Various arguments have been put forward to show that Zeno-like paradoxes are still with us. A particularly interesting one involves a cube composed of colored slabs that geometrically decrease in thickness. We first point out that this argument has already been nullified by Paul Benacerraf. Then we show that nevertheless a further problem remains, one that withstands Benacerraf’s critique. We explain that the new problem is isomorphic to two other Zeno-like predicaments: a problem described by Alper and Bridger in 1998 (...) and a modified version of the problem that Benardete introduced in 1964. Finally, we present a solution to the three isomorphic problems. (shrink)

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 (...) the time the supertask is due to be completed, or else they rely on the application of the time-reversal transformation to states which are not well-defined. Consequently, it is unjustified to conclude that the paradoxical results are arising from within the framework of Newtonian mechanics. In the last part of this article, we discuss various aspects of the physics of these supertasks. (shrink)

Recently, Alper, Bridger, Earman and Norton have all proposed examples of dynamic systems that, in their view, are incompatible with classical (Newtonian) mechanics. In the first section of the present paper I shall show that their arguments are all undermined by the same fallacy. The second section proves that their conclusions of incompatibility are indeed false, and that what we are really looking at are new forms of indeterminist evolution of the same kind as that found recently in the literature (...) on supertasks. In the third section of the paper, I argue that one of these new forms of evolution is particularly interesting, and that analysis of it leads to a new vision of the relation between interaction by contact and impenetrability. 1. Introduction2. The fallacy3. Understanding some physical supertasks4. A philosophically interesting implication: contact and impenetrability. (shrink)

An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy nonconservation and creatio ex nihilo no longer occur. A numerical analysis of finite systems of colliding balls is given, and the asymptotic behaviour that corresponds to the potentially infinite system is (...) inferred. (shrink)

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)

Recently, Alper, Bridger, Earman and Norton have all proposed examples of dynamic systems that, in their view, are incompatible with classical (Newtonian) mechanics. In the first section of the present paper I shall show that their arguments are all undermined by the same fallacy. The second section proves that their conclusions of incompatibility are indeed false, and that what we are really looking at are new forms of indeterminist evolution of the same kind as that found recently in the literature (...) on supertasks. In the third section of the paper, I argue that one of these new forms of evolution is particularly interesting, and that analysis of it leads to a new vision of the relation between interaction by contact and impenetrability. Introduction The fallacy Understanding some physical supertasks A philosophically interesting implication: contact and impenetrability. (shrink)