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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 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. 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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  15. 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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  16. 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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  17. 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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  18. 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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  19. 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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  20. 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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  21. 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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  22. 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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  23. 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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  24. 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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  25. 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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  26. 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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  27. 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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  28. 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.
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  29. 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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  30. 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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  31. 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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  32. 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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  33. John D. Norton (2010). Time Really Passes. Humana. Mente: Journal of Philosophical Studies 13:23-24.
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  34. 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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  35. 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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  36. 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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  37. 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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  38. John D. Norton (2007). Causation as Folk Science. In Huw Price & Richard Corry (eds.), Causation, Physics, and the Constitution of Reality: Russell's Republic Revisited. 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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  39. John D. Norton (2007). Disbelief as the Dual of Belief. 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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  40. John D. Norton (2007). Einstein, Nordstrom, and the Early Demise of Scalar, Lorentz Covariant Theories of Gravitation. 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 (...)
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  41. John D. Norton (2007). Probability Disassembled. British Journal for the Philosophy of Science 58 (2):141 - 171.
    While there is no universal logic of induction, the probability calculus succeeds as a logic of induction in many contexts through its use of several notions concerning inductive inference. They include Addition, through which low probabilities represent disbelief as opposed to ignorance; and Bayes property, which commits the calculus to a 'refute and rescale' dynamics for incorporating new evidence. These notions are independent and it is urged that they be employed selectively according to needs of the problem at hand. It (...)
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  42. John D. Norton, Gunnar NORDSTRÖM & Albert Einstein (2007). A Field Theory of Gravitation in the Framework of Special Relativity. Boston Studies in the Philosophy of Science 250.
     
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  43. John D. Norton (2006). Atoms, Entropy, Quanta: Einstein's Miraculous Argument of 1905. 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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  44. John D. Norton, Discovering the Relativity of Simultaneity How Did Einstein Take "the Step"?
    It is routinely assumed that Einstein discovered the relativity of simultaneity by thinking about how clocks can be synchronized by light signals, much in accord with the analysis he gave in his 1905 special relativity paper. Yet that is just supposition. We have no real evidence that it actually happened this way. In later recollections, Einstein stressed the importance of several thought experiments in the thinking that led up to the final theory. They include his chasing a light beam thought (...)
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  45. John D. Norton (2006). How the Formal Equivalence of Grue and Green Defeats What is New in the New Riddle of Induction. 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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  46. John D. Norton (2005). Eaters of the Lotus: Landauer's Principle and the Return of Maxwell's Demon. 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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  47. John D. Norton (2004). On Thought Experiments: Is There More to the Argument? 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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  48. John D. Norton (2004). Why Thought Experiments Do Not Transcend Empiricism. In Christopher Hitchcock (ed.), Contemporary Debates in the Philosophy of Science. Blackwell. 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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  49. John D. Norton, A Little Survey of Induction.
    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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  50. John D. Norton (2003). A Material Theory of Induction. 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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