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)

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.

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.1Introduction2The ‘impact without contact’ argument3Taking self‐excitations seriously4Some interesting implications. (shrink)

In a recent volume of this journal, L. Angel ([2002]) proposed a collision mechanics leading to such strange results as the possibility that a particle may be in several places at the same time, or the existence of unprepared spatially-separated correlations. I will here show that neither of these results follows from his theory or, if it does, the theory, contrary to what Angel claims, is not a plausible extension of Newtonian collision dynamics. 1. No bilocation2. No quantum leap3. No (...) unprepared spatially-separated correlations. (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)

Accepting MacIntyre's teleological argument that the notion of individual rights is an invention or fiction, the article argues, against MacIntyre, that such a fiction may be interpreted as a creative response to the social requirements of modernity. Such rights language discloses the essential features of modernity but also the underlying teleological and moral structure of all human association. But whether rights language is perceived as a fall from morality or as a creative differentiation of moral language depends on a reading (...) of history and especially on the interpretation of the Enlightenment project. Jürgen Habermas is used for an alternative reading of the Enlightenment and the relation of rights to the normative teleology of language itself. But both readings of history turn out to be theodicies, dependent upon hidden theological assumptions. Whether a society centered on a notion of rights can be governed by teleology can only be answered theologically. (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)

Participants struck 500 golf balls to a concealed target. Outcome feedback was presented at the subjective or objective threshold of awareness of each participant or at a supraliminal threshold. Participants who received fully perceptible feedback learned to strike the ball onto the target, as did participants who received feedback that was only marginally perceptible . Participants who received feedback that was not perceptible showed no learning. Upon transfer to a condition in which the target was unconcealed, performance increased in both (...) the subjective and the objective threshold condition, but decreased in the supraliminal condition. In all three conditions, participants reported minimal declarative knowledge of their movements, suggesting that deliberate hypothesis testing about how best to move in order to perform the motor task successfully was disrupted by the impoverished disposition of the visual outcome feedback. It was concluded that sub-optimally perceptible visual feedback evokes implicit processes. (shrink)

(No abstract is available for this citation).

Salmon was the first to speak explicitly of paradoxes of kinematics. In this short note I introduce a new class of infinity puzzles. Following natural terminology, they should actually be called static paradoxes.

There is a well-known variety of contact paradoxes which are significantly linked to topology. The aim of this paper is to present a new paradox concerning contact with bodies composed of a denumerable infinity of parts. This paradox establishes the logical necessity, in a Newtonian context, of contact forces that violate what is probably our most basic causal intuition, embodied in what I call the Principle of Influence: any force exerted on a body B induces change of movement of B (...) or the emergence of internal forces in B. However, the above paradox can be made strictly compatible with a Newtonian framework by introducing phantom forces as ideal elements in the Hilbert sense, though it will be seen that this does not solve all the problems. (shrink)

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.

The paper analyses Benardete's paradox of the gods from a more general perspective (the convergence approach) than several of the most important proposals made to date, but in close relation (and sharp contrast) with them. The new theory, based on the notion of limit, is systematically applicable in different possible scenarios involving a denumerable infinity of objects. In particular, it reveals in what way ω-consistency can be compromised in an otherwise consistent description of such "infinitary" situations.

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.

In this short note I argue that, using the type of configurations put forward in a recent paper by Laraudogoitia in this same journal, new paradoxes of infinity of a completely different nature can be formulated.

This paper shows that, in Newtonian mechanics, unstable three-dimensional rigid bodies must exist. Laraudogoitia recently provided examples of one- and two-dimensional homogeneous unstable rigid bodies, conjecturing the instability would persist for three-dimensional bodies in four-dimensional space. My result proves that, if one admits non homogeneous balls or hollow spheres, then the conjecture is true without having to resort to tetra-dimensionality. Furthermore, I show that instability also holds for at least certain simple classes of elastic bodies. Altogether, the laws of (...) classical dynamics actually lead to the existence of unstable material bodies belonging to the three types of entities accepted therein: point particles, rigid bodies and continuous deformable bodies. A whole range of forms of indeterminism which, until now, has not been considered in the literature. I end with a new conjecture on the connection existing between all these forms of instability and the dimensionality of space. (shrink)

In this short note I argue that, using the type of configurations put forward in a recent paper by Laraudogoitia in this same journal, new paradoxes of infinity of a completely different nature can be formulated.

A new problem about 'if...then...' is posed which is related to Curry's paradox much as the barber's paradox parallels Russell's paradox. However, it is not obvious how to solve it.

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 (...) be eternal, as has been erroneously assumed, especially since the time of Newton. (shrink)

Norton’s very simple case of indeterminism in classical mechanics has given rise to a literature critical of his result. I am interested here in posing a new objection different from the ones made to date. The first section of the paper expounds the essence of Norton’s model and my criticism of it. I then propose a specific modification in the absence of gravitational interaction. The final section takes into consideration a surprising consequence for classical mechanics from the new model introduced (...) here. (shrink)

The paper takes a detailed look at a surprising new aspect of the dynamics of rigid bodies. Far from the usual consideration of rigid body theory as a merely technical chapter of classical physics, I demonstrate here that there are solutions to the conservation equations of mechanics that imply the spontaneous, unpredictable splitting of a rigid body in free rotation, something that has direct implications for the problem of causality. The paper also shows that the instability revealed in indeterminist splitting (...) processes does not depend solely on the bodies’ inertial properties but also on the number of dimensions of the physical space they inhabit. The paper concludes with a conjecture on the behavior of rigid bodies in four-dimensional space. (shrink)

This paper considers a recent criticism of the physical possibility of supertasks which involves Achilles’s staccato run. It is held that the criticism fails and that the underlying fallacy can be linked with interesting developments in the modern literature on physical supertasks.

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)

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.