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25Some surprising instabilities in idealized dynamical systemsSynthese 197 (7): 3007-3026. 2020.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 …Read more
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26The Convergence Approach to Benardete’s ParadoxPhilosophia 51 (3): 1353-1367. 2023.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 "infini…Read more
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21Unmoved movers: a very simple and novel form of indeterminismEuropean Journal for Philosophy of Science 12 (3): 1-23. 2022.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. …Read more
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15Fluids, Molecules and Paradoxes of InfinityPhilosophia 50 (4): 1945-1953. 2022.Several paradoxes of infinity have recently featured in this journal involving gases distributed in a denumerable infinite series of compartments. I shall demonstrate in this paper that:a) None of these new paradoxes applies where the gases comply with both Boyle’s law and Avogadro’s law. As several of these new paradoxes expressly require compliance with Boyle’s law, it is unclear, in principle, as to whether there is a plausible model of gas that is able to uphold them all.b) Notwithstanding a…Read more
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23Undeformable Bodies that are Not Rigid Bodies: A Philosophical Journey Through Some (Unexpected) SupertasksAxiomathes 32 (4): 605-625. 2022.There is broad consensus as to what a rigid body is in classical mechanics. The idea is that a rigid body is an undeformable body. In this paper I show that, if this identification is accepted, there are therefore rigid bodies which are unstable. Instability here means that the evolution of certain rigid bodies, even when isolated from all external influence, may be such that their identity is not preserved over time. The result is followed by analyzing supertasks that are possible in infinite s…Read more
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17Discussion. Earman and Norton on supertasks that generate indeterminismBritish Journal for the Philosophy of Science 50 (1): 137-141. 1999.In a recent discussion, Earman and Norton [(1998)] propose a classification of supertasks that generate indeterminism which is flawed. An emendation is presented here.
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7An Infinite System with GravitationSynthese 135 (3): 339-346. 2003.The paper shows a new example of nonuniqueness of the solutionto Newtonian equations of motion for infinite gravitational systems. Unlike otherexamples, the gravitational field presents no singularity, nor are the non-gravitational forcesintroduced in the model singular (in particular, there are no collisions). The result is also ofinterest because it points to an interesting limitation of the elementary (Newtonian) formulationof classical mechanics.
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15A Note on some New Infinity PuzzlesPhilosophia 48 (4): 1483-1491. 2020.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.
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23A Note on some New Infinity PuzzlesPhilosophia 48 (4): 1483-1491. 2020.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.
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36Some New Infinity PuzzlesPhilosophia 48 (3): 1093-1099. 2020.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.
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26The Magic Potion ParadoxPhilosophia 45 (3): 1227-1234. 2017.This paper introduces a new infinite paradox. The main novelty is that it poses problems of causality in a very different form from to the one in use until now. By means of a probabilistic generalization, the paradox shows that the disposition to act according to a specific plan is not always necessary to derive causal effects in Benardete-type contexts involving infinity. It also suggests that, in such cases, the explanation for those causal effects requires a propensity interpretation of proba…Read more
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61What the Tortoise Said to AchillesPhilosophia 42 (2): 405-411. 2014.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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50Why dynamical self-excitation is possibleSynthese 119 (3): 313-323. 1999.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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76The inverse spaceship paradoxSynthese 178 (3): 429-435. 2011.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
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22Rigidity, instability and dimensionalitySynthese 195 (9): 4047-4062. 2018.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 indete…Read more
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143Some relativistic and higher order supertasksPhilosophy of Science 65 (3): 502-517. 1998.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 co…Read more
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22The New String ParadoxPhilosophy of Science 80 (1): 143-154. 2013.I shall begin by discussing Benardete’s string paradox. Then, a new puzzle involving supertasks and causality is proposed and discussed. Finally, the new string paradox facilitates the discovery of a surprising example of irreversible mechanical process.
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72On the dynamics of Alper and BridgerSynthese 131 (2). 2002.Bridger and Alper (1999) maintain that the nonphysical featuresof the supertasks described by Pérez Laraudogoitia (1996) involving a system containing an infinite number of particles may be avoided by introducing, in a specific way, Hilbert space in classical dynamics. I argue that it is possible to interpret their proposal in two ways, neither of which is acceptable for the purpose for which it was introduced.
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114The supertask argument against countable additivityPhilosophical Studies 168 (3): 619-628. 2014.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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63Zeno and flow of informationSynthese 190 (3): 439-447. 2013.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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45Taking Self‐Excitations Seriously: On Angel's Initial ConditionBritish Journal for the Philosophy of Science 54 (2): 319-326. 2003.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 Int…Read more
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210Infinity machines and creation ex nihiloSynthese 115 (2): 259-265. 1998.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, a…Read more
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16On The Dynamics Of Alper And BridgerSynthese 131 (2): 157-171. 2002.Bridger and Alper (1999) maintain that the nonphysical featuresof the supertasks described by Pérez Laraudogoitia (1996) involving a system containing an infinite number of particles may be avoided by introducing, in a specific way, Hilbert space in classical dynamics. I argue that it is possible to interpret their proposal in two ways, neither of which is acceptable for the purpose for which it was introduced.
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University of the Basque CountryProfessor
Areas of Specialization
Paradoxes, Miscellaneous |
Paradoxes |
Areas of Interest
Paradoxes, Miscellaneous |
Paradoxes |