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  1. Infinite Time Turing Machines.Joel David Hamkins - 2002 - Minds and Machines 12 (4):567-604.
    Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.
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  • The Impossibility of Superfeats.Michael B. Burke - 2000 - Southern Journal of Philosophy 38 (2):207-220.
    Is it logically possible to perform a "superfeat"? That is, is it logically possible to complete, in a finite time, an infinite sequence of distinct acts? In opposition to the received view, I argue that all physical superfeats have kinematic features that make them logically impossible.
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  • 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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  • Erik-Jon Gaizka, the Magician of Infinity.J. Perez Laraudogoitia - 2010 - Analysis 70 (3):451-456.
    (No abstract is available for this citation).
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  • Prompting Challenges.John Turri - 2010 - Analysis 70 (3):456-462.
    I consider a serious objection to the knowledge account of assertion and develop a response. In the process I introduce important new data on prompting assertion, which all theorists working in the area should take note of.
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  • Accelerating Turing Machines.B. Jack Copeland - 2002 - Minds and Machines 12 (2):281-300.
    Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of contains n consecutive 7s, for any n; solve the Turing-machine halting problem; and decide the predicate calculus. Are accelerating Turing machines, then, logically impossible devices? I argue that they are not. There are implications concerning the nature of effective procedures and the theoretical limits of computability. Contrary (...)
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  • Can an Infinitude of Operations Be Performed in a Finite Time?Adolf Grünbaum - 1969 - British Journal for the Philosophy of Science 20 (3):203-218.
  • A Discrete Solution for the Paradox of Achilles and the Tortoise.Vincent Ardourel - 2015 - Synthese 192 (9):2843-2861.
    In this paper, I present a discrete solution for the paradox of Achilles and the tortoise. I argue that Achilles overtakes the tortoise after a finite number of steps of Zeno’s argument if time is represented as discrete. I then answer two objections that could be made against this solution. First, I argue that the discrete solution is not an ad hoc solution. It is embedded in a discrete formulation of classical mechanics. Second, I show that the discrete solution cannot (...)
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  • Neologicist Nominalism.Rafal Urbaniak - 2010 - Studia Logica 96 (2):149-173.
    The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those (...)
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