8 found
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Allan F. Randall [8]Allan Frederick Randall [1]
  1. A Critique of the Kantian View of Geometry.Allan F. Randall - unknown
    A survey of Kant's views on space, time, geometry and the synthetic nature of mathematics. I concentrate mostly on geometry, but comment briefly on the syntheticity of logic and arithmetic as well. I believe the view of many that Kant's system denied the possibility of non-Euclidean geometries is clearly mistaken, as Kant himself used a non-Euclidean geometry (spherical geometry, used in his day for navigational purposes) in order to explain his idea, which amounts to an anticipation of the later discovery (...)
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  2. Computational Platonism.Allan F. Randall - unknown
    Plato's theory of forms is developed and compared to the modern theory of recursion. I show how Plato's theory, as it applies to mathematical objects, is essentially a primitve version of modern recursion theory, which has all the essential elements of the ancient theory. However, Plato himself thought there was more than mathematics to his forms. He believed that form had a noncomposite, unanalyzable component. So, while recursion theory provides an adequate formalization of Plato's theory, it cannot be considered identical (...)
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  3. Truth, Coherence and Correspondence in the Metaphysics of F.H. Bradley.Allan F. Randall - unknown
    An overview of Bradley's metaphysics and epistemology, which had much of the basic structure of quantum mechanics, but was all but ignored in the years following the formal quantum theories discovered by Heisenberg and Schrödinger. Bradley's version of absolute idealism was infected with the mentalism that was generally associated with idealism in the late nineteenth century. I develop his ideas from a standpoint somewhat more friendly to modern formal methods, although this is not much of a stretch, as Bradley had (...)
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  4. Logic, Idealism and Materialism in Early and Late Wittgenstein.Allan F. Randall - unknown
    Wittgenstein's philosophies, from both the Tractatus and the Philosophical Investigations, are explained and developed. Wittgenstein uses a primitive version of recursion theory to develop his attempt at a purely logical metaphysics in the Tractatus. However, due to his implicit materialist assumptions, he could not make the system completely logical, and built in a mystical division of possible worlds into the true and the false. This incoherence eventually lead him to reject logic as a method for doing metaphysics, and indeed to (...)
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  5. Quantum Phenomenology.Allan F. Randall - unknown
    Starting with the Descartes' cogito, "I think, therefore I am"--and taking an uncompromisingly rational, rigorously phenomenological approach--I attempt to derive the basic principles of recursion theory (the backbone of all mathematics and logic), and from that the principles of feedback control theory (the backbone of all biology), leading to the basic ideas of quantum mechanics (the backbone of all physics). What is derived is not the full quantum theory, but a basic framework--derived from a priori principles along with common everyday (...)
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  6. Quantum Superposition, Necessity and the Identity of Indiscernibles.Allan F. Randall - unknown
    Those who interpret quantum mechanics literally are forced to follow some variant of Everett's relative state formulation (or "many worlds" interpretation). It is generally assumed that this is a rather bizarre result that many physicists (especially cosmologists) have been forced into because of the evidence. I look at the history of philosophy, however, reveals that rationalism has always flirted with this very idea, from Parmenides to Leibniz to modern times. I will survey some of the philosophical history, and show how (...)
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  7. Computational Metaphysics: An Overview.Allan F. Randall - unknown
    While the essays on this web site, taken together, explain most of the essentials of my metaphysical system, some material is not covered, and the different essays take quite different approaches. The essays were mostly written for undergraduate and graduate courses in philosophy at the University of Toronto and York University. Thus, each essay is slanted to the issues that were addressed in whatever course it was written for. However, I hope soon to pull all this material together into a (...)
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  8. Modality in Computational Metaphysics.Allan F. Randall - unknown
    The many worlds anthropic principle is explored here from the a priori perspective of rationalist metaphysics, within the framework of modal logic. It is shown how the apparent contradictions of quantum superposition can be thought of in terms of different levels of world models. The framework of modal logic is used, but given the rationalist assumption that all possible worlds exist. There is thus no absolute distinction between possibility and necessity. To take the point of view of a conscious being (...)
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