Search results for 'supertask' (try it on Scholar)

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  1.  92
    Andrew Bacon (2011). A Paradox for Supertask Decision Makers. Philosophical Studies 153 (2):307.
    I consider two puzzles in which an agent undergoes a sequence of decision problems. In both cases it is possible to respond rationally to any given problem yet it is impossible to respond rationally to every problem in the sequence, even though the choices are independent. In particular, although it might be a requirement of rationality that one must respond in a certain way at each point in the sequence, it seems it cannot be a requirement to respond as such (...)
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  2.  53
    John Norton (1999). A Quantum Mechanical Supertask. Foundations of Physics 29 (8):1265-1302.
    That quantum mechanical measurement processes are indeterministic is widely known. The time evolution governed by the differential Schrödinger equation can also be indeterministic under the extreme conditions of a quantum supertask, the quantum analogue of a classical supertask. Determinism can be restored by requiring normalizability of the supertask state vector, but it must be imposed as an additional constraint on the differential Schrödinger equation.
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  3.  39
    Jon Pérez Laraudogoitia (1997). Classical Particle Dynamics, Indeterminism and a Supertask. British Journal for the Philosophy of Science 48 (1):49-54.
    In this paper a model in particle dynamics of a well-known supertask is constructed. As a consequence, a new and simple result about the failure of determinism of classical particle dynamics can be proved which is related to the non-existence of boundary conditions at spatial infinity. This result is much more accessible to the non-technical reader than similar ones in the scientific literature.
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  4.  26
    Jon Pérez Laaraudogoitia, Mark Bridger & Joseph S. Alper (2002). Two Ways of Looking at a Newtonian Supertask. Synthese 131 (2):173 - 189.
    A supertask is a process in which an infinite number of individuated actions are performed in a finite time. A Newtonian supertask is one that obeys Newton''s laws of motion. Such supertasks can violate energy and momentum conservation and can exhibit indeterministic behavior. Perez Laraudogoitia, who proposed several Newtonian supertasks, uses a local, i.e., particle-by-particle, analysis to obtain these and other paradoxical properties of Newtonian supertasks. Alper and Bridger use a global analysis, embedding the system of particles in (...)
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  5. Jon Perez Laraudogoitia (1996). A Beautiful Supertask. Mind 105 (417):81-83.
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  6.  20
    Catherine Legg (2008). Argument-Forms Which Turn Invalid Over Infinite Domains: Physicalism as Supertask? Contemporary Pragmatism 5 (1):1-11.
    Argument-forms exist which are valid over finite but not infinite domains. Despite understanding of this by formal logicians, philosophers can be observed treating as valid arguments which are in fact invalid over infinite domains. In support of this claim I will first present an argument against the classical pragmatist theory of truth by Mark Johnston. Then, more ambitiously, I will suggest the fallacy lurks in certain arguments for physicalism taken for granted by many philosophers today.
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  7.  11
    Jon Pérez Laraudogoitia (forthcoming). A Simple and Interesting Classical Mechanical Supertask. Synthese:1-26.
    This paper presents three interesting consequences that follow from admitting an ontology of rigid bodies in classical mechanics. First, it shows that some of the most characteristic properties of supertasks based on binary collisions between particles, such as the possibility of indeterminism or the non-conservation of energy, persist in the presence of gravitational interaction. This makes them gravitational supertasks radically different from those that have appeared in the literature to date. Second, Sect. 6 proves that the role of gravitation in (...)
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  8.  27
    John Earman & John D. Norton (1998). Comments on Laraudogoitia's 'Classical Particle Dynamics, Indeterminism and a Supertask'. British Journal for the Philosophy of Science 49 (1):123-133.
    We discuss two supertasks invented recently by Laraudogoitia [1996, 1997]. Both involve an infinite number of particle collisions within a finite amount of time and both compromise determinism. We point out that the sources of the indeterminism are rather different in the two cases—one involves unbounded particle velocities, the other involves particles with no lower bound to their sizes—and consequently that the implications for determinism are rather different—one form of indeterminism affects Newtonian but not relativistic physics, while the other form (...)
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  9.  49
    Jon Pérez Laraudogoitia (2014). The Supertask Argument Against Countable Additivity. Philosophical Studies 168 (3):619-628.
    This paper proves that certain supertasks constitute counterexamples to countable additivity even in the frame of an objective (not subjective, à la de Finetti) conception of probability. The argument requires taking conditional probability as a primitive notion.
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  10.  9
    Jon Pérez Laraudogoitia (2002). Just as Beautiful but Not (Necessarily) a Supertask. Mind 111 (442):281-288.
    In this paper I will put forward a simple case of a dynamical system which can exhibit both the indeterminism linked to escape to infinity and that linked to self-excitation. The case depends neither on the gravitational interaction between particles nor on their mutual collisions, and thus reveals the existence of a new kind of constraint that Newton's laws lay on the predictive power of classical dynamics.
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  11.  12
    Mark Bridger & Joseph S. Alper (1999). On the Dynamics of Perez Lauraudogoitia's Supertask. Synthese 119 (3):325-337.
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  12.  1
    Jon Pérez Laaraudogoitia, Mark Bridger & Joseph Alper (2004). Two Ways Of Looking At A Newtonian Supertask. Synthese 131 (2):173-189.
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  13.  45
    Joel David Hamkins (2002). Infinite Time Turing Machines. 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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  14.  46
    Joel David Hamkins & Andy Lewis (2000). Infinite Time Turing Machines. Journal of Symbolic Logic 65 (2):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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  15.  17
    Jon Pérez Laraudogoitia (2014). What the Tortoise Said to Achilles. Philosophia 42 (2):405-411.
    Continuing the conversation between Achilles and the tortoise begun by Carroll, this paper proves that, in a supertask context, there are free actions (in general, contingent states of affairs) that can be predicted by means of purely logical reasons.
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  16.  22
    Jon Pérez Laraudogoitia (2013). Zeno and Flow of Information. Synthese 190 (3):439-447.
    Although the current literature on supertasks concentrates largely on their supposed physical implications (extending the tradition of Zeno’s classical paradoxes of movement), in this study I propose a new model of supertask that explores for the first time some of their information-related consequences and I defend these consequences from a possible criticism.
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  17. Jan Willem Wieland (2012). And So On. Two Theories of Regress Arguments in Philosophy. Ghent University.
    This dissertation is on infinite regress arguments in philosophy. Its main goals are to explain what such arguments from many distinct philosophical debates have in common, and to provide guidelines for using and evaluating them. Two theories are reviewed: the Paradox Theory and the Failure Theory. According to the Paradox Theory, infinite regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that (...)
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  18.  82
    B. Jack Copeland & Oron Shagrir (2007). Physical Computation: How General Are Gandy's Principles for Mechanisms? Minds and Machines 17 (2):217-231.
    What are the limits of physical computation? In his ‘Church’s Thesis and Principles for Mechanisms’, Turing’s student Robin Gandy proved that any machine satisfying four idealised physical ‘principles’ is equivalent to some Turing machine. Gandy’s four principles in effect define a class of computing machines (‘Gandy machines’). Our question is: What is the relationship of this class to the class of all (ideal) physical computing machines? Gandy himself suggests that the relationship is identity. We do not share this view. We (...)
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  19. Vincent C. Müller (2011). On the Possibilities of Hypercomputing Supertasks. Minds and Machines 21 (1):83-96.
    This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such (...)
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  20. Jeffrey A. Barrett & Frank Arntzenius (2002). Why the Infinite Decision Puzzle is Puzzling. Theory and Decision 52 (2):139-147.
    Pulier (2000, Theory and Decision 49: 291) and Machina (2000, Theory and Decision 49: 293) seek to dissolve the Barrett–Arntzenius infinite decision puzzle (1999, Theory and Decision 46: 101). The proposed dissolutions, however, are based on misunderstandings concerning how the puzzle works and the nature of supertasks more generally. We will describe the puzzle in a simplified form, address the recent misunderstandings, and describe possible morals for decision theory.
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  21.  19
    Chunghyoung Lee (2013). The Staccato Roller Coaster: A Simple Physical Model of the Staccato Run. Synthese 190 (3):549-562.
    I present a simple model of Grünbaum’s staccato run in classical mechanics, the staccato roller coaster. It consists of a bead sliding on a frictionless wire shaped like a roller coaster track with infinitely many hills of diminishing size, each of which is a one-dimensional variant of the so-called Norton dome. The staccato roller coaster proves beyond doubt the dynamical (and hence logical) possibility of supertasks in classical mechanics if the Norton dome is a proper system of classical mechanics with (...)
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  22.  53
    Eric Steinhart (2003). Supermachines and Superminds. Minds and Machines 13 (1):155-186.
    If the computational theory of mind is right, then minds are realized by machines. There is an ordered complexity hierarchy of machines. Some finite machines realize finitely complex minds; some Turing machines realize potentially infinitely complex minds. There are many logically possible machines whose powers exceed the Church–Turing limit (e.g. accelerating Turing machines). Some of these supermachines realize superminds. Superminds perform cognitive supertasks. Their thoughts are formed in infinitary languages. They perceive and manipulate the infinite detail of fractal objects. They (...)
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  23.  13
    D. E. Seabold & J. D. Hamkins (2001). Infinite Time Turing Machines With Only One Tape. Mathematical Logic Quarterly 47 (2):271-287.
    Infinite time Turing machines with only one tape are in many respects fully as powerful as their multi-tape cousins. In particular, the two models of machine give rise to the same class of decidable sets, the same degree structure and, at least for partial functions f : ℝ → ℕ, the same class of computable functions. Nevertheless, there are infinite time computable functions f : ℝ → ℝ that are not one-tape computable, and so the two models of infinitary computation (...)
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  24.  60
    B. Jack Copeland & Oron Shagrir (2011). Do Accelerating Turing Machines Compute the Uncomputable? Minds and Machines 21 (2):221-239.
  25.  81
    Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. British Journal for the Philosophy of Science 54 (2):181-223.
    A version of the Church-Turing Thesis states that every effectively realizable physical system can be defined by Turing Machines (‘Thesis P’); in this formulation the Thesis appears an empirical, more than a logico-mathematical, proposition. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. These models depend on infinite computation, explicitly or implicitly, and appear physically implausible; moreover, even if infinite computation were realizable, the Halting Problem would not be affected. Therefore, (...)
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  26. David Atkinson (2007). Losing Energy in Classical, Relativistic and Quantum Mechanics. Studies in History and Philosophy of Science Part B 38 (1):170-180.
    A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. Relativistic mechanics, on the other hand, implies that energy and momentum conservation are always violated. Quantum mechanics, however, seems to rule out the Zeno configuration as an inconsistent system.
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  27.  49
    Gustavo E. Romero (2014). The Collapse of Supertasks. Foundations of Science 19 (2):209-216.
    A supertask consists in the performance of an infinite number of actions in a finite time. I show that any attempt to carry out a supertask will produce a divergence of the curvature of spacetime, resulting in the formation of a black hole. I maintain that supertaks, contrarily to a popular view among philosophers, are physically impossible. Supertasks, literally, collapse under their own weight.
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  28. Thomas Mormann, Topological Games, Supertasks, and (Un)Determined Experiments.
    The general aim of this paper is to introduce some ideas of the theory of infinite topological games into the philosophical debate on supertasks. First, we discuss the elementary aspects of some infinite topological games, among them the Banach-Mazur game.Then it is shown that the Banach-Mazur game may be conceived as a Newtonian supertask.In section 4 we propose to conceive physical experiments as infinite games. This leads to the distinction between determined and undetermined experiments and the problem of how (...)
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  29.  76
    Joseph S. Alper & Mark Bridger (1998). Newtonian Supertasks: A Critical Analysis. Synthese 114 (2):355-369.
    In two recent papers Perez Laraudogoitia has described a variety of supertasks involving elastic collisions in Newtonian systems containing a denumerably infinite set of particles. He maintains that these various supertasks give examples of systems in which energy is not conserved, particles at rest begin to move spontaneously, particles disappear from a system, and particles are created ex nihilo. An analysis of these supertasks suggests that they involve systems that do not satisfy the mathematical conditions required of Newtonian systems at (...)
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  30.  26
    Michael B. Burke (2000). The Staccato Run: A Contemporary Issue in the Zenonian Tradition. Modern Schoolman 78 (1):1-8.
    The “staccato run,” in which a runner stops infinitely often while running from one point to another, is a prototype of the “superfeat” (or "supertask”), that is, a feat involving the completion in a finite time of an infinite sequence of distinct, physically individuated acts. There is no widely accepted demonstration that superfeats are impossible logically, but I argue here, contra Grunbaüm, that they are impossible dynamically. Specifically, I show that the staccato run is excluded by Newton’s three laws (...)
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  31.  84
    Josh Parsons (2006). Topological Drinking Problems. Analysis 66 (290):149–154.
    In my (2004), I argued that it is possible to drink any finite amount of alcohol without ever suffering a hangover by completing a certain kind of supertask. Assume that a drink causes drunkenness to ensue immediately and to last for a period proportional to the quantity of alcohol consumed; that a hangover begins immediately at the time the drunkenness ends and lasts for the same length of time as the drunkenness; and that at any time during which you (...)
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  32.  37
    Luis Carlos Medina (2009). Evolution Nodes in Newtonian Supertasks. Theoria 24 (2):229-247.
    The present article provides an analysis of the instants of a system that performs a Newtonian supertask. For each instant it studied the possibility of the system having, from the instant in question, more than one possible course of evolution; i.e. the possibility of it being an evolution node. This analysis shows that some supertasks presented as deterministic in Perez Laraudogoitia (2007) are in fact indeterministic and specifies the difficulties ahead in showing the radical indeterminism suggested by Atkinson & (...)
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  33.  48
    Alasdair M. Richmond (2013). Hilbert's Inferno: Time Travel for the Damned. Ratio 26 (3):233-249.
    Combining time travel with certain kinds of supertask, this paper proposes a novel model for Hell. Temporally-closed spacetimes allow otherwise impossible opportunities for material kinds of damnation and reveal surprising limitations on metaphysical objections to Hell. Prima facie, eternal damnation requires either infinite amounts of time or time for the damned to speed-up arbitrarily. However, spatiotemporally finite ‘time travel’ universes can host unending personal torment for infinitely many physical beings, while keeping fixed finite limits on rates of temporal passage. (...)
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  34.  15
    Joel David Hamkins & Andrew Lewis (2002). Post's Problem for Supertasks has Both Positive and Negative Solutions. Archive for Mathematical Logic 41 (6):507-523.
    The infinite time Turing machine analogue of Post's problem, the question whether there are semi-decidable supertask degrees between 0 and the supertask jump 0∇, has in a sense both positive and negative solutions. Namely, in the context of the reals there are no degrees between 0 and 0∇, but in the context of sets of reals, there are; indeed, there are incomparable semi-decidable supertask degrees. Both arguments employ a kind of transfinite-injury construction which generalizes canonically to oracles.
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  35.  37
    Jon Perez Laraudogoitia (1998). Infinity Machines and Creation Ex Nihilo. Synthese 115 (2):259-265.
    In this paper a simple model in particle dynamics of a well-known supertask is constructed (the supertask was introduced by Max Black some years ago). As a consequence, a new and simple result about creation ex nihilo of particles can be proved compatible with classical dynamics. This result cannot be avoided by imposing boundary conditions at spatial infinity, and therefore is really new in the literature. It follows that there is no reason why even a world of rigid (...)
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  36.  44
    David Atkinson (2006). A Relativistic Zeno Effect. Synthese 160 (1):5 - 12.
    A Zenonian supertask involving an infinite number of identical colliding balls is generalized to include balls with different masses. Under the restriction that the total mass of all the balls is finite, classical mechanics leads to velocities that have no upper limit. Relativistic mechanics results in velocities bounded by that of light, but energy and momentum are not conserved, implying indeterminism. The notion that both determinism and the conservation laws might be salvaged via photon creation is shown to be (...)
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  37.  13
    Jon Pérez Laraudogoitia (2014). Dispositions and the Trojan Fly. Noûs 48 (4):773-780.
    A detailed consideration of the Trojan fly supertask reveals certain unsuspected characteristics relating to determinism and causation. I propose here a solution to the new difficulty in terms of bare dispositions.
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  38.  23
    Alisa Bokulich (2003). Quantum Measurements and Supertasks. International Studies in the Philosophy of Science 17 (2):127 – 136.
    This article addresses the question whether supertasks are possible within the context of non-relativistic quantum mechanics. The supertask under consideration consists of performing an infinite number of quantum mechanical measurements in a finite amount of time. Recent arguments in the physics literature claim to show that continuous measurements, understood as N discrete measurements in the limit where N goes to infinity, are impossible. I show that there are certain kinds of measurements in quantum mechanics for which these arguments break (...)
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  39.  13
    Jon Pérez Laraudogoitia (1999). Why Dynamical Self-Excitation is Possible. Synthese 119 (3):313-323.
    In Pérez Laraudogoitia (1996), I introduced a simple example of a supertask that involved the possibility of spontaneous self-excitation and, therefore, of a particularly interesting form of indeterminism in classical dynamics. Alper and Bridger (1998) criticised (among other things) this result. In the present article, I answer their criticisms. In what follows I assume familiarity both with Pérez Laraudogoitia (1996) and Alper and Bridger’s subsequent article.
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  40.  7
    Martin C. Cooke (2003). Infinite Sequences: Finitist Consequence. British Journal for the Philosophy of Science 54 (4):591-599.
    A simultaneous collision that produces paradoxical indeterminism (involving N0 hypothetical particles in a classical three-dimensional Euclidean space) is described in Section 2. By showing that a similar paradox occurs with long-range forces between hypothetical particles, in Section 3, the underlying cause is seen to be that collections of such objects are assumed to have no intrinsic ordering. The resolution of allowing only finite numbers of particles is defended (as being the least ad hoc) by looking at both -sequences (in the (...)
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  41. Eric Steinhart (2007). Infinitely Complex Machines. In Intelligent Computing Everywhere. Springer 25-43.
    Infinite machines (IMs) can do supertasks. A supertask is an infinite series of operations done in some finite time. Whether or not our universe contains any IMs, they are worthy of study as upper bounds on finite machines. We introduce IMs and describe some of their physical and psychological aspects. An accelerating Turing machine (an ATM) is a Turing machine that performs every next operation twice as fast. It can carry out infinitely many operations in finite time. Many ATMs (...)
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