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 (...) context of a very basic supertask, in Section 4) and *-sequences (reversed -sequences, in the form of paradoxical results from the recent literature). Introduction The simultaneous collision The paradox in other contexts The basic problem is N0 things The recent literature Generating N0 things. (shrink)

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 down. (...) This suggests that there is a new context in which quantum mechanics, in principle, permits the performance of a supertask. (shrink)

A model of a new version of Zeno's arrow paradox is presented in a plausible extension of Newtonian collision mechanics. In exploring various avenues for resolution of the paradox, it becomes evident that a prerelativistic classical physical topology which is locally deterministic can mechanically generate nonclassical ontological properties such as the appearance of a particle in many places at once. It can also mimic some properties of quantum physics, including unprepared spatially-separated correlations. 1 Zeno's arrow paradox 2 Newtonian collision mechanics (...) and extensions of it 3 Our initial condition (IC) 4 Demonstrating the model paradox 5 Resolving the paradox 6 Unprepared correlations in spatially-separated events 7 Lessons. (shrink)

Benardete presents a version of Zeno's dichotomy in which an infinite sequence of gods each intends to raise a barrier iff a traveller reaches the position where they intend to raise their barrier. In this paper, I demonstrate the abstract form of the Benardete Dichotomy. I show that the diagnosis based on that form can do philosophical work not done by earlier papers rejecting Priest's version of the Benardete Dichotomy, and that the diagnosis extends to a paradox not normally classified (...) as a dichotomy. I show how the form is exploited to generate paradox. Introduction The form of the Benardete dichotomy 2.1 The unsatisfiable pair diagnosis Applying the unsatisfiable pair diagnosis 3.1 Perez Laraudogoitia 3.2 Hawthorne 3.3 Angel 3.4 Yablo and Sorensen Exploiting the form. (shrink)

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 (...) plausible continuity principles. However, the question of its triviality is here moot, since I show that, except in one case, Corral-Villate’s disproofs fail, and with a correction, the original arguments are unrefuted. Consequently, of the two contenders for the outcome of my supertask, the Nothing from Infinity paradox has won out. (shrink)

In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. I (...) then show how this leads to the Infinity from Nothing paradox, in which we have the spontaneous eruption of infinite mass and energy out of nothing. I conclude by showing how our supertask models at least something of an old conundrum, the question of what happens when the immovable object meets the irresistible force. (shrink)

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...

It is common knowledge that the Aristotelian idea of an unmoved mover was abandoned definitively with the advent of modern science and, in particular, Newton’s precise formulation of mechanics. Here I show that the essential attribute of an unmoved mover is not incompatible with such mechanics; quite the contrary, it makes this possible. The unmoved mover model proposed does not involve supertasks, and leads both to an outrageous form of indeterminism and a new, accountable form of interaction. The process presents (...) a more precise characterization of the crucial going-to-the-limit operation. It has long been acknowledged in the existing literature that, theoretically, in infinite Newtonian systems, masses can move from rest to motion through supertasks. Numerous minor variations on the original schemes have already been published. Against this backdrop, this paper introduces three significant additions: 1) It formulates for the first time a limit postulate for systematically addressing infinite systems; 2) It shows that an Aristotelian unmoved mover is possible in systems of infinitely many particles that interact with each other solely by contact collision; 3) It shows how interaction at a distance can emerge in systems of infinitely many particles that interact with each other solely by contact. (shrink)

In a recent article, L. Angel ([2001]) argues that if we do not implement Newtonian physics adding to it a certain usual type of boundary condition, then this leads to the rejection of what he calls the P principle: ‘the composition of contact interactions does not create a noncontact interaction.’ Here I shall demonstrate that this conclusion does not follow. However, as will be made clear, this in no way diminishes the interest or importance of the model introduced by Angel (...) in his paper. 1 Introduction 2 The ‘impact without contact’ argument 3 Taking self-excitations seriously 4 Some interesting implications. (shrink)

In this article I propose what I call the inverse spaceship paradox. The article's interest lies in the fact that, contrary to what appears to be an implicit agreement in the literature on indeterminism, it shows that coming from infinity can be a perfectly predictable and therefore deterministic process in a classical universe.

The first aim of this paper is to introduce a new way of looking at supertasks in the light of special relativity which makes use of the elementary dynamics of relativistic point particles subjected to elastic binary collisions and constrained to move unidimensionally. In addition, this will enable us to draw new physical consequences from the possibility of supertasks whose ordinal type is higher than the usual ω or ω * considered so far in the literature. Thus, the paper shows (...) how an entire collection of infinitely many particles may place itself spontaneously in motion (mechanical self-acceleration) or even reach the speed of light in a way compatible with special relativity. Interesting implications for classical mechanics are also derived, particularly the possibility of a system of particles disappearing spontaneously in spatial infinity even under the condition of the non-existence of non-collision singularities. (shrink)

Until the present, the Newtonian theory of gravitation has only been studied in any detail through the usual, presupposed ontology of point particles. This paper shows that changing our ontology into one which makes use of continuous bodies (non-point particles) allows us to obtain in a simple way two important results relevant to the theory: (a) The Newtonian theory of gravitation is indeterministic in a way apparently unparalleled when non-point particle models of it are used. (b) In the Newtonian theory (...) of gravitation it is possible to find non-collision singularities qualitatively different from the ones presented in point particle models. (shrink)

In this paper, an example is presented for a dynamic system analysable in the framework of the mechanics of rigid bodies. Interest in the model lies in three fundamental features. First, it leads to a paradox in classical mechanics which does not seem to be explainable with the conceptual resources currently available. Second, it is possible to find a solution to it by extending in a natural way the idea of global interaction in the context of what is called interaction (...) by impenetrability. Third, the solution presented throws light on a problem posed and discussed in the recent literature in connection with the mass conservation principle. (shrink)

In a recent discussion, Earman and Norton [(1998)] propose a classification of supertasks that generate indeterminism which is flawed. An emendation is presented here.

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 is insensitive to the classical vs relativistic distinction. We also note some interesting linkages among supertasks, indeterminism and foundations problems in the general theory of relativity. (shrink)

It is widely held that the paradox of Achilles and the Tortoise, introduced by Zeno of Elea around 460 B.C., was solved by mathematical advances in the nineteenth century. The techniques of Weierstrass, Dedekind and Cantor made it clear, according to this view, that Achilles’ difficulty in traversing an infinite number of intervals while trying to catch up with the tortoise does not involve a contradiction, let alone a logical absurdity. Yet ever since the nineteenth century there have been dissidents (...) claiming that the apparatus of Weierstrass et al. has not resolved the paradox, and that serious problems remain. It seems that these claims have received unexpected support from recent developments in mathematical physics. This support has however remained largely unnoticed by historians of philosophy, presumably because the relevant debates are cast in mathematical-technical terms that are only accessible to people with the relevant training. That is unfortunate, since the debates in question might well profit from input by philosophers in general and historians of philosophy in particular. Below we will first recall the Achilles paradox, and describe the way in which nineteenth century mathematics supposedly solved it. Then we discuss recent work that contests this solution, reiterating the dissident dogma that no mathematical approach whatsoever can even come close to solving the original Achilles. We shall argue that this dissatisfaction with a mathematical solution is inadequate as it stands, but that it can perhaps be reformulated in the light of new developments in mathematical physics. (shrink)

I show how classical and quantum physics approach the problem of randomness and probability. Contrary to popular opinions, neither we can prove that classical mechanics is a deterministic theory, nor that quantum mechanics is a nondeterministic one. In other words it is not possible to show that randomness in classical mechanics has a purely epistemic character and that of quantum mechanics an ontic one. Nevertheless, recent developments of quantum theory and increasing experimental possibilities to check its predictions call for returning (...) to the problem of comparing possibilities given by classical and quantum physics to accommodate and prove the existence of a `genuine randomness'. Recent results concerning `amplification of randomness' show that, in certain sense, quantum physics is in fact ‘more random’ that classical and outperforms it in producing a `truly random process'. (shrink)

There are many ontologies of the world or of specific phenomena such as time, matter, space, and quantum mechanics1. However, ontologies of information are rather rare. One of the reasons behind this is that information is most frequently associated with communication and computing, and not with ‘the furniture of the world’. But what would be the nature of an ontology of information? For it to be of significant import it should be amenable to formalization in a logico-grammatical formalism. A candidate (...) ontology satisfying such a requirement can be found in some of the ideas of K. Turek, presented in this paper. Turek outlines the ontology of information conceived of as a part of nature, and provides the ‘missing link’ to the Z axiomatic set theory, offering a proposal for developing a formal ontology of information both in its philosophical and logicogrammatical representations. (shrink)