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Discrete or Continuous? the Quest for Fundamental Length in Modern Physics

New York: Cambridge University Press (2014)

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  1. Mathematics and Metaphilosophy.Justin Clarke-Doane - 2022 - Cambridge: Cambridge University Press.
    This book discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the problem of explaining the (defeasible) justification of our mathematical beliefs (‘the justificatory challenge’), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the problem of explaining their reliability (‘the reliability challenge’), arises to the extent that we could have easily had different beliefs. The book shows that mathematical facts are not, in general, empirically accessible, contra Quine, (...)
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  • Measuring the present: What is the duration of ‘now’?Brittany A. Gentry - 2020 - Synthese 198 (10):9357-9371.
    Presentists argue that only the present is real. In this paper, I ask what duration the present has on a presentist’s account. While several answers are available, each of them requires the adoption of a measure and, with that adoption, additional work must be done to define the present. Whether presentists conclude that a reductionist account of duration is acceptable, that duration is not an applicable concept for their notion of the present, that the present has a duration of zero, (...)
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  • Renormalizability, Fundamentality, and a Final Theory: The Role of UV-Completion in the Search for Quantum Gravity.Karen Crowther & Niels Linnemann - 2019 - British Journal for the Philosophy of Science 70 (2):377-406.
    Principles are central to physical reasoning, particularly in the search for a theory of quantum gravity, where novel empirical data are lacking. One principle widely adopted in the search for QG is ultraviolet completion: the idea that a theory should hold up to all possible high energies. We argue— contra standard scientific practice—that UV-completion is poorly motivated as a guiding principle in theory-construction, and cannot be used as a criterion of theory-justification in the search for QG. For this, we explore (...)
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  • Defining a crisis: the roles of principles in the search for a theory of quantum gravity.Karen Crowther - 2021 - Synthese 198 (Suppl 14):3489-3516.
    In times of crisis, when current theories are revealed as inadequate to task, and new physics is thought to be required—physics turns to re-evaluate its principles, and to seek new ones. This paper explores the various types, and roles of principles that feature in the problem of quantum gravity as a current crisis in physics. I illustrate the diversity of the principles being appealed to, and show that principles serve in a variety of roles in all stages of the crisis, (...)
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  • Renormalizability, fundamentality and a final theory: The role of UV-completion in the search for quantum gravity.Karen Crowther & Niels Linnemann - 2017 - British Journal for the Philosophy of Science 70 (2):377–406.
    Principles are central to physical reasoning, particularly in the search for a theory of quantum gravity (QG), where novel empirical data is lacking. One principle widely adopted in the search for QG is UV completion: the idea that a theory should (formally) hold up to all possible high energies. We argue---/contra/ standard scientific practice---that UV-completion is poorly-motivated as a guiding principle in theory-construction, and cannot be used as a criterion of theory-justification in the search for QG. For this, we explore (...)
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  • Ed Fredkin and the Physics of Information - An Inside Story of an Outsider Scientist.Amit Hagar - 2016 - Information and Culture 51 (3):419-443.
    This article tells the story of Ed Fredkin, a pilot, programmer, engineer, hardware designer and entrepreneur, whose work inside and outside academia has influenced major developments in computer science and in the foundations of theoretical physics for the past fifty years.
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  • Location and Mereology.Cody Gilmore, Claudio Calosi & Damiano Costa - 2013 - Stanford Encyclopedia of Philosophy.
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  • Lorentz Transformation Under a Discrete Dynamical Time and Continuous Space.Roland Riek - 2022 - Foundations of Physics 52 (5):1-12.
    The Lorentz transformation of space and time between two reference frames is one of the pillars of the special relativity theory. As a result of the Lorentz transformation, space and time are only relative and are entangled, while the Minkowski metric is Lorentz invariant. For this reason, the Lorentz transformation is one of the major obstructions in the development of physical theories with quantized space and time. Here is described the Lorentz transformation of a physical system with a discrete dynamical (...)
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  • The philosophy of quantum gravity – lessons from Nicolai Hartmann.Simonluca Pinna - 2015 - European Journal for Philosophy of Science 5 (3):279-296.
    An astonishing thesis in the philosophy of quantum gravity is that spacetime ”disappears” at the fundamental level of reality, and that the geometrical notions of ”length” and ”duration” are derived from the dynamics of the basic non–geometrical building blocks of the theory. Unveiling here the analysis of the concepts of spacetime, measure, and magnitude, given by the philosopher Nicolai Hartmann, I argue that the ”disappearance” thesis is too strong. The fundamental geometrical notions are, on the contrary, primitive and cannot be (...)
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  • Discrete and continuous: a fundamental dichotomy in mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
    The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article (...)
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  • Effective Field Theories: A Philosophical Appraisal.Dimitrios Athanasiou - unknown
    The word “effective” has become the standard label attached to scientific theories these days. An effective theory allows us to make accurate predictions about a physical system at a certain (energy, length) scale while being largely ignorant of the details at more fundamental levels. One does not need to know anything about the deeper, quantum structure of water molecules to describe the macroscopic behaviour of waves or water in a glass. Although effective descriptions so broadly construed have been part of (...)
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  • Quantum gravity.Steven Weinstein - 2008 - Stanford Encyclopedia of Philosophy.
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  • Finitism in geometry.Jean-Paul Van Bendegem - 2002 - Stanford Encyclopedia of Philosophy.
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