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Switch to: References
Citations of:
Achilles and the Tortoise
In Wesley Charles Salmon (ed.), Zeno’s Paradoxes. Indianapolis, IN, USA: Bobbs-Merrill. pp. 67-81 (1970)
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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 (...) |
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The objective of this article is to provide a discussion that counters the infinite particle disappearance conclusion argued by Shackel, 417–433, 2018). In order to do this, clear criteria to disprove the results of the applications of his continuity principles are provided, in addition to the consideration of the fundamental Classical Mechanical principle of mass conservation as an independent and clear basis for this disproof. |
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In this article, I take on a classic objection to Kant’s arguments in the Antinomy of Pure Reason: that the arguments are question-begging, as they draw illicit inferences from claims about representation to claims about reality. While extant attempts to vindicate Kant try to show that he does not make such inferences, I attempt to vindicate Kant’s arguments in a different way: I show that, given Kant’s philosophical backdrop, the inferences in question are not illicit. This is because the transcendental (...) |
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It’s well known that one way to cure a hangover is by a “hair of the dog” — another alcoholic drink. The drawback of this method is that, so it would appear, it cannot be used to completely cure a hangover, since the cure simply induces a further hangover at a later time, which must in turn either be cured or suffered through. |
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John Cook Wilson (1849–1915) was Wykeham Professor of Logic at New College, Oxford and the founder of ‘Oxford Realism’, a philosophical movement that flourished at Oxford during the first decades of the 20th century. Although trained as a classicist and a mathematician, his most important contribution was to the theory of knowledge, where he argued that knowledge is factive and not definable in terms of belief, and he criticized ‘hybrid’ and ‘externalist’ accounts. He also argued for direct realism in perception, (...) |
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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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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 spheres should (...) |
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Much of the debate about the mathematical refutation of Zeno’s paradoxes surrounds the logical possibility of completing supertasks—tasks made up of an infinite number of subtasks. Max Black and J.F. Thomson attempt to show that supertasks entail logical contradictions, but their arguments come up short. In this paper, I take a different approach to the mathematical refutations. I argue that even if supertasks are possible, we do not have a non-question-begging reason to think that Achilles’ supertask is possible. The justification (...) |
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We explore the better known paradoxes of Zeno including modern variants based on infinite processes, from the point of view of standard, classical analysis, from which there is still much to learn (especially concerning the paradox of division), and then from the viewpoints of non-standard and non-classical analysis (the logic of the latter being intuitionist).The standard, classical or Cantorian notion of the continuum, modeled on the real number line, is well known, as is the definition of motion as the time (...) |
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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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Louis Loeb has argued that Hume is pessimistic while Peirce is optimistic about the attainment of fully stable beliefs. In contrast, we argue that Hume was optimistic about such attainment but only if the scope of philosophical investigation is limited to first-order explanatory questions. Further, we argue that Peirce, after reformulating the pragmatic maxim to accommodate the reality of counterfactuals, was pessimistic about such attainment. Finally, we articulate and respond to Peirce's objection that Hume's skeptical arguments in T 1.4.1 and (...) |
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There are two distinct but interrelated questions concerning Aristotle’s account of infinity that have been the subject of recurring debate. The first of these, what I call here the interpretative question, asks for a charitable and internally coherent interpretation of the limited pieces of text where Aristotle outlines his view of the ‘potential’ (and not ‘actual’) infinite. The second, what I call here the philosophical question, asks whether there is a way to make Aristotle’s notion of the potential infinite coherent (...) |
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It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical (...) |
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It is usually supposed that, with his dichotomy paradox, Zeno gave birth to the modern so-called supertask debate – the debate of whether carrying out an infinite sequence of actions or operations... |
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The Nothing from Infinity paradox arises when the combination of two infinitudes of point particles meet in a supertask and disappear. Corral-Villate claims that my arguments for disappearance fail and concedes that this failure also produces an extreme kind of indeterminism, which I have called plenitudinous. So my supertask at least poses a dilemma of extreme indeterminism within Newtonian point particle mechanics. Plenitudinous indeterminism might be trivial, although easy attempts to prove it so seem to fail in the face of (...) |
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Mixed strategies have been used to show that Pascal’s Wager fails to offer sufficient pragmatic reasons for believing in God. Their proponents have argued that, in addition to outright belief in God, rational agents can follow alternatives strategies whose expected utility is infinite as well. One objection that has been raised against this way of blocking Pascal’s Wager is that applying a mixed strategy in Pascal’s case is tantamount to applying an iterated mixed strategy which, properly understood, collapses into the (...) |
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In this paper the claim that Zeno's paradoxes have been solved is contested. Although "no one has ever touched Zeno without refuting him" (Whitehead), it will be our aim to show that, whatever it was that was refuted, it was certainly not Zeno. The paper is organised in two parts. In the first part we will demonstrate that upon direct analysis of the Greek sources, an underlying structure common to both the Paradoxes of Plurality and the Paradoxes of Motion can (...) |
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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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This work analyzes two perspectives, Atomism and Infinite Divisibility, in the light of modern mathematical knowledge and recent developments in computer graphics. A developmental perspective is taken which relates ideas leading to atomism and infinite divisibility. A detailed analysis of and a new resolution for Zeno's paradoxes are presented. Aristotle's arguments are analyzed. The arguments of some other philosophers are also presented and discussed. All arguments purporting to prove one position over the other are shown to be faulty, mostly by (...) |
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This catalogue is divided into two parts. Part 1 presents basic bibliographical information on books and journal issues that consist exclusively or in large part in papers devoted to the Presocratics and the Sophists. Part 2 lists the papers on Presocratic and Sophistic topics found in the volumes, providing name of author, title, and page numbers, and in the case of reprinted papers, the year of original publication. In some cases Part 2 lists the complete contents of volumes, not only (...) |
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In "Action without interaction" I showed that one might act on a physical system, without interacting with it, by the procedure of making it disappear. This paper presents further extensions and a critique of that result. These extensions show why physical actions without interaction are possible, while underscoring the philosophical fertility of a characteristic approach to the actual infinite inaugurated by Benardete. |
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Las máquinas aceleradas de Turing (ATMs) son dispositivos capaces de ejecutar súper-tareas. Sin embargo, el simple ejercicio de definirlas ha generado varias paradojas. En el presente artículo se definirán las nociones de súper-tarea y ATM de manera exhaustiva y se aclarará qué debe entenderse en un contexto lógico-formal cuando se pregunta por la existencia de un objeto. A partir de la distinción entre posibilidades lógicas y físicas se disolverán las paradojas y se concluirá que las ATMs son posibles y existen (...) |
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