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.

Philosophy of science has a complicated – almost schizophrenic – relationship with metaphysics. Studying topics such as the nature of causation, laws of nature, and spacetime, it clearly engages in activities that deserve to be classified as metaphysics. Yet the academic discipline itself was born in opposition to the field. Carnap, Reichenbach, Feigl, Neurath, and Popper, for example, were united in a shared distrust of metaphysics. Their suspicion ran so deep as to motivate a search for a demarcation between science (...) and non-science, and science and speculative metaphysics in particular. Philosophy of science appears caught in what Einstein (1933) calls the "eternal antithesis between the two inseparable components of our knowledge—the empirical and the rational" (271). It wants to employ metaphysical speculation, but impressed with the methods of the subject it studies, it fears over-reaching. Philosophy of science thus tries to walk a fine line between scientifically motivated or grounded metaphysics and its more speculative cousins. (shrink)

This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not continuous but (...) discontinuous and random. This result suggests a new interpretation of the wave function, according to which the wave function is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wave function disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the random discontinuous motion of particles may provide an appropriate random source to collapse the wave function. (shrink)

Recent developments in cosmology indicate that every history having a non-zero probability is realized in infinitely many distinct regions of spacetime. Thus, it appears that the universe contains infinitely many civilizations exactly like our own, as well as infinitely many civilizations that differ from our own in any way permitted by physical laws. We explore the implications of this conclusion for ethical theory and for the doomsday argument. In the infinite universe, we find that the doomsday argument applies only to (...) effects which change the average lifetime of all civilizations, and not those which affect our civilization alone. (shrink)

Since he proved his theorem in 1982, Fine has been challenging the traditional interpretation of the experimental violation of the Bell Inequalities (BI). A natural interpretation of Fine's theorem is that it provides us with an alternative set of assumptions on which to place blame for the failure of the BI, and opens to a new interpretation of the violation of the BI. Fine has a stronger interpretation for his theorem. He claims that his result undermines the traditional interpretation in (...) terms of local realism. The aim of this paper is to understand and to assess Fine's claim. We distinguish three different strategies that Fine uses in order to support his view. We show that none of these strategies is successful. Fine fails to prove that local realism is not at stake in the violation of the BI by quantum phenomena. (shrink)

At present the basic intellectual aim of academic inquiry is to improve knowledge. Much of the structure, the whole character, of academic inquiry, in universities all over the world, is shaped by the adoption of this as the basic intellectual aim. But, judged from the standpoint of making a contribution to human welfare, academic inquiry of this type is damagingly irrational. Three of four of the most elementary rules of rational problem-solving are violated. A revolution in the aims and methods (...) of academic inquiry is needed so that the basic aim becomes to promote wisdom, conceived of as the capacity to realize what is of value, for oneself and others, thus including knowledge and technological know-how, but much else besides. This urgently needed revolution would affect every branch and aspect of the academic enterprise. (shrink)

Most scientists and philosophers of science recognize that, when it comes to accepting and rejecting theories in science, considerations that have to do with simplicity, unity, symmetry, elegance, beauty or explanatory power have an important role to play, in addition to empirical considerations. Until recently, however, no one has been able to give a satisfactory account of what simplicity (etc.) is, or how giving preference to simple theories is to be justified. But in the last few years, two different but (...) related accounts have appeared, both of which address the above issues. On the one hand, James McAllister has argued that aesthetic criteria in science reflect scientists' judgements about what kind of theory is most likely to be empirically successful, based on the relative empirical success and failure of different kinds of theories in the past. Scientists employ what McAllister dubs "the aesthetic induction". On the other hand, I have argued that we need to see science as making a hierarchy of metaphysical assumptions about the comprehensibility and knowability of the universe, these assumptions asserting less and less as one ascends the hierarchy. One of the more substantial of these assumptions is that the universe is physically comprehensible. The key non-empirical feature a body of fundamental theories in physics must possess to be acceptable is unity. The better such a body of theory exemplifies the metaphysical thesis that the universe is physically comprehensible, in the sense that it has a unified dynamic structure, so the more acceptable such a body of theory is, from this standpoint. This affects not just theoretical physics, but the whole of natural science. In this paper I compare and contrast, and try to assess impartially the relative merits of, these two views. (shrink)

In this three-part paper, my concern is to expound and defend a conception of science, close to Einstein's, which I call aim-oriented empiricism. I argue that aim-oriented empiricsim has the following virtues. (i) It solve the problem of induction; (ii) it provides decisive reasons for rejecting van Fraassen's brilliantly defended but intuitively implausible constructive empiricism; (iii) it solves the problem of verisimilitude, the problem of explicating what it can mean to speak of scientific progress given that science advances from one (...) false theory to another; (iv) it enables us to hold that appropriate scientific theories, even though false, can nevertheless legitimately be interpreted realistically, as providing us with genuine , even if only approximate, knowledge of unobservable physical entities; (v) it provies science with a rational, even though fallible and non-mechanical, method for the discovery of fundamental new theories in physics. In the third part of the paper I show that Einstein made essential use of aim-oriented empiricism in scientific practice in developing special and general relativity. I conclude by considering to what extent Einstein came explicitly to advocate aim-oriented empiricism in his later years. (shrink)

In their recent book Every Thing Must Go Ladyman and Ross (Ladyman et al. 2007) claim: (1) Physics is analytically complete since it is the only science that cannot be left incomplete (cf. Ladyman et al. 2007, 283). (2) There might not be an ontologically fundamental level (cf. Ladyman et al. 2007, 178). (3) We should not admit anything into our ontology unless it has explanatory and predictive utility (cf. Ladyman et al. 2007, 179). In this discussion note I aim (...) to show that the ontological commitment in (3) implies that the completeness of no science can be achieved where no fundamental level exists. Therefore, if claim (1) requires a science to actually be complete in order to be considered as physics, (1), and if Ladyman and Ross’s “tentative metaphysical hypothesis […] that there is no fundamental level” (178) is true, (2), then there simply is no physics. Ladyman and Ross can, however, avoid this unwanted result if they merely require physics to ever strive for completeness rather than to already be complete. (shrink)