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  1. John D. Norton, A Quantum Inductive Logic.
    The material theory of induction requires that good inductive inferences must be warranted by facts within their domain of application. In earlier chapters, we have seen many examples of individual inductive inferences warranted by specific facts. Marie Curie, for example, inferred the crystallographic system of all crystals of radium chloride from inspection of just a few specks of the substance. The inference was warranted by facts contained in crystallographic principles from the preceding century, not by some universal inductive inference schema.
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  2. John D. Norton, And the Return of Maxwell's Demon.
    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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  3. John D. Norton, Canadian Journal of Philosophy.
    Whatever the original intent, the introduction of the term 'thought experiment' has proved to be one of the great public relations coups of science writing, For generations of readers of scientific literature, the term has planted the seed of hope that the fragment of text they have just read is more than mundane. Because it was a thought experiment, does it not tap into that infallible font of all wisdom in empiricist science, the experiment? And because it was conducted in (...)
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  4. John D. Norton, Infinite Idealizations.
    In my talk at the celebration of the 20th Anniversary of the Vienna Circle Institute, I sketched results of recent work on approximation and idealization (Norton, forthcoming). A goal of that work was to clarify the widespread use of infinite limits in statistical physics to introduce what are informally described as idealizations. This literature examines the behavior of systems composed of very many—but always finitely many—components. Certain properties of these systems settle down to stable values if the number of components (...)
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  5. John D. Norton, Over General Covariance.
    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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  6. John D. Norton, The Burning Fuse Model of Unbecoming in Time.
    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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  7. John D. Norton, The N-Stein Family.
    The work of Newstein is now so familiar to us, thanks to Professor Stachel's efforts, that it bears only the briefest recapitulation. Sometime after 1880 but before the advent of general relativity, Newstein brooded on the equality of inertial and gravitational mass. Through an ingenious thought experiment — the Newstein elevator — he hit upon the idea of an essential unity of gravitation and inertia. This was expressed in the indistinguishability of the effects of acceleration in a uniformly accelerated..
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  8. John Norton, A Conjecture on Einstein, the Independent Reality of Spacetime Coordinate Systems and the Disaster of 1913.
    Two fundamental errors led Einstein to reject generally covariant gravitational field equations for over two years as he was developing his general theory of relativity. The first is well known in the literature. It was the presumption that weak, static gravitational fields must be spatially flat and a corresponding assumption about his weak field equations. I conjecture that a second hitherto unrecognized error also defeated Einstein's efforts. The same error, months later, allowed the hole argument to convince Einstein that all (...)
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  9. John Norton, Challenges to Bayesian Confirmation Theory.
    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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  10. John Norton, Draft.
    The use of the material theory of induction to vindicate a scientist’s claims of evidential warrant is illustrated with the cases of Einstein’s thermodynamic argument for light quanta of 1905 and his recovery of the anomalous motion of Mercury from general relativity in 1915. In a survey of other accounts of inductive inference applied to these examples, I show that, if it is to succeed, each account must presume the same material facts as the material theory and, in addition, some (...)
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  11. John Norton, Do the Causal Principles of Modern Physics Contradict Causal Anti-Fundamentalism?
    In Norton(2003), it was urged that the world does not conform at a fundamental level to some robust principle of causality. To defend this view, I now argue that the causal notions and principles of modern physics do not express some universal causal principle, brought to light by discoveries in physics. Rather they merely assert that, according to relativity theory, spacetime has an invariant velocity, that of light; and that theories of matter admit no propagations faster than light.
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  12. John Norton, Einstein for Everyone.
    For over a decade I have taught an introductory, undergraduate class, "Einstein for Everyone," at the University of Pittsburgh to anyone interested enough to walk through door. The course is aimed at people who have a strong sense that what Einstein did changed everything. However they do not know enough physics to understand what he did and why it was so important. The course presents just enough of Einstein's physics to give students an independent sense of what he achieved and (...)
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  13. John Norton, Einstein's Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies That Led Him to It.
    Modern readers turning to Einstein’s famous 1905 paper on special relativity may not find what they expect. Its title, “On the electrodynamics of moving bodies,” gives no inkling that it will develop an account of space and time that will topple Newton’s system. Even its first paragraph just calls to mind an elementary experimental result due to Faraday concerning the interaction of a magnet and conductor. Only then does Einstein get down to the business of space and time and lay (...)
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  14. John Norton, Induction Without Probabilities12.
    A simple indeterministic system is displayed and it is urged that we cannot responsibly infer inductively over it if we presume that the probability calculus is the appropriate logic of induction. The example illustrates the general thesis of a material theory of induction, that the logic appropriate to a particular domain is determined by the facts that prevail there.
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  15. John Norton, Vol. 3, No. 4: John D. Norton, "Causation as Folk Science".
    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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  16. John D. Norton, Addendum.
    After preparing the main text of this chapter, I found that it overlooked some material that further illuminated Einstein’s attitude to David Hume.1 A revealing remark is made in Reiser’s biography2 that notes Einstein’s early philosophical reading: He approached the broader aspects of thought through philosophical studies, chiefly through his readings in Kant and Schopenhauer, and later through his study of Hume, with whom he felt a special kinship. We have good reason to accept the report of “special kinship” (...)
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  17. John D. Norton, A Survey of Inductive Generalization.
    Inductive generalization asserts that what obtains in known instances can be generalized to all. Its original form is enumerative induction, the earliest form of inductive inference, and it has been elaborated in various ways, largely with the goal of extending its reach. Its principal problem is that it supplies no intrinsic notion of strength of support so that one cannot tell if the generalization has weak or strong support.
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  18. John D. Norton, Center for Philosophy of Science And.
    Footnote: My thanks to Zvi Biener and Balazs Gyenis for comments. 1. What is the relationship between philosophy and physics? What should the relationship be? To someone who does not work in philosophy of physics, it can be hard to distinguish what a theoretical physicist does from what a philosopher of physics does. The differences lie in two areas: their goals and their methods. The highest goal of theoretical physicists is to find the next theory. That profoundly colors the way (...)
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  19. John D. Norton, Chasing the Light Einsteinʼs Most Famous Thought Experiment.
    At the age of sixteen, Einstein imagined chasing after a beam of light. He later recalled that the thought experiment had played a memorable role in his development of special relativity. Famous as it is, it has proven difficult to understand just how the thought experiment delivers its results. It fails to generate problems for an ether-based electrodynamics. I propose that Einstein’s canonical statement of the thought experiment from his 1946 “Autobiographical Notes,” makes most sense not as an argument against (...)
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  20. John D. Norton, Einstein's Investigations of Galilean Covariant Electrodynamics Prior to 1905.
    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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  21. John D. Norton, Einstein's Miraculous Argument of 1905: The Thermodynamic Grounding of Light Quanta.
    A major part of Einstein’s 1905 light quantum paper is devoted to arguing that high frequency heat radiation bears the characteristic signature of a microscopic energy distribution of independent, spatially localized components. The content of his light quantum proposal was precarious in that it contradicted the great achievement of nineteenth century physics, the wave theory of light and its accommodation in electrodynamics. However the methods used to arrive at it were both secure and familiar to Einstein in 1905. A mainstay (...)
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  22. John D. Norton, Rehabilitated.
    Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this (...)
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  23. John D. Norton, The Inductive Significance of Observationally Indistinguishable Spacetimes: (Peter Achinstein has the Last Laugh).
    For several years, through the “material theory of induction,” I have urged that inductive inferences are not licensed by universal schemas, but by material facts that hold only locally (Norton, 2003, 2005). My goal has been to defend inductive inference against inductive skeptics by demonstrating when and how inductive inferences are properly made. Since I have always admired Peter Achinstein as a staunch defender of induction, it was a surprise when Peter..
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  24. John D. Norton, Waiting.
    Landauer's Principle asserts that there is an unavoidable cost in thermodynamic entropy when data is erased. It is sometimes deduced from a version of the second law of thermodynamics or it is posited as a way of protecting the law from violation by a Maxwell's demon. Yet the standard processes assumed in the thermodynamics of computation can be combined to produce devices that both violate the second law and erase data without entropy cost, indicating an inconsistency in the standard system. (...)
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  25. John D. Norton, What Can We Learn About the Ontology of Space and Time From the Theory of Relativity?
    In the exuberance that followed Einstein’s discoveries, philosophers at one time or another have proposed that his theories support virtually every conceivable moral in ontology. I present an opinionated assessment, designed to avoid this overabundance. We learn from Einstein’s theories of novel entanglements of categories once held distinct: space with time; space and time with matter; and space and time with causality. We do not learn that all is relative, that time in the fourth dimension in any non-trivial sense, that (...)
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  26. John D. Norton (forthcoming). Must Evidence Underdetermine Theory. 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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  27. John D. Norton (2014). The End of the Thermodynamics of Computation: A No-Go Result. Philosophy of Science 80 (5):1182-1192.
    The thermodynamics of computation assumes that computational processes at the molecular level can be brought arbitrarily close to thermodynamic reversibility and that thermodynamic entropy creation is unavoidable only in data erasure or the merging of computational paths, in accord with Landauer’s principle. The no-go result shows that fluctuations preclude completion of thermodynamically reversible processes. Completion can be achieved only by irreversible processes that create thermodynamic entropy in excess of the Landauer limit.
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  28. John D. Norton (2013). A Material Dissolution of the Problem of Induction. 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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  29. John D. Norton (2013). Author's Reply to Landauer Defended. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (3):272.
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  30. John D. Norton (2013). Brownian Computation Is Thermodynamically Irreversible. 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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  31. Claus Beisbart & John D. Norton (2012). Why Monte Carlo Simulations Are Inferences and Not Experiments. 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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  32. John D. Norton (2012). Approximation and Idealization: Why the Difference Matters. 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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  33. John D. Norton (2012). The Scaling of Speeds and Distances in Galileo's Two New Sciences: A Reply to Palmerino and Laird. Centaurus 54 (2):182-191.
    In this reply, we respond to the comments of Palmerino and Laird on our article, "Galileo's Refutation of the Speed Distance Law of Fall Rehabilitated," published in the same issue of Centaurus.
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  34. John D. Norton & Bryan W. Roberts (2012). Galileo's Refutation of the Speed-Distance Law of Fall Rehabilitated. Centaurus 54 (2):148-164.
    Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this (...)
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  35. John D. Norton (2011). History of Science and the Material Theory of Induction: Einstein's Quanta, Mercury's Perihelion. [REVIEW] European Journal for Philosophy of Science 1 (1):3-27.
    The use of the material theory of induction to vindicate a scientist's claims of evidential warrant is illustrated with the cases of Einstein's thermodynamic argument for light quanta of 1905 and his recovery of the anomalous motion of Mercury from general relativity in 1915. In a survey of other accounts of inductive inference applied to these examples, I show that, if it is to succeed, each account must presume the same material facts as the material theory and, in addition, some (...)
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  36. John D. Norton (2011). Little Boxes: A Simple Implementation of the Greenberger, Horne, and Zeilinger Result for Spatial Degrees of Freedom. 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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  37. John D. Norton (2011). Observationally Indistinguishable Spacetimes: A Challenge for Any Inductivist. In Gregory J. Morgan (ed.), Philosophy of Science Matters: The Philosophy of Peter Achinstein. Oxford University Press. 164.
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  38. John D. Norton (2011). Waiting for Landauer. 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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  39. John Norton (2010). Deductively Definable Logies of Induction. Journal of Philosophical Logic 39 (6):617 - 654.
    A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This no-go (...)
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  40. John D. Norton (2010). Cosmic Confusions: Not Supporting Versus Supporting Not. 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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  41. John D. Norton (2010). There Are No Universal Rules for Induction. 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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  42. John D. Norton (2010). Time Really Passes. Humana. Mente: Journal of Philosophical Studies 13:23-24.
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  43. Oron Shagrir, John D. Norton, Holger Andreas, Jouni-Matti Kuukkanen, Aris Spanos, Eckhart Arnold, Elliott Sober, Peter Gildenhuys & Adela Helena Roszkowski (2010). 1. Marr on Computational-Level Theories Marr on Computational-Level Theories (Pp. 477-500). Philosophy of Science 77 (4).
     
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  44. John Norton (2009). Is There an Independent Principle of Causality in Physics? 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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  45. John D. Norton, Cosmology and Inductive Inference: A Bayesian Failure.
    A probabilistic logic of induction is unable to separate cleanly neutral support from disfavoring evidence (or ignorance from disbelief). Thus, the use of probabilistic representations may introduce spurious results stemming from its expressive inadequacy. That such spurious results arise in the Bayesian “doomsday argument” is shown by a reanalysis that employs fragments of an inductive logic able to represent evidential neutrality. Further, the improper introduction of inductive probabilities is illustrated with the “self-sampling assumption.”.
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  46. John D. Norton (2009). How Hume and Mach Helped Einstein Find Special Relativity. In Michael Friedman, Mary Domski & Michael Dickson (eds.), Discourse on a New Method: Reinvigorating the Marriage of History and Philosophy of Science. Open Court. 359--86.
    In recounting his discovery of special relativity, Einstein recalled a debt to the philosophical writings of Hume and Mach. I review the path Einstein took to special relativity and urge that, at a critical juncture, he was aided decisively not by any specific doctrine of space and time, but by a general account of concepts that Einstein found in Hume and Mach’s writings. That account required that concepts, used to represent the physical, must be properly grounded in experience. In so (...)
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  47. John D. Norton, The Inductive Significance of Observationally Indistinguishable Spacetimes.
    Results on the observational indistinguishability of spacetimes demonstrate the impossibility of determining by deductive inference which is our spacetime, no matter how extensive a portion of the spacetime is observed. These results do not illustrate an underdetermination of theory by evidence, since they make no decision between competing theories and they make little contact with the inductive considerations that must ground such a decision. Rather, these results express a variety of indeterminism in which a specification of the observable past always (...)
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  48. John Norton (2008). Ignorance and Indifference. 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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  49. John Norton, Is There an Independent Principle of Causality in Physics? A Comment on Matthias Frisch, 'Causal Reasoning in Physics.'.
    Earlier version on philsci-archive.pitt.edu; latest version.
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  50. John Norton (2008). The Dome: An Unexpectedly Simple Failure of Determinism. 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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