evidence necessarily underdetermines any scientific theory. Thus it is often argued that our agreement on the content of mature scientific theories must be due to social and other factors. Drawing on a long standing tradition of criticism, I shall argue that the underdetermination thesis is little more than speculation based on an impoverished account of induction. A more careful look at accounts of induction does not support an assured underdetermination or the holism usually associated (...)
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  15. A Material Dissolution of the Problem of Induction.John D. Norton - 2013 - Synthese 191 (4):1-20.
    In a formal theory of induction, inductive inferences are licensed by universal schemas. In a material theory of induction, inductive inferences are licensed by facts. With this change in the conception of the nature of induction, I argue that the celebrated “problem of induction” can no longer be set up and is thereby dissolved. Attempts to recreate the problem in the material theory of induction fail. They require relations of inductive support to conform to an unsustainable, hierarchical empiricism.
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  16.  56
    Causation as Folk Science.John D. Norton - 2003 - Philosophers' Imprint 3 (4):1-22.
    I deny that the world is fundamentally causal, deriving the skepticism on non-Humean grounds from our enduring failures to find a contingent, universal principle of causality that holds true of our science. I explain the prevalence and fertility of causal notions in science by arguing that a causal character for many sciences can be recovered, when they are restricted to appropriately hospitable domains. There they conform to loose and varying collections of causal notions that form folk sciences of causation. This (...)
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  17.  75
    Cosmic Confusions: Not Supporting Versus Supporting Not.John D. Norton - 2010 - Philosophy of Science 77 (4):501-523.
    Bayesian probabilistic explication of inductive inference conflates neutrality of supporting evidence for some hypothesis H (“not supporting H”) with disfavoring evidence (“supporting not-H”). This expressive inadequacy leads to spurious results that are artifacts of a poor choice of inductive logic. I illustrate how such artifacts have arisen in simple inductive inferences in cosmology. In the inductive disjunctive fallacy, neutral support for many possibilities is spuriously converted into strong support for their disjunction. The Bayesian “doomsday argument” is shown to rely entirely (...)
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  18.  42
    What Was Einstein's Principle of Equivalence?John Norton - 1985 - Studies in History and Philosophy of Science Part A 16 (3):203-246.
    sn y™to˜er —nd xovem˜er IWHUD just over two ye—rs —fter the ™ompletion of his spe™i—l theory of rel—tivityD iinstein m—de the ˜re—kthrough th—t set him on the p—th to the gener—l theory of rel—tivityF ‡hile prep—ring — review —rti™le on his new spe™i—l theory of rel—tivityD he ˜e™—me ™onvin™ed th—t the key to the extension of the prin™iple of rel—tivity to —™™eler—ted motion l—y in the rem—rk—˜le —nd unexpl—ined empiri™—l ™oin™iden™e of the equ—lity of inerti—l —nd gr—vit—tion—l m—ssesF „o interpret (...)
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  19.  47
    Einstein, Nordstrom, and the Early Demise of Scalar, Lorentz Covariant Theories of Gravitation.John D. Norton - 2007 - Boston Studies in the Philosophy of Science 250 (3).
    The advent of the special theory of relativity in 1905 brought many problems for the physics community. One, it seemed, would not be a great source of trouble. It was the problem of reconciling Newtonian gravitation theory with the new theory of space and time. Indeed it seemed that Newtonian theory could be rendered compatible with special relativity by any number of small modifications, each of which would be unlikely to lead to any significant deviations from the empirically testable conse- (...)
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  20. There Are No Universal Rules for Induction.John D. Norton - 2010 - Philosophy of Science 77 (5):765-777.
    In a material theory of induction, inductive inferences are warranted by facts that prevail locally. This approach, it is urged, is preferable to formal theories of induction in which the good inductive inferences are delineated as those conforming to some universal schema. An inductive inference problem concerning indeterministic, non-probabilistic systems in physics is posed and it is argued that Bayesians cannot responsibly analyze it, thereby demonstrating that the probability calculus is not the universal logic of induction.
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  21. On Thought Experiments: Is There More to the Argument?John D. Norton - 2004 - Philosophy of Science 71 (5):1139-1151.
    Thought experiments in science are merely picturesque argumentation. I support this view in various ways, including the claim that it follows from the fact that thought experiments can err but can still be used reliably. The view is defended against alternatives proposed by my cosymposiasts.
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  22.  37
    General Covariance and the Foundations of General Relativity: Eight Decades of Dispute.John D. Norton - 1993 - Reports of Progress in Physics 56:791--861.
    iinstein oered the prin™iple of gener—l ™ov—ri—n™e —s the fund—ment—l physi™—l prin™iple of his gener—l theory of rel—tivityD —nd —s responsi˜le for extending the prin™iple of rel—tivity to —™™eler—ted motionF „his view w—s disputed —lmost immedi—tely with the ™ounterE™l—im th—t the prin™iple w—s no rel—tivity prin™iple —nd w—s physi™—lly v—™uousF „he dis—greeE ment persists tod—yF „his —rti™le reviews the development of iinstein9s thought on gener—l ™ov—ri—n™eD its rel—tion to the found—tions of gener—l rel—tivity —nd the evolution of the ™ontinuing de˜—te (...)
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  23.  83
    Challenges to Bayesian Confirmation Theory.John Norton - 2011 - In Prasanta S. Bandyopadhyay & Malcolm R. Forster (eds.), Handbook of the Philosophy of Science, Vol. 7: Philosophy of Statistics. Elsevier B.V.. pp. 391-440.
    Proponents of Bayesian confirmation theory believe that they have the solution to a significant, recalcitrant problem in philosophy of science. It is the identification of the logic that governs evidence and its inductive bearing in science. That is the logic that lets us say that our catalog of planetary observations strongly confirms Copernicus’ heliocentric hypothesis; or that the fossil record is good evidence for the theory of evolution; or that the 3oK cosmic background radiation supports big bang cosmology. The definitive (...)
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  24.  88
    Atoms, Entropy, Quanta: Einstein's Miraculous Argument of 1905.John D. Norton - 2006 - Studies in History and Philosophy of Science Part B 37 (1):71-100.
    In the sixth section of his light quantum paper of 1905, Einstein presented the miraculous argument, as I shall call it. Pointing out an analogy with ideal gases and dilute solutions, he showed that the macroscopic, thermodynamic properties of high frequency heat radiation carry a distinctive signature of finitely many, spatially localized, independent components and so inferred that it consists of quanta. I describe how Einstein’s other statistical papers of 1905 had already developed and exploited the idea that the ideal (...)
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  25.  25
    Observationally Indistinguishable Spacetimes: A Challenge for Any Inductivist.John D. Norton - 2011 - In Gregory J. Morgan (ed.), Philosophy of Science Matters: The Philosophy of Peter Achinstein. Oxford University Press. pp. 164.
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  26. Forever is a Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes.John Earman & John D. Norton - 1993 - Philosophy of Science 60 (1):22-42.
    The standard theory of computation excludes computations whose completion requires an infinite number of steps. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed, timelike half-curves of infinite proper length. We investigate the physical properties of these spacetimes and ask whether they and other spacetimes allow the observer to know the outcome of a computation with infinitely many steps.
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  27.  55
    General Covariance, Gauge Theories and the Kretschmann Objection.John D. Norton - 2003 - In Katherine Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press. pp. 110--123.
    How can we reconcile two claims that are now both widely accepted: Kretschmann's claim that a requirement of general covariance is physically vacuous and the standard view that the general covariance of general relativity expresses the physically important diffeomorphism gauge freedom of general relativity? I urge that both claims can be held without contradiction if we attend to the context in which each is made.
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  28.  56
    Disbelief as the Dual of Belief.John D. Norton - 2007 - International Studies in the Philosophy of Science 21 (3):231 – 252.
    The duality of truth and falsity in a Boolean algebra of propositions is used to generate a duality of belief and disbelief. To each additive probability measure that represents belief there corresponds a dual additive measure that represents disbelief. The dual measure has its own peculiar calculus, in which, for example, measures are added when propositions are combined under conjunction. A Venn diagram of the measure has the contradiction as its total space. While additive measures are not self-dual, the epistemic (...)
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  29.  41
    The Force of Newtonian Cosmology: Acceleration is Relative.John D. Norton - 1995 - Philosophy of Science 62 (4):511-522.
  30. The Hole Argument.John Norton - 1988 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:56 - 64.
    I give an informal outline of the hole argument which shows that spacetime substantivalism leads to an undesirable indeterminism in a broad class of spacetime theories. This form of the argument depends on the selection of differentiable manifolds within a spacetime theory as representing spacetime. I consider the conditions under which the argument can be extended to address versions of spacetime substantivalism which select these differentiable manifolds plus some further structure to represent spacetime. Finally, I respond to the criticisms of (...)
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  31. 1. Marr on Computational-Level Theories Marr on Computational-Level Theories (Pp. 477-500).Oron Shagrir, John D. Norton, Holger Andreas, Jouni-Matti Kuukkanen, Aris Spanos, Eckhart Arnold, Elliott Sober, Peter Gildenhuys & Adela Helena Roszkowski - 2010 - Philosophy of Science 77 (4).
  32.  32
    `Nature is the Realisation of the Simplest Conceivable Mathematical Ideas': Einstein and the Canon of Mathematical Simplicity.John D. Norton - 2000 - Studies in History and Philosophy of Science Part B 31 (2):135-170.
    Einstein proclaimed that we could discover true laws of nature by seeking those with the simplest mathematical formulation. He came to this viewpoint later in his life. In his early years and work he was quite hostile to this idea. Einstein did not develop his later Platonism from a priori reasoning or aesthetic considerations. He learned the canon of mathematical simplicity from his own experiences in the discovery of new theories, most importantly, his discovery of general relativity. Through his neglect (...)
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  33.  34
    Time Really Passes.John D. Norton - 2010 - Humana. Mente: Journal of Philosophical Studies 13:23-24.
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  34.  94
    A Little Survey of Induction.John D. Norton - unknown
    My purpose in this chapter is to survey some of the principal approaches to inductive inference in the philosophy of science literature. My first concern will be the general principles that underlie the many accounts of induction in this literature. When these accounts are considered in isolation, as is more commonly the case, it is easy to overlook that virtually all accounts depend on one of very few basic principles and that the proliferation of accounts can be understood as efforts (...)
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  35.  50
    The Determination of Theory by Evidence: The Case for Quantum Discontinuity, 1900–1915.John D. Norton - 1993 - Synthese 97 (1):1 - 31.
    The thesis that observation necessarily fails to determine theory is false in the sense that observation can provide overwhelming evidence for a particular theory or even a hypothesis within the theory. The saga of quantum discontinuity illustrates the power of evidence to determine theory and shows how that power can be underestimated by inadequate caricatures of the evidential case. That quantum discontinuity can save the phenomena of black body radiation is the widely known result, but it leaves open the possibilities (...)
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  36.  54
    A Quantum Mechanical Supertask.John Norton - 1999 - Foundations of Physics 29 (8):1265-1302.
    That quantum mechanical measurement processes are indeterministic is widely known. The time evolution governed by the differential Schrödinger equation can also be indeterministic under the extreme conditions of a quantum supertask, the quantum analogue of a classical supertask. Determinism can be restored by requiring normalizability of the supertask state vector, but it must be imposed as an additional constraint on the differential Schrödinger equation.
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  37.  38
    Why Monte Carlo Simulations Are Inferences and Not Experiments.Claus Beisbart & John D. Norton - 2012 - International Studies in the Philosophy of Science 26 (4):403-422.
    Monte Carlo simulations arrive at their results by introducing randomness, sometimes derived from a physical randomizing device. Nonetheless, we argue, they open no new epistemic channels beyond that already employed by traditional simulations: the inference by ordinary argumentation of conclusions from assumptions built into the simulations. We show that Monte Carlo simulations cannot produce knowledge other than by inference, and that they resemble other computer simulations in the manner in which they derive their conclusions. Simple examples of Monte Carlo simulations (...)
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  38. Einstein's Investigations of Galilean Covariant Electrodynamics Prior to 1905.John D. Norton - manuscript
    Einstein learned from the magnet and conductor thought experiments how to use field transformation laws to extend the covariance to Maxwell’s electrodynamics. If he persisted in his use of this device, he would have found that the theory cleaves into two Galilean covariant parts, each with different field transformation laws. The tension between the two parts reflects a failure not mentioned by Einstein: that the relativity of motion manifested by observables in the magnet and conductor thought experiment does not extend (...)
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  39.  82
    Did Einstein Stumble? The Debate Over General Covariance.John D. Norton - 1995 - Erkenntnis 42 (2):223 - 245.
    The objection that Einstein's principle of general covariance is not a relativity principle and has no physical content is reviewed. The principal escapes offered for Einstein's viewpoint are evaluated.
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  40.  66
    Infinite Idealizations.John Norton - 2014 - Vienna Circle Institute Yearbook 17:197-210.
    1. Approximations of arbitrarily large but finite systems are often mistaken for infinite idealizations in statistical and thermal physics. The problem is illustrated by thermodynamically reversible processes. They are approximations of processes requiring arbitrarily long, but finite times to complete, not processes requiring an actual infinity of time.2. The present debate over whether phase transitions comprise a failure of reduction is confounded by a confusion of two senses of “level”: the molecular versus the thermodynamic level and the few component versus (...)
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  41.  63
    What Should Philosophers of Science Learn From the History of the Electron?Jonathan Bain & John Norton - 2001 - In A. Warwick (ed.), Histories of the Electron: The Birth of Microphysics. pp. 451--465.
    We have now celebrated the centenary of J. J. Thomson’s famous paper (1897) on the electron and have examined one hundred years of the history of our first fundamental particle. What should philosophers of science learn from this history? To some, the fundamental moral is already suggested by the rapid pace of this history. Thomson’s concern in 1897 was to demonstrate that cathode rays are electrified particles and not aetherial vibrations, the latter being the “almost unanimous opinion of German physicists” (...)
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  42.  49
    Coordinates and Covariance: Einstein's View of Space-Time and the Modern View. [REVIEW]John Norton - 1989 - Foundations of Physics 19 (10):1215-1263.
    Where modern formulations of relatively theory use differentiable manifolds to space-time, Einstein simply used open sets of R 4 , following the then current methods of differential geometry. This fact aids resolution of a number of outstanding puzzles concerning Einstein's use of coordinate systems and covariance principles, including the claimed physical significance of covariance principles, their connection to relativity principles, Einstein's apparent confusion of coordinate systems and frames of reference, and his failure to distinguish active and passive transformations, especially in (...)
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  43.  43
    The Logical Inconsistency of the Old Quantum Theory of Black Body Radiation.John Norton - 1987 - Philosophy of Science 54 (3):327-350.
    The old quantum theory of black body radiation was manifestly logically inconsistent. It required the energies of electric resonators to be both quantized and continuous. To show that this manifest inconsistency was inessential to the theory's recovery of the Planck distribution law, I extract a subtheory free of this manifest inconsistency but from which Planck's law still follows.
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  44.  43
    Science and Certainty.John D. Norton - 1994 - Synthese 99 (1):3 - 22.
    I am grateful to Peter Achinstein, Don Howard, and the other participants at the conference, 'The Role of Experiments in Scientific Changer', Virginia Polytechnic Institute and State University, 30 March to 1 April, 1990, for helpful discussion, and especially to Ron Laymon for his discussion comments presented at the conference on an earlier version of this paper.
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  45.  8
    Curie’s Truism.John D. Norton - unknown
    Curie’s principle asserts that every symmetry of a cause manifests as a symmetry of the effect. It can be formulated as a tautology that is vacuous until it is instantiated. However instantiation requires us to know the correct way to map causal terminology onto the terms of a science. Causal metaphysics has failed to provide a unique, correct way to carry out the mapping. Thus successful or unsuccessful instantiation merely reflects our freedom of choice in the mapping.
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  46.  3
    Eaters of the Lotus: Landauer's Principle and the Return of Maxwell's Demon.John D. Norton - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (2):375-411.
    Landauer’s principle is the loosely formulated notion that the erasure of n bits of information must always incur a cost of k ln n in thermodynamic entropy. It can be formulated as a precise result in statistical mechanics, but for a restricted class of erasure processes that use a thermodynamically irreversible phase space expansion, which is the real origin of the law’s entropy cost and whose necessity has not been demonstrated. General arguments that purport to establish the unconditional validity of (...)
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  47.  41
    The Burning Fuse Model of Unbecoming in Time.John D. Norton - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52:103-105.
    Please imagine a long fuse hanging down from the ceiling. It is a carefully woven tube of fabric that holds a core of gunpowder. We note that it is beautifully made, with brightly colored threads intertwined with the coarser bare cotton. It a masterpiece of the modern weaver's art.
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  48. Little Boxes: A Simple Implementation of the Greenberger, Horne, and Zeilinger Result for Spatial Degrees of Freedom.John D. Norton - 2011 - American Journal of Physics 79:182--188.
    A Greenberger, Horne and Zeilinger - type construction is realized in the position properties of three particles whose wave functions are distributed over three two - chambered boxes. The same system is modeled more realistically using three spatially separated, singly ionized hydrogen molecules.
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  49.  77
    Exorcist XIV: The Wrath of Maxwell's Demon. Part II. From Szilard to Landauer and Beyond.John Norton - 1999 - Studies in History and Philosophy of Science Part B 30 (1):1-40.
    In this second part of our two-part paper we review and analyse attempts since 1950 to use information theoretic notions to exorcise Maxwell’s Demon. We argue through a simple dilemma that these attempted exorcisms are ineffective, whether they follow Szilard in seeking a compensating entropy cost in information acquisition or Landauer in seeking that cost in memory erasure. In so far as the Demon is a thermodynamic system already governed by the Second Law, no further supposition about information and entropy (...)
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  50. Brownian Computation Is Thermodynamically Irreversible.John D. Norton - 2013 - Foundations of Physics 43 (11):1-27.
    Brownian computers are supposed to illustrate how logically reversible mathematical operations can be computed by physical processes that are thermodynamically reversible or nearly so. In fact, they are thermodynamically irreversible processes that are the analog of an uncontrolled expansion of a gas into a vacuum.
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