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)

A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. Relativistic mechanics, on the other hand, implies that energy and momentum conservation are always violated. Quantum mechanics, however, seems to rule out the Zeno configuration as an inconsistent system.

A Zenonian supertask involving an infinite number of identical colliding balls is generalized to include balls with different masses. Under the restriction that the total mass of all the balls is finite, classical mechanics leads to velocities that have no upper limit. Relativistic mechanics results in velocities bounded by that of light, but energy and momentum are not conserved, implying indeterminism. The notion that both determinism and the conservation laws might be salvaged via photon creation is shown to be flawed.

A Zenonian supertask involving an infinite number of identical colliding balls is generalized to include balls with different masses. Under the restriction that the total mass of all the balls is finite, classical mechanics leads to velocities that have no upper limit. Relativistic mechanics results in velocities bounded by that of light, but energy and momentum are not conserved, implying indeterminism. The notion that both determinism and the conservation laws might be salvaged via photon creation is shown to be flawed.

Los experimentos mentales son dispositivos epistémicos de la imaginación, o de análisis de problemas filosóficos, que recorren las fronteras de aquella, desde el sillón. Dichas fronteras tocan dilemas perennes de la filosofía: cuestiones de la metafísica, como el tiempo, el espacio y la realidad, el problema de la libertad y el determinismo, la naturaleza de la mente, la identidad personal, los argumentos acerca del significado, las posibilidades, fuentes y condiciones del conocimiento, las relaciones entre discurso y lógica, la ética, cuestiones (...) de la filosofía social y política, y la estética. Muchos problemas de la filosofía han sido abordados mediante experimentos mentales, una herramienta útil de la caja de herramientas del filósofo. No todas las herramientas son populares, no obstante. Los experimentos mentales son, pese a sus defensores, falibles, incluso si son argumentos bien planteados. Justamente, este libro recopila artículos con las principales defensas y ataques a los experimentos mentales, especialmente en términos de su confiabilidad para llegar a conclusiones, o bien de su relevancia en términos de su origen: el sillón de la filosofía. Este ha sido vapuleado por los nuevos aires de la filosofía analítica, que trata al sillón como un viejo artefacto del análisis a priori. De hecho, hay posturas que critican a los experimentos mentales por constituir bombas de intuiciones no confiables. Por supuesto, no hay razón irrefutable para aceptar los experimentos mentales y las filosofías de sillón. Pero ¿hay alguna en la filosofía? El libro no pretende convencer al lector del valor de los experimentos mentales y las filosofías de sillón. Por el contrario, su objetivo es formar una imagen propia de estos dispositivos epistémicos, tanto en relación con sus virtudes y limitaciones. Si ello se logra, habrá valido el esfuerzo llevado a cabo en esta compilación de artículos, los que muestran los límites, desafíos y críticas de la experimentación mental desde el sillón. (shrink)

Newton’s equations of motion tell us that a mass at rest at the apex of a dome with the shape specified here can spontaneously move. It has been suggested that this indeterminism should be discounted since it draws on an incomplete rendering of Newtonian physics, or it is “unphysical,” or it employs illicit idealizations. I analyze and reject each of these reasons. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, PA (...) 15260; e‐mail: [email protected]. (shrink)

In a material theory of induction, inductive inferences are warranted by facts that prevail locally. This approach, it is urged, is preferable to formal theories of induction in which the good inductive inferences are delineated as those conforming to some universal schema. An inductive inference problem concerning indeterministic, non-probabilistic systems in physics is posed and it is argued that Bayesians cannot responsibly analyze it, thereby demonstrating that the probability calculus is not the universal logic of induction.

While there is no universal logic of induction, the probability calculus succeeds as a logic of induction in many contexts through its use of several notions concerning inductive inference. They include Addition, through which low probabilities represent disbelief as opposed to ignorance; and Bayes property, which commits the calculus to a ‘refute and rescale’ dynamics for incorporating new evidence. These notions are independent and it is urged that they be employed selectively according to needs of the problem at hand. It (...) is shown that neither is adapted to inductive inference concerning some indeterministic systems. (shrink)

I argue that, contrary to thestandard view, the Newtonian universe containsno contingency. I do this by arguing (i) thatno contingency is introduced into the Newtonianuniverse by the initial conditions of physicalsystems in the universe, and (ii) that theclaim that the Newtonian universe as a wholehas contingent properties leads to incoherence.This result suggests that Newtonian physics iseither inconsistent or incomplete, since thelaws of Newtonian physics are too weak todetermine all the properties of the Newtonianuniverse uniquely.

The examples of dynamic supertasks analyzed to date in the philosophical literature, in which both determinism and the classical laws of conservation of energy and momentum are violated, all share the important limitation of requiring material systems of infinite mass. This paper demonstrates that this limitation is not necessary. This has important consequences for the scope and meaning of such violations.

A simple indeterministic system is displayed and it is urged that we cannot responsibly infer inductively over it if we presume that the probability calculus is the appropriate logic of induction. The example illustrates the general thesis of a material theory of induction, that the logic appropriate to a particular domain is determined by the facts that prevail there.